From 84caa87951fb81fe53912db4643417554a7cf311 Mon Sep 17 00:00:00 2001
From: Antonio De Lucreziis <antonio.delucreziis@gmail.com>
Date: Fri, 17 Jan 2025 22:44:34 +0100
Subject: [PATCH 1/7] initial commit of domande esami branch

---
 src/pages/domande-esami/index.astro | 31 ++++++++++++++++++++
 src/styles/pages.scss               | 45 +++++++++++++++++++++++++++++
 2 files changed, 76 insertions(+)
 create mode 100644 src/pages/domande-esami/index.astro

diff --git a/src/pages/domande-esami/index.astro b/src/pages/domande-esami/index.astro
new file mode 100644
index 0000000..40db5ab
--- /dev/null
+++ b/src/pages/domande-esami/index.astro
@@ -0,0 +1,31 @@
+---
+import { PhosphorIcon } from '@/client/Icon'
+import Footer from '@/components/Footer.astro'
+import Header from '@/components/Header.astro'
+import BaseLayout from '@/layouts/BaseLayout.astro'
+---
+
+<BaseLayout title="Domande Esami | PHC" pageTags={'domande-esami'}>
+    <Header />
+    <main>
+        <h1>Domande Esami</h1>
+
+        <div class="search">
+            <input type="text" placeholder="Cerca una domanda per un easme..." />
+            <PhosphorIcon client:load name="magnifying-glass" />
+        </div>
+
+        <h2>Corsi</h2>
+
+        <div class="courses card large" style={{ '--card-base': 'hsl(180, 100%, 81%)' }}>
+            <details class="course-group">
+                <summary>
+                    <PhosphorIcon client:load name="caret-down" />
+                    <PhosphorIcon client:load name="caret-up" />
+                    <div class="title">Analisi 1</div>
+                </summary>
+            </details>
+        </div>
+    </main>
+    <Footer />
+</BaseLayout>
diff --git a/src/styles/pages.scss b/src/styles/pages.scss
index f16f952..a7250eb 100644
--- a/src/styles/pages.scss
+++ b/src/styles/pages.scss
@@ -437,6 +437,51 @@
         }
     }
 
+    .domande-esami {
+        background: hsl(180, 100%, 95%);
+
+        main {
+            justify-self: center;
+
+            display: flex;
+            flex-direction: column;
+            align-items: center;
+
+            padding: 5rem 0;
+
+            gap: 5rem;
+
+            max-width: 80ch;
+
+            .search-result {
+                background: hsl(180, 100%, 87%);
+            }
+
+            button {
+                background: hsl(180, 100%, 72%);
+            }
+        }
+
+        .courses {
+            padding: 0;
+
+            hr {
+                width: 100%;
+                border: none;
+                height: 2px;
+                background: #000d;
+                margin: 0;
+            }
+
+            .text {
+                > * {
+                    margin: 1rem 0;
+                    padding: 0 1rem;
+                }
+            }
+        }
+    }
+
     // .login {
     //     background: #ddfaff;
 

From 7c36f8714961eee9a21fd5a9035549df134f8181 Mon Sep 17 00:00:00 2001
From: Antonio De Lucreziis <antonio.delucreziis@gmail.com>
Date: Fri, 7 Feb 2025 00:20:27 +0100
Subject: [PATCH 2/7] finished minimal working prototype

---
 bun.lockb                              | Bin 337012 -> 337358 bytes
 package.json                           |   1 +
 src/data/domande-esami.yaml            | 160 +++++++++++++++++++++++++
 src/files.d.ts                         |  20 ++++
 src/pages/domande-esami/[course].astro |  50 ++++++++
 src/pages/domande-esami/index.astro    |  62 +++++++---
 src/styles/components.scss             |  40 +++++++
 src/styles/pages.scss                  |  34 ++----
 src/styles/typography.scss             |   4 +
 9 files changed, 331 insertions(+), 40 deletions(-)
 create mode 100644 src/data/domande-esami.yaml
 create mode 100644 src/pages/domande-esami/[course].astro

diff --git a/bun.lockb b/bun.lockb
index 97337a6c0e08d44b9253fcb0fb22698615d68f0f..fe08456d92cb617bf66c2018e98ca65ea2d924fc 100755
GIT binary patch
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z7*C$1L}Ys3I4ff2Rzu+W;NZkW?R%|=&DTorc;RZQW~8G(nAFLWJxn_$d)PND@;`#U
B8N>hp

diff --git a/package.json b/package.json
index 373431d..4d7fdde 100644
--- a/package.json
+++ b/package.json
@@ -27,6 +27,7 @@
         "fuse.js": "^7.0.0",
         "katex": "^0.16.9",
         "lucide-static": "^0.468.0",
+        "marked": "^15.0.6",
         "preact": "^10.19.6",
         "typescript": "^5.3.3"
     },
diff --git a/src/data/domande-esami.yaml b/src/data/domande-esami.yaml
new file mode 100644
index 0000000..3549afe
--- /dev/null
+++ b/src/data/domande-esami.yaml
@@ -0,0 +1,160 @@
+names:
+    aritmetica: Aritmetica
+    geometria-1: Geometria 1
+    analisi-1: Analisi 1
+    algebra-1: Algebra 1
+    geometria-2: Geometria 2
+    analisi-2: Analisi 2
+    algebra-2: Algebra 2
+    analisi-3: Analisi 3
+    ricerca-operativa: Ricerca Operativa
+    fisica-3: Fisica 3
+    meccanica-razionale: Meccanica Razionale
+    istituzioni-di-geometria: Istituzioni di Geometria
+    istituzioni-di-analisi: Istituzioni di Analisi
+    istituzioni-di-algebra: Istituzioni di Algebra
+    istituzioni-di-fisica: Istituzioni di Fisica
+    istituzioni-di-probabilità: Istituzioni di Probabilità
+    geometria-e-topologia-differenziale: Geometria e Topologia Differenziale
+    analisi-armonica: Analisi Armonica
+    elementi-di-analisi-complessa: Elementi di Analisi Complessa
+
+groups:
+    - id: triennale-anno-1
+      name: Triennale - Anno I
+      items:
+          - aritmetica
+          - geometria-1
+          - analisi-1
+          - algebra-1
+
+    - id: triennale-anno-2
+      name: Triennale - Anno II
+      items:
+          - geometria-2
+          - analisi-2
+          - algebra-1
+
+    - id: triennale-anno-3
+      name: Triennale - Anno III
+      items:
+          - ricerca-operativa
+          - fisica-3
+          - meccanica-razionale
+
+    - id: istituzioni
+      name: Istituzioni
+      items:
+          - istituzioni-di-geometria
+          - istituzioni-di-analisi
+          - istituzioni-di-algebra
+          - istituzioni-di-fisica
+          - istituzioni-di-probabilità
+
+    - id: other
+      name: Esami a scelta
+      items:
+          - geometria-e-topologia-differenziale
+          - analisi-armonica
+          - elementi-di-analisi-complessa
+
+questions:
+    - course: geometria-1
+      year: 2024
+      content: |
+          Dimostrare il teorema spettrale reale
+
+    - course: gtd
+      year: 2024
+      content: |
+          Calcolare la curvatura gaussiana di una sfera di raggio $r$
+
+    - course: geometria-1
+      year: 2023
+      content: |
+          Dimostrare che _l'area_ di un cerchio è $A = \pi r^2$
+
+    - course: algebra-1
+      year: 2024
+      content: |
+          Dimostrare il teorema di Sylow
+
+    - course: algebra-1
+      year: 2023
+      content: |
+          Dimostrare che ogni sottogruppo di un gruppo ciclico è ciclico
+
+    - course: analisi-1
+      year: 2024
+      content: |
+          Dimostrare il teorema di Weierstrass
+
+    - course: analisi-1
+      year: 2023
+      content: |
+          Dimostrare che se $f$ è continua su $[a,b]$, allora $f$ è limitata
+
+    - course: analisi-2
+      year: 2024
+      content: |
+          Dimostrare il teorema di Stokes
+
+    - course: analisi-2
+      year: 2023
+      content: |
+          Dimostrare il teorema di Green
+
+    - course: analisi-3
+      year: 2024
+      content: |
+          Dimostrare il teorema di Cauchy
+
+    - course: analisi-3
+      year: 2023
+      content: |
+          Dimostrare il teorema di Liouville
+
+    - course: algebra-2
+      year: 2024
+      content: |
+          Dimostrare il teorema di struttura per i gruppi abeliani finiti
+
+    - course: algebra-2
+      year: 2023
+      content: |
+          Dimostrare il teorema di struttura per i gruppi finiti
+
+    - course: ricerca-operativa
+      year: 2024
+      content: |
+          Dimostrare il teorema di dualità per i problemi di programmazione lineare
+
+    - course: geometria-topologia-differenziale
+      year: 2024
+      content: |
+          Dimostrare il teorema di Poincaré-Hopf
+
+    - course: analisi-armonica
+      year: 2024
+      content: |
+          Dimostrare il teorema di Hahn-Banach
+
+    - course: analisi-complessa
+      year: 2024
+      content: |
+          Dimostrare il teorema di Morera
+
+    - course: analisi-complessa
+      year: 2023
+      content: |
+          Dimostrare il teorema degli zeri di Weierstrass
+
+    - course: analisi-complessa
+      year: 2022
+      content: |
+          Dimostrare il teorema della mappa aperta
+
+    - course: analisi-complessa
+      year: 2021
+      content: |
+          Dimostrare il teorema della mappa aperta
diff --git a/src/files.d.ts b/src/files.d.ts
index bdad603..975bb65 100644
--- a/src/files.d.ts
+++ b/src/files.d.ts
@@ -15,3 +15,23 @@ declare module '@/data/macchinisti.yaml' {
     const value: Macchinista[]
     export default value
 }
+
+declare module '@/data/domande-esami.yaml' {
+    type Question = {
+        course: string
+        year: number
+        content: string
+    }
+
+    type Group = {
+        id: string
+        name: string
+        items: Array<string>
+    }
+
+    const names: Record<string, string>
+    const groups: Group[]
+    const questions: Question[]
+
+    export { names, groups, questions }
+}
diff --git a/src/pages/domande-esami/[course].astro b/src/pages/domande-esami/[course].astro
new file mode 100644
index 0000000..ddaf9be
--- /dev/null
+++ b/src/pages/domande-esami/[course].astro
@@ -0,0 +1,50 @@
+---
+import type { GetStaticPaths } from 'astro'
+import BaseLayout from '@/layouts/BaseLayout.astro'
+import Footer from '@/components/Footer.astro'
+import Header from '@/components/Header.astro'
+
+import { PhosphorIcon } from '@/client/Icon'
+
+import { marked } from 'marked'
+
+import database from '@/data/domande-esami.yaml'
+
+export const getStaticPaths = (() => {
+    return Object.keys(database.names).map(course => ({
+        params: { course },
+    }))
+}) satisfies GetStaticPaths
+
+const { course } = Astro.params
+---
+
+<BaseLayout title="Domande Esami | PHC" pageTags={'domande-esami'}>
+    <Header />
+    <main>
+        <h1>{course}</h1>
+
+        <div class="search">
+            <input type="text" placeholder="Cerca una domanda per un esame..." />
+            <PhosphorIcon client:load name="magnifying-glass" />
+        </div>
+
+        <div class="wide-card-list">
+            {
+                database.questions
+                    .filter(question => question.course === course)
+                    .map(question => (
+                        <div class="card">
+                            <div class="text">
+                                <Fragment set:html={marked(question.content)} />
+                            </div>
+                            <div class="metadata">
+                                <div class="chip">{question.year}</div>
+                            </div>
+                        </div>
+                    ))
+            }
+        </div>
+    </main>
+    <Footer />
+</BaseLayout>
diff --git a/src/pages/domande-esami/index.astro b/src/pages/domande-esami/index.astro
index 40db5ab..069ff78 100644
--- a/src/pages/domande-esami/index.astro
+++ b/src/pages/domande-esami/index.astro
@@ -3,29 +3,61 @@ import { PhosphorIcon } from '@/client/Icon'
 import Footer from '@/components/Footer.astro'
 import Header from '@/components/Header.astro'
 import BaseLayout from '@/layouts/BaseLayout.astro'
+
+import database from '@/data/domande-esami.yaml'
+
+const courseQuestionCounts = Object.fromEntries(
+    database.questions.reduce((acc, question) => {
+        acc.set(question.course, (acc.get(question.course) || 0) + 1)
+        return acc
+    }, new Map())
+)
 ---
 
 <BaseLayout title="Domande Esami | PHC" pageTags={'domande-esami'}>
     <Header />
     <main>
         <h1>Domande Esami</h1>
-
-        <div class="search">
-            <input type="text" placeholder="Cerca una domanda per un easme..." />
-            <PhosphorIcon client:load name="magnifying-glass" />
+        <div class="card large">
+            <div class="text">
+                <p>
+                    [Copilot] Benvenuto nella sezione delle domande d'esame! Qui puoi trovare domande di esami
+                    passati per prepararti al meglio per il tuo prossimo esame.
+                </p>
+                <ul>
+                    <li><a href="#triennale-anno-1">Triennale - Anno I</a></li>
+                    <li><a href="#triennale-anno-2">Triennale - Anno II</a></li>
+                    <li><a href="#triennale-anno-3">Triennale - Anno III</a></li>
+                    <li><a href="#istituzioni">Istituzioni</a></li>
+                    <li><a href="#other">Esami a Scelta</a></li>
+                </ul>
+                <p>
+                    Se volessi contribuire con nuove domande, puoi <a href="#">facendo una pull request</a>,
+                    inviandole al
+                    <a href="#">form domande</a> oppure <a href="#">mandandoci una email</a>.
+                </p>
+            </div>
         </div>
 
-        <h2>Corsi</h2>
-
-        <div class="courses card large" style={{ '--card-base': 'hsl(180, 100%, 81%)' }}>
-            <details class="course-group">
-                <summary>
-                    <PhosphorIcon client:load name="caret-down" />
-                    <PhosphorIcon client:load name="caret-up" />
-                    <div class="title">Analisi 1</div>
-                </summary>
-            </details>
-        </div>
+        {
+            database.groups.map(group => (
+                <>
+                    <h2 id={group.id}>{group.name}</h2>
+                    <div class="wide-card-list">
+                        {group.items.map(course => (
+                            <a href={`/domande-esami/${course}`}>
+                                <div class="card">
+                                    <h2>{database.names[course]}</h2>
+                                    <div class="text">
+                                        <p>{courseQuestionCounts[course] || 0} domande disponibili</p>
+                                    </div>
+                                </div>
+                            </a>
+                        ))}
+                    </div>
+                </>
+            ))
+        }
     </main>
     <Footer />
 </BaseLayout>
diff --git a/src/styles/components.scss b/src/styles/components.scss
index 51f0834..c4e424f 100644
--- a/src/styles/components.scss
+++ b/src/styles/components.scss
@@ -592,6 +592,24 @@
             }
         }
 
+        .metadata {
+            display: grid;
+            grid-auto-flow: column;
+            justify-content: start;
+            gap: 0.5rem;
+
+            .chip {
+                background: #0003;
+                font-size: 13px;
+
+                padding: 0 0.25rem;
+                border-radius: 0.25rem;
+                line-height: 1.5;
+
+                font-weight: 600;
+            }
+        }
+
         @media screen and (max-width: $screen-desktop-min) {
             padding: 0.9rem;
 
@@ -609,6 +627,10 @@
         }
     }
 
+    a:has(> .card) {
+        display: contents;
+    }
+
     //
     // Card List
     //
@@ -875,4 +897,22 @@
             }
         }
     }
+
+    .wide-card-list {
+        display: grid;
+        grid-template-columns: repeat(auto-fit, minmax(auto, 30rem));
+        gap: 2rem;
+        padding: 2rem;
+
+        width: 100%;
+
+        justify-content: center;
+
+        @media screen and (max-width: $screen-desktop-min) {
+            grid-template-columns: 1fr;
+
+            padding: 0;
+            gap: 1rem;
+        }
+    }
 }
diff --git a/src/styles/pages.scss b/src/styles/pages.scss
index a7250eb..b83e059 100644
--- a/src/styles/pages.scss
+++ b/src/styles/pages.scss
@@ -438,7 +438,8 @@
     }
 
     .domande-esami {
-        background: hsl(180, 100%, 95%);
+        background: hsl(45, 100%, 95%);
+        --card-base: hsl(45, 100%, 80%);
 
         main {
             justify-self: center;
@@ -447,37 +448,20 @@
             flex-direction: column;
             align-items: center;
 
-            padding: 5rem 0;
-
-            gap: 5rem;
+            padding: 4rem 0;
 
-            max-width: 80ch;
+            gap: 2rem;
 
-            .search-result {
-                background: hsl(180, 100%, 87%);
+            .search {
+                max-width: 80ch;
             }
 
             button {
-                background: hsl(180, 100%, 72%);
+                background: hsl(45, 100%, 72%);
             }
-        }
 
-        .courses {
-            padding: 0;
-
-            hr {
-                width: 100%;
-                border: none;
-                height: 2px;
-                background: #000d;
-                margin: 0;
-            }
-
-            .text {
-                > * {
-                    margin: 1rem 0;
-                    padding: 0 1rem;
-                }
+            .card a {
+                color: color-mix(in srgb, var(--card-base-internal), #000 80%);
             }
         }
     }
diff --git a/src/styles/typography.scss b/src/styles/typography.scss
index 9186e23..40fe7b0 100644
--- a/src/styles/typography.scss
+++ b/src/styles/typography.scss
@@ -204,6 +204,10 @@
             }
         }
 
+        li + li {
+            margin-top: 0.5rem;
+        }
+
         a,
         a:visited {
             color: var(--zone-color, #1e6733);

From 4757c3e0a9e02bec2c9f1e5a31de50a6f40d4dcb Mon Sep 17 00:00:00 2001
From: Antonio De Lucreziis <antonio.delucreziis@gmail.com>
Date: Sat, 8 Feb 2025 01:39:47 +0100
Subject: [PATCH 3/7] prototype mostly finished

---
 astro.config.mjs                             |   7 +-
 bun.lockb                                    | Bin 337358 -> 338816 bytes
 package.json                                 |   1 +
 src/client/DomandeEsamiCourse.tsx            | 116 ++++++++++++++++
 src/data/domande-esami.yaml                  |  87 ++++++++----
 src/files.d.ts                               |  17 ++-
 src/layouts/BaseLayout.astro                 |   9 +-
 src/pages/domande-esami/[course].astro       |  28 +---
 src/pages/domande-esami/api.json.ts          |  11 ++
 src/pages/domande-esami/api/[course].json.ts |  24 ++++
 src/pages/domande-esami/index.astro          |  46 +++----
 src/styles/components.scss                   | 131 ++++++++++++++-----
 src/styles/controls.scss                     |  43 ++++++
 src/styles/main.scss                         |   4 +
 src/styles/typography.scss                   |  12 ++
 15 files changed, 418 insertions(+), 118 deletions(-)
 create mode 100644 src/client/DomandeEsamiCourse.tsx
 create mode 100644 src/pages/domande-esami/api.json.ts
 create mode 100644 src/pages/domande-esami/api/[course].json.ts

diff --git a/astro.config.mjs b/astro.config.mjs
index e9a6363..1831c87 100644
--- a/astro.config.mjs
+++ b/astro.config.mjs
@@ -18,6 +18,11 @@ export default defineConfig({
             theme: 'github-light',
         },
     },
-    integrations: [preact(), mdx()],
+    integrations: [
+        preact({
+            compat: true,
+        }),
+        mdx(),
+    ],
     output: 'static',
 })
diff --git a/bun.lockb b/bun.lockb
index fe08456d92cb617bf66c2018e98ca65ea2d924fc..d1ef97b443a8196bb5f33c383b8d0e4f71783575 100755
GIT binary patch
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AssI20

diff --git a/package.json b/package.json
index 4d7fdde..9eefc62 100644
--- a/package.json
+++ b/package.json
@@ -21,6 +21,7 @@
         "@fontsource/source-sans-pro": "^5.0.8",
         "@fontsource/space-mono": "^5.0.20",
         "@phosphor-icons/core": "^2.1.1",
+        "@phosphor-icons/react": "^2.1.7",
         "@preact/signals": "^1.3.0",
         "@types/jsdom": "^21.1.7",
         "astro": "5.1.0",
diff --git a/src/client/DomandeEsamiCourse.tsx b/src/client/DomandeEsamiCourse.tsx
new file mode 100644
index 0000000..259177b
--- /dev/null
+++ b/src/client/DomandeEsamiCourse.tsx
@@ -0,0 +1,116 @@
+import { useEffect, useState } from 'preact/hooks'
+import { Funnel } from '@phosphor-icons/react'
+import { marked } from 'marked'
+
+import type { Database } from '@/data/domande-esami.yaml'
+
+const useRemoteValue = <T,>(url: string): T | null => {
+    const [value, setValue] = useState<T | null>(null)
+
+    useEffect(() => {
+        fetch(url)
+            .then(response => response.json())
+            .then(value => setValue(value))
+    }, [url])
+
+    return value
+}
+
+type Props = {
+    course: string
+}
+
+export const DomandeEsamiCourse = ({ course }: Props) => {
+    const database = useRemoteValue<Database>(`/domande-esami/api/${course}.json`)
+    if (!database) {
+        return <>Loading...</>
+    }
+
+    // @ts-ignore
+    requestIdleCallback(() => window.renderMath())
+
+    console.log(database)
+
+    const courseTags = [
+        ...new Set(
+            database.questions
+                .filter(question => question.course === course)
+                .flatMap(question => question.tags)
+        ),
+    ]
+
+    const [selectedTags, setSelectedTags] = useState<string[]>([])
+
+    const filteredQuestions = database.questions
+        .filter(question => question.course === course)
+        .filter(
+            question => selectedTags.length === 0 || selectedTags.every(tag => question.tags.includes(tag))
+        )
+
+    return (
+        <>
+            <div class="grid-center">
+                <h3>
+                    <a href="/domande-esami">Domande Esami</a>
+                </h3>
+                <h1>{database.names[course]}</h1>
+            </div>
+
+            <div class="card filter">
+                <div class="grid-h">
+                    <Funnel />
+                    <strong>Filtra Tag</strong>
+                </div>
+                <div class="flex-row-wrap">
+                    {selectedTags.length === 0
+                        ? courseTags.map(tag => (
+                              <div class="chip clickable" onClick={() => setSelectedTags([tag])}>
+                                  {tag}
+                              </div>
+                          ))
+                        : courseTags.map(tag => (
+                              <div
+                                  class={
+                                      selectedTags.includes(tag)
+                                          ? 'chip clickable'
+                                          : 'chip clickable disabled'
+                                  }
+                                  onClick={() =>
+                                      setSelectedTags(
+                                          selectedTags.includes(tag)
+                                              ? selectedTags.filter(t => t !== tag)
+                                              : [...selectedTags, tag]
+                                      )
+                                  }
+                              >
+                                  {tag}
+                              </div>
+                          ))}
+                </div>
+            </div>
+            <div class="wide-card-list" id="questions">
+                {filteredQuestions.length === 0 ? (
+                    <div class="grid-center">
+                        <em>No questions found</em>
+                    </div>
+                ) : (
+                    filteredQuestions.map(question => (
+                        <div class="card">
+                            <div
+                                class="text"
+                                dangerouslySetInnerHTML={{
+                                    __html: marked(question.content, { async: false }),
+                                }}
+                            />
+                            <div class="metadata">
+                                {question.tags.map(tag => (
+                                    <div class="chip small">{tag}</div>
+                                ))}
+                            </div>
+                        </div>
+                    ))
+                )}
+            </div>
+        </>
+    )
+}
diff --git a/src/data/domande-esami.yaml b/src/data/domande-esami.yaml
index 3549afe..2ed339d 100644
--- a/src/data/domande-esami.yaml
+++ b/src/data/domande-esami.yaml
@@ -21,7 +21,7 @@ names:
 
 groups:
     - id: triennale-anno-1
-      name: Triennale - Anno I
+      name: I Anno Triennale
       items:
           - aritmetica
           - geometria-1
@@ -29,14 +29,14 @@ groups:
           - algebra-1
 
     - id: triennale-anno-2
-      name: Triennale - Anno II
+      name: II Anno Triennale
       items:
           - geometria-2
           - analisi-2
           - algebra-1
 
     - id: triennale-anno-3
-      name: Triennale - Anno III
+      name: III Anno Triennale
       items:
           - ricerca-operativa
           - fisica-3
@@ -60,101 +60,142 @@ groups:
 
 questions:
     - course: geometria-1
-      year: 2024
       content: |
           Dimostrare il teorema spettrale reale
+      tags:
+          - 2024
 
     - course: gtd
-      year: 2024
       content: |
           Calcolare la curvatura gaussiana di una sfera di raggio $r$
+      tags:
+          - 2024
 
     - course: geometria-1
-      year: 2023
       content: |
           Dimostrare che _l'area_ di un cerchio è $A = \pi r^2$
+      tags:
+          - 2023
 
     - course: algebra-1
-      year: 2024
       content: |
           Dimostrare il teorema di Sylow
+      tags:
+          - 2024
 
     - course: algebra-1
-      year: 2023
       content: |
           Dimostrare che ogni sottogruppo di un gruppo ciclico è ciclico
+      tags:
+          - 2023
 
     - course: analisi-1
-      year: 2024
       content: |
           Dimostrare il teorema di Weierstrass
+      tags:
+          - 2024
 
     - course: analisi-1
-      year: 2023
       content: |
           Dimostrare che se $f$ è continua su $[a,b]$, allora $f$ è limitata
+      tags:
+          - 2023
 
     - course: analisi-2
-      year: 2024
       content: |
           Dimostrare il teorema di Stokes
+      tags:
+          - 2024
 
     - course: analisi-2
-      year: 2023
       content: |
           Dimostrare il teorema di Green
+      tags:
+          - 2023
 
     - course: analisi-3
-      year: 2024
       content: |
           Dimostrare il teorema di Cauchy
+      tags:
+          - 2024
 
     - course: analisi-3
-      year: 2023
       content: |
           Dimostrare il teorema di Liouville
+      tags:
+          - 2023
 
     - course: algebra-2
-      year: 2024
       content: |
           Dimostrare il teorema di struttura per i gruppi abeliani finiti
+      tags:
+          - 2024
 
     - course: algebra-2
-      year: 2023
       content: |
           Dimostrare il teorema di struttura per i gruppi finiti
+      tags:
+          - 2023
 
     - course: ricerca-operativa
-      year: 2024
       content: |
           Dimostrare il teorema di dualità per i problemi di programmazione lineare
+      tags:
+          - 2024
 
     - course: geometria-topologia-differenziale
-      year: 2024
       content: |
           Dimostrare il teorema di Poincaré-Hopf
+      tags:
+          - 2024
 
     - course: analisi-armonica
-      year: 2024
       content: |
           Dimostrare il teorema di Hahn-Banach
+      tags:
+          - 2024
 
     - course: analisi-complessa
-      year: 2024
       content: |
           Dimostrare il teorema di Morera
+      tags:
+          - 2024
 
     - course: analisi-complessa
-      year: 2023
       content: |
           Dimostrare il teorema degli zeri di Weierstrass
+      tags:
+          - 2023
 
     - course: analisi-complessa
-      year: 2022
       content: |
           Dimostrare il teorema della mappa aperta
+      tags:
+          - 2022
 
     - course: analisi-complessa
-      year: 2021
       content: |
           Dimostrare il teorema della mappa aperta
+      tags:
+          - 2021
+
+    - course: geometria-2
+      content: |
+          Dimostrare il teorema di Van Kampen
+      tags:
+          - 2024
+          - Frigerio
+
+    - course: geometria-2
+      content: |
+          Definizione di gruppo fondamentale
+      tags:
+          - 2023
+          - Frigerio
+
+    - course: geometria-2
+      content: |
+          Dimostrare il teorema Cauchy
+      tags:
+          - 2022
+          - Abate
diff --git a/src/files.d.ts b/src/files.d.ts
index 975bb65..fb0b88c 100644
--- a/src/files.d.ts
+++ b/src/files.d.ts
@@ -17,21 +17,24 @@ declare module '@/data/macchinisti.yaml' {
 }
 
 declare module '@/data/domande-esami.yaml' {
-    type Question = {
+    export type Question = {
         course: string
-        year: number
         content: string
+        tags: string[]
     }
 
-    type Group = {
+    export type Group = {
         id: string
         name: string
         items: Array<string>
     }
 
-    const names: Record<string, string>
-    const groups: Group[]
-    const questions: Question[]
+    export type Database = {
+        names: Record<string, string>
+        groups: Group[]
+        questions: Question[]
+    }
 
-    export { names, groups, questions }
+    const value: Database
+    export default value
 }
diff --git a/src/layouts/BaseLayout.astro b/src/layouts/BaseLayout.astro
index 57c35b7..0929185 100644
--- a/src/layouts/BaseLayout.astro
+++ b/src/layouts/BaseLayout.astro
@@ -44,7 +44,7 @@ const { title, description, thumbnail, pageTags } = Astro.props
         <script>
             import renderMathInElement from 'katex/contrib/auto-render'
 
-            document.addEventListener('DOMContentLoaded', function () {
+            const renderMath = () => {
                 renderMathInElement(document.body, {
                     delimiters: [
                         { left: '$$', right: '$$', display: true },
@@ -54,7 +54,12 @@ const { title, description, thumbnail, pageTags } = Astro.props
                     ],
                     throwOnError: false,
                 })
-            })
+            }
+
+            document.addEventListener('DOMContentLoaded', () => renderMath())
+
+            // @ts-ignore
+            window.renderMath = renderMath
         </script>
 
         <script is:inline>
diff --git a/src/pages/domande-esami/[course].astro b/src/pages/domande-esami/[course].astro
index ddaf9be..65bc2b3 100644
--- a/src/pages/domande-esami/[course].astro
+++ b/src/pages/domande-esami/[course].astro
@@ -4,11 +4,11 @@ import BaseLayout from '@/layouts/BaseLayout.astro'
 import Footer from '@/components/Footer.astro'
 import Header from '@/components/Header.astro'
 
-import { PhosphorIcon } from '@/client/Icon'
-
 import { marked } from 'marked'
 
 import database from '@/data/domande-esami.yaml'
+import PhosphorIcon from '@/components/PhosphorIcon.astro'
+import { DomandeEsamiCourse } from '@/client/DomandeEsamiCourse'
 
 export const getStaticPaths = (() => {
     return Object.keys(database.names).map(course => ({
@@ -22,29 +22,7 @@ const { course } = Astro.params
 <BaseLayout title="Domande Esami | PHC" pageTags={'domande-esami'}>
     <Header />
     <main>
-        <h1>{course}</h1>
-
-        <div class="search">
-            <input type="text" placeholder="Cerca una domanda per un esame..." />
-            <PhosphorIcon client:load name="magnifying-glass" />
-        </div>
-
-        <div class="wide-card-list">
-            {
-                database.questions
-                    .filter(question => question.course === course)
-                    .map(question => (
-                        <div class="card">
-                            <div class="text">
-                                <Fragment set:html={marked(question.content)} />
-                            </div>
-                            <div class="metadata">
-                                <div class="chip">{question.year}</div>
-                            </div>
-                        </div>
-                    ))
-            }
-        </div>
+        <DomandeEsamiCourse client:load course={course} />
     </main>
     <Footer />
 </BaseLayout>
diff --git a/src/pages/domande-esami/api.json.ts b/src/pages/domande-esami/api.json.ts
new file mode 100644
index 0000000..12016fa
--- /dev/null
+++ b/src/pages/domande-esami/api.json.ts
@@ -0,0 +1,11 @@
+import type { APIRoute } from 'astro'
+
+import database from '@/data/domande-esami.yaml'
+
+export const GET: APIRoute = ({}) => {
+    return new Response(JSON.stringify(database), {
+        headers: {
+            'content-type': 'application/json',
+        },
+    })
+}
diff --git a/src/pages/domande-esami/api/[course].json.ts b/src/pages/domande-esami/api/[course].json.ts
new file mode 100644
index 0000000..1904e98
--- /dev/null
+++ b/src/pages/domande-esami/api/[course].json.ts
@@ -0,0 +1,24 @@
+import type { APIRoute, GetStaticPaths } from 'astro'
+
+import database from '@/data/domande-esami.yaml'
+
+export const getStaticPaths = (() => {
+    return Object.keys(database.names).map(course => ({
+        params: { course },
+    }))
+}) satisfies GetStaticPaths
+
+export const GET: APIRoute = ({ params: { course } }) => {
+    return new Response(
+        JSON.stringify({
+            groups: [],
+            names: Object.fromEntries(Object.entries(database.names).filter(([key]) => key === course)),
+            questions: database.questions.filter(question => question.course === course),
+        }),
+        {
+            headers: {
+                'content-type': 'application/json',
+            },
+        }
+    )
+}
diff --git a/src/pages/domande-esami/index.astro b/src/pages/domande-esami/index.astro
index 069ff78..0429116 100644
--- a/src/pages/domande-esami/index.astro
+++ b/src/pages/domande-esami/index.astro
@@ -18,46 +18,42 @@ const courseQuestionCounts = Object.fromEntries(
     <Header />
     <main>
         <h1>Domande Esami</h1>
-        <div class="card large">
-            <div class="text">
-                <p>
-                    [Copilot] Benvenuto nella sezione delle domande d'esame! Qui puoi trovare domande di esami
-                    passati per prepararti al meglio per il tuo prossimo esame.
-                </p>
-                <ul>
-                    <li><a href="#triennale-anno-1">Triennale - Anno I</a></li>
-                    <li><a href="#triennale-anno-2">Triennale - Anno II</a></li>
-                    <li><a href="#triennale-anno-3">Triennale - Anno III</a></li>
-                    <li><a href="#istituzioni">Istituzioni</a></li>
-                    <li><a href="#other">Esami a Scelta</a></li>
-                </ul>
-                <p>
-                    Se volessi contribuire con nuove domande, puoi <a href="#">facendo una pull request</a>,
-                    inviandole al
-                    <a href="#">form domande</a> oppure <a href="#">mandandoci una email</a>.
-                </p>
-            </div>
-        </div>
-
         {
             database.groups.map(group => (
-                <>
-                    <h2 id={group.id}>{group.name}</h2>
+                <details open>
+                    <summary>
+                        <h2 id={group.id}>
+                            <div class="details-closed">
+                                <PhosphorIcon name="caret-down" />
+                            </div>
+                            <div class="details-openned">
+                                <PhosphorIcon name="caret-up" />
+                            </div>
+                            {group.name}
+                        </h2>
+                    </summary>
                     <div class="wide-card-list">
                         {group.items.map(course => (
                             <a href={`/domande-esami/${course}`}>
                                 <div class="card">
                                     <h2>{database.names[course]}</h2>
                                     <div class="text">
-                                        <p>{courseQuestionCounts[course] || 0} domande disponibili</p>
+                                        <p>{courseQuestionCounts[course] || 0} domande</p>
                                     </div>
                                 </div>
                             </a>
                         ))}
                     </div>
-                </>
+                </details>
             ))
         }
+
+        <h3>Come Contribuire</h3>
+        <div class="card large">
+            <div class="text">
+                <p>Se hai raccolte di domande da condividere, puoi...</p>
+            </div>
+        </div>
     </main>
     <Footer />
 </BaseLayout>
diff --git a/src/styles/components.scss b/src/styles/components.scss
index c4e424f..dc3874d 100644
--- a/src/styles/components.scss
+++ b/src/styles/components.scss
@@ -14,7 +14,7 @@
         width: 22px;
         height: 22px;
 
-        display: grid;
+        display: grid inline;
         place-content: center;
     }
 
@@ -79,29 +79,6 @@
         }
     }
 
-    .flex-column {
-        display: flex;
-        flex-direction: column;
-        gap: 1rem;
-    }
-
-    .flex-row {
-        display: flex;
-        flex-direction: row;
-        gap: 1rem;
-    }
-
-    // just to know for reference
-    .fake-masonry {
-        display: grid;
-        grid-template-columns: repeat(var(--columns), 1fr);
-        grid-auto-flow: dense;
-
-        & > * {
-            grid-row: span var(--masonry-height);
-        }
-    }
-
     .search-results {
         width: 100%;
 
@@ -597,17 +574,6 @@
             grid-auto-flow: column;
             justify-content: start;
             gap: 0.5rem;
-
-            .chip {
-                background: #0003;
-                font-size: 13px;
-
-                padding: 0 0.25rem;
-                border-radius: 0.25rem;
-                line-height: 1.5;
-
-                font-weight: 600;
-            }
         }
 
         @media screen and (max-width: $screen-desktop-min) {
@@ -627,6 +593,33 @@
         }
     }
 
+    .chip {
+        user-select: none;
+
+        display: grid;
+        place-content: center;
+        place-items: center;
+
+        background: #0003;
+
+        padding: 0 0.25rem;
+        border-radius: 0.25rem;
+        line-height: 1.5;
+
+        font-size: 16px;
+        font-weight: 500;
+
+        &.small {
+            font-size: 13px;
+            font-weight: 600;
+        }
+
+        &.disabled {
+            color: #0005;
+            background: #0002;
+        }
+    }
+
     a:has(> .card) {
         display: contents;
     }
@@ -908,6 +901,10 @@
 
         justify-content: center;
 
+        .text > * {
+            max-width: none;
+        }
+
         @media screen and (max-width: $screen-desktop-min) {
             grid-template-columns: 1fr;
 
@@ -915,4 +912,68 @@
             gap: 1rem;
         }
     }
+
+    .filter {
+        min-width: 15rem;
+    }
+
+    .flex-column {
+        display: flex;
+        flex-direction: column;
+        gap: 0.5rem;
+    }
+
+    .flex-row {
+        display: flex;
+        flex-direction: row;
+        gap: 0.5rem;
+    }
+
+    .flex-row-wrap {
+        display: flex;
+        flex-direction: row;
+        gap: 0.5rem;
+        flex-wrap: wrap;
+    }
+
+    .grid-h {
+        display: grid;
+        grid-auto-flow: column;
+        justify-content: start;
+        align-items: center;
+
+        gap: 0.5rem;
+    }
+
+    .grid-v {
+        display: grid;
+        justify-items: start;
+        align-content: start;
+
+        grid-auto-flow: row;
+        gap: 0.5rem;
+    }
+
+    .grid-center {
+        display: grid;
+        place-content: center;
+        place-items: center;
+        gap: 0.5rem;
+        grid-auto-flow: row;
+    }
+
+    .clickable {
+        cursor: pointer;
+    }
+
+    // just to know for reference
+    .fake-masonry {
+        display: grid;
+        grid-template-columns: repeat(var(--columns), 1fr);
+        grid-auto-flow: dense;
+
+        & > * {
+            grid-row: span var(--masonry-height);
+        }
+    }
 }
diff --git a/src/styles/controls.scss b/src/styles/controls.scss
index 18ccc38..f0560c9 100644
--- a/src/styles/controls.scss
+++ b/src/styles/controls.scss
@@ -129,4 +129,47 @@
             justify-self: center;
         }
     }
+
+    details {
+        width: 100%;
+
+        summary {
+            display: grid;
+            place-content: center;
+            place-items: center;
+
+            list-style: none;
+            &::-webkit-details-marker {
+                display: none;
+            }
+        }
+
+        .details-openned,
+        .details-closed {
+            display: contents;
+        }
+
+        &:not([open]) {
+            .details-openned {
+                display: none;
+            }
+        }
+
+        &[open] {
+            summary {
+                padding-bottom: 1rem;
+            }
+
+            .details-closed {
+                display: none;
+            }
+        }
+
+        @media screen and (max-width: $screen-desktop-min) {
+            summary {
+                place-content: stretch;
+                place-items: stretch;
+            }
+        }
+    }
 }
diff --git a/src/styles/main.scss b/src/styles/main.scss
index ed95dd4..46ceb26 100644
--- a/src/styles/main.scss
+++ b/src/styles/main.scss
@@ -208,6 +208,10 @@ body {
         @media screen and (max-width: $screen-desktop-min) {
             padding: 3rem 1rem;
             gap: 3rem;
+
+            .card {
+                width: 100%;
+            }
         }
     }
 
diff --git a/src/styles/typography.scss b/src/styles/typography.scss
index 40fe7b0..5f51a81 100644
--- a/src/styles/typography.scss
+++ b/src/styles/typography.scss
@@ -33,6 +33,18 @@
 @layer typography {
     @include geometric-headings;
 
+    strong {
+        font-weight: 600;
+    }
+
+    em {
+        font-style: italic;
+    }
+
+    .text-center {
+        text-align: center;
+    }
+
     .text {
         // text-align: justify;
         // hyphens: auto;

From d46f62dd3f6f26279f5dd25fc67ff20862e9377d Mon Sep 17 00:00:00 2001
From: Antonio De Lucreziis <antonio.delucreziis@gmail.com>
Date: Sun, 9 Feb 2025 19:20:51 +0100
Subject: [PATCH 4/7] added initial batch of questions

---
 .prettierrc                         |    9 -
 .prettierrc.mjs                     |   26 +
 .vscode/settings.json               |   10 +-
 bun.lockb                           |  Bin 338816 -> 341081 bytes
 package.json                        |    3 +
 src/client/DomandeEsamiCourse.tsx   |   29 +-
 src/data/domande-esami.yaml         | 2212 ++++++++++++++++++++++++---
 src/pages/domande-esami/index.astro |   22 +-
 src/styles/components.scss          |   12 +-
 9 files changed, 2094 insertions(+), 229 deletions(-)
 delete mode 100644 .prettierrc
 create mode 100644 .prettierrc.mjs

diff --git a/.prettierrc b/.prettierrc
deleted file mode 100644
index 6f80c3f..0000000
--- a/.prettierrc
+++ /dev/null
@@ -1,9 +0,0 @@
-{
-    "printWidth": 110,
-    "singleQuote": true,
-    "quoteProps": "consistent",
-    "tabWidth": 4,
-    "useTabs": false,
-    "semi": false,
-    "arrowParens": "avoid"
-}
diff --git a/.prettierrc.mjs b/.prettierrc.mjs
new file mode 100644
index 0000000..577489f
--- /dev/null
+++ b/.prettierrc.mjs
@@ -0,0 +1,26 @@
+/** @type {import("prettier").Config} */
+export default {
+    printWidth: 120,
+    singleQuote: true,
+    quoteProps: 'consistent',
+    tabWidth: 4,
+    useTabs: false,
+    semi: false,
+    arrowParens: 'avoid',
+
+    plugins: ['prettier-plugin-astro'],
+    overrides: [
+        {
+            files: '*.astro',
+            options: {
+                parser: 'astro',
+            },
+        },
+        {
+            files: '*.{yml,yaml,json}',
+            options: {
+                tabWidth: 2,
+            },
+        },
+    ],
+}
diff --git a/.vscode/settings.json b/.vscode/settings.json
index 76e80fa..6415250 100644
--- a/.vscode/settings.json
+++ b/.vscode/settings.json
@@ -1,3 +1,11 @@
 {
-    "npm.packageManager": "bun"
+  "npm.packageManager": "bun",
+  "editor.defaultFormatter": "esbenp.prettier-vscode",
+  "[astro]": {
+    "editor.defaultFormatter": "esbenp.prettier-vscode"
+  },
+  "[yaml]": {
+    "editor.tabSize": 2,
+    "editor.defaultFormatter": "esbenp.prettier-vscode"
+  }
 }
diff --git a/bun.lockb b/bun.lockb
index d1ef97b443a8196bb5f33c383b8d0e4f71783575..371588a5a44a856b9d611ceb322e2edc6064692a 100755
GIT binary patch
delta 65704
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diff --git a/package.json b/package.json
index 9eefc62..28c58fc 100644
--- a/package.json
+++ b/package.json
@@ -29,6 +29,7 @@
         "katex": "^0.16.9",
         "lucide-static": "^0.468.0",
         "marked": "^15.0.6",
+        "marked-extended-latex": "^1.1.0",
         "preact": "^10.19.6",
         "typescript": "^5.3.3"
     },
@@ -39,6 +40,8 @@
         "jsdom": "^24.1.1",
         "linkedom": "^0.18.4",
         "npm-run-all": "^4.1.5",
+        "prettier": "^3.5.0",
+        "prettier-plugin-astro": "^0.14.1",
         "rehype-autolink-headings": "^7.1.0",
         "rehype-slug": "^6.0.0",
         "remark-math": "^6.0.0",
diff --git a/src/client/DomandeEsamiCourse.tsx b/src/client/DomandeEsamiCourse.tsx
index 259177b..356693e 100644
--- a/src/client/DomandeEsamiCourse.tsx
+++ b/src/client/DomandeEsamiCourse.tsx
@@ -2,6 +2,19 @@ import { useEffect, useState } from 'preact/hooks'
 import { Funnel } from '@phosphor-icons/react'
 import { marked } from 'marked'
 
+// @ts-ignore
+import extendedLatex from 'marked-extended-latex'
+
+marked.use(
+    extendedLatex({
+        lazy: false,
+        render: (formula: string, display: boolean) => {
+            console.log('rendering', formula)
+            return display ? '$$' + formula + '$$' : '$' + formula + '$'
+        },
+    }),
+)
+
 import type { Database } from '@/data/domande-esami.yaml'
 
 const useRemoteValue = <T,>(url: string): T | null => {
@@ -33,9 +46,7 @@ export const DomandeEsamiCourse = ({ course }: Props) => {
 
     const courseTags = [
         ...new Set(
-            database.questions
-                .filter(question => question.course === course)
-                .flatMap(question => question.tags)
+            database.questions.filter(question => question.course === course).flatMap(question => question.tags),
         ),
     ]
 
@@ -43,9 +54,7 @@ export const DomandeEsamiCourse = ({ course }: Props) => {
 
     const filteredQuestions = database.questions
         .filter(question => question.course === course)
-        .filter(
-            question => selectedTags.length === 0 || selectedTags.every(tag => question.tags.includes(tag))
-        )
+        .filter(question => selectedTags.length === 0 || selectedTags.every(tag => question.tags.includes(tag)))
 
     return (
         <>
@@ -70,16 +79,12 @@ export const DomandeEsamiCourse = ({ course }: Props) => {
                           ))
                         : courseTags.map(tag => (
                               <div
-                                  class={
-                                      selectedTags.includes(tag)
-                                          ? 'chip clickable'
-                                          : 'chip clickable disabled'
-                                  }
+                                  class={selectedTags.includes(tag) ? 'chip clickable' : 'chip clickable disabled'}
                                   onClick={() =>
                                       setSelectedTags(
                                           selectedTags.includes(tag)
                                               ? selectedTags.filter(t => t !== tag)
-                                              : [...selectedTags, tag]
+                                              : [...selectedTags, tag],
                                       )
                                   }
                               >
diff --git a/src/data/domande-esami.yaml b/src/data/domande-esami.yaml
index 2ed339d..e849968 100644
--- a/src/data/domande-esami.yaml
+++ b/src/data/domande-esami.yaml
@@ -1,201 +1,2021 @@
 names:
-    aritmetica: Aritmetica
-    geometria-1: Geometria 1
-    analisi-1: Analisi 1
-    algebra-1: Algebra 1
-    geometria-2: Geometria 2
-    analisi-2: Analisi 2
-    algebra-2: Algebra 2
-    analisi-3: Analisi 3
-    ricerca-operativa: Ricerca Operativa
-    fisica-3: Fisica 3
-    meccanica-razionale: Meccanica Razionale
-    istituzioni-di-geometria: Istituzioni di Geometria
-    istituzioni-di-analisi: Istituzioni di Analisi
-    istituzioni-di-algebra: Istituzioni di Algebra
-    istituzioni-di-fisica: Istituzioni di Fisica
-    istituzioni-di-probabilità: Istituzioni di Probabilità
-    geometria-e-topologia-differenziale: Geometria e Topologia Differenziale
-    analisi-armonica: Analisi Armonica
-    elementi-di-analisi-complessa: Elementi di Analisi Complessa
+  aritmetica: Aritmetica
+  geometria-1: Geometria 1
+  analisi-1: Analisi 1
+  algebra-1: Algebra 1
+  geometria-2: Geometria 2
+  analisi-2: Analisi 2
+  algebra-2: Algebra 2
+  analisi-3: Analisi 3
+  ricerca-operativa: Ricerca Operativa
+  fisica-3: Fisica 3
+  meccanica-razionale: Meccanica Razionale
+  istituzioni-di-geometria: Istituzioni di Geometria
+  istituzioni-di-analisi: Istituzioni di Analisi
+  istituzioni-di-algebra: Istituzioni di Algebra
+  istituzioni-di-fisica: Istituzioni di Fisica
+  istituzioni-di-probabilità: Istituzioni di Probabilità
+  geometria-e-topologia-differenziale: Geometria e Topologia Differenziale
+  analisi-armonica: Analisi Armonica
+  elementi-di-analisi-complessa: Elementi di Analisi Complessa
+  eti: Elementi di Teoria degli Insiemi
 
 groups:
-    - id: triennale-anno-1
-      name: I Anno Triennale
-      items:
-          - aritmetica
-          - geometria-1
-          - analisi-1
-          - algebra-1
-
-    - id: triennale-anno-2
-      name: II Anno Triennale
-      items:
-          - geometria-2
-          - analisi-2
-          - algebra-1
-
-    - id: triennale-anno-3
-      name: III Anno Triennale
-      items:
-          - ricerca-operativa
-          - fisica-3
-          - meccanica-razionale
-
-    - id: istituzioni
-      name: Istituzioni
-      items:
-          - istituzioni-di-geometria
-          - istituzioni-di-analisi
-          - istituzioni-di-algebra
-          - istituzioni-di-fisica
-          - istituzioni-di-probabilità
-
-    - id: other
-      name: Esami a scelta
-      items:
-          - geometria-e-topologia-differenziale
-          - analisi-armonica
-          - elementi-di-analisi-complessa
+  - id: triennale-anno-1
+    name: I Anno Triennale
+    items:
+      - aritmetica
+      - geometria-1
+      - analisi-1
+
+  - id: triennale-anno-2
+    name: II Anno Triennale
+    items:
+      - geometria-2
+      - analisi-2
+      - algebra-1
+
+  - id: triennale-anno-3
+    name: III Anno Triennale
+    items:
+      - ricerca-operativa
+      - fisica-3
+      - meccanica-razionale
+
+  - id: istituzioni
+    name: Istituzioni
+    items:
+      - istituzioni-di-geometria
+      - istituzioni-di-analisi
+      - istituzioni-di-algebra
+      - istituzioni-di-fisica
+      - istituzioni-di-probabilità
+
+  - id: other
+    name: Esami a scelta
+    items:
+      - geometria-e-topologia-differenziale
+      - analisi-armonica
+      - elementi-di-analisi-complessa
+      - eti
+
+# Gruppo fondamentale dei proiettivi reali o complessi.
+# Compattezza in spazi metrici.
+# “Esercizio”: caratterizzare le funzioni intere olomorfe iniettive.
+
+# Domande 20/6/2022
+
+# Primo enunciato di Riemann-Weierstrass
+# • Calcolare il π1(S1). (∼= Z)
+# • Formula di Cauchy per funzioni olomorfe.
+# • π1(P^n(R)) (discorso generale).
+# • Come ottenere Pn(R) da Dn (dettagliata).
+# • Equazione di Cauchy-Riemann.
+# • Esempio di funzione continua differenziabile non olomorfa [ f(z) = \bar{z} ]
+# • Cos’è un punto singolare di una curva proiettiva.
+# • Conica singolare => degenere con K = C.
+# • il toro è omeomorfo al toro meno un punto?
+# • Chi è il rivestimento universale del toro?
+
+# Marzenta Giovanni:
+# Caratterizzazione dei rivestimenti regolari tramite il 1; un esempio di rivestimento regolare e uno di un rivestimento non regolare per il bouquet di due circonferenze.
+# Caratterizzare le funzioni olomorfe intere (da C in C) tali che |f(z)||z|d .
+
+# • X = [0; 1), topologia di base: (a; b), con a > 0, e [0; a)U(b; 1), con 0 < a < b < 1.
+# E più o meno fine della topologia Euclidea? Assiomi di topologia? Connesso? ` E`
+# compatto? Conosci un compatto famoso che ne è omeomorfo? (S1) Un esempio di tale
+# omeomorfismo? (t -> e^2πit).
+# • Gruppo fondamentale degli spazi proiettivi complessi
+
+# 21/6/2022
+
+# Che relazione c'è tra connessione e connessione per archi? Connesso per archi => Connesso
+# (dimostrazione) e Connesso non implica Connesso per archi (dimostrazione).
+# • Data f : U \{z0} → C, punti di singolarità? A riguardo, cosa succede a lim z→z0 |f(z)|?
+# Esempio di funzione con singolarità`a essenziale? [f(z) = e^(1/z) ]
+# Dimostrazione del secondo enunciato di Riemann-Weierstrass
+# • X topologico e Y sottoinsieme, se Y e compatto e chiuso, che relazioni ci sono tra compattezza e chiusura?
+# • Come calcolare Zeri e Poli di una funzione, eventualmente con molteplicità?
+# • Consideriamo la striscia in R2 tra le rette x = 0 e x = 1 comprese e quozientiamolo con la
+# relazione (0; y) ∼ (1; -y) . Come ti immagini questo quoziente? E una varietà topologica? `
+# Togliendo il segmento [0; 1], il quoziente è connesso per archi? Qual è il suo gruppo fondamentale? (Calcolarlo).
+# • Si può retrarre il nastro di Mobius sul suo bordo?
+# • Quanti punti di intersezione può avere al massimo una curva C = [F] in C con una retta?
+# • Come costruiresti uno spazio topologico con gruppo fondamentale Z/3?
+# • Prendiamo due triple di rette in P2(C), quando è possibile mandare le prime tre nelle seconde
+# tre?
+# • Definizione di Topologia Quoziente. Caratterizzazione degli aperti. Prendiamo X = R, x ∼
+# y sse x - y \in Q: la topologia quoziente si può descrivere facilmente... Chi sono gli aperti di
+# questa topologia quoziente? (Topologia indiscreta).
+# • Definizione di Rivestimento.
+# Condizione su E affinché qualunque rivestimento sia di grado finito.
+# • Teorema fondamentale dell’Algebra.
+# • Una cubica C = [p], può avere una retta tangente in due punti? Se invece ha grado 4?
+# • Teorema di Riemann-Weierstrass.
 
 questions:
-    - course: geometria-1
-      content: |
-          Dimostrare il teorema spettrale reale
-      tags:
-          - 2024
-
-    - course: gtd
-      content: |
-          Calcolare la curvatura gaussiana di una sfera di raggio $r$
-      tags:
-          - 2024
-
-    - course: geometria-1
-      content: |
-          Dimostrare che _l'area_ di un cerchio è $A = \pi r^2$
-      tags:
-          - 2023
-
-    - course: algebra-1
-      content: |
-          Dimostrare il teorema di Sylow
-      tags:
-          - 2024
-
-    - course: algebra-1
-      content: |
-          Dimostrare che ogni sottogruppo di un gruppo ciclico è ciclico
-      tags:
-          - 2023
-
-    - course: analisi-1
-      content: |
-          Dimostrare il teorema di Weierstrass
-      tags:
-          - 2024
-
-    - course: analisi-1
-      content: |
-          Dimostrare che se $f$ è continua su $[a,b]$, allora $f$ è limitata
-      tags:
-          - 2023
-
-    - course: analisi-2
-      content: |
-          Dimostrare il teorema di Stokes
-      tags:
-          - 2024
-
-    - course: analisi-2
-      content: |
-          Dimostrare il teorema di Green
-      tags:
-          - 2023
-
-    - course: analisi-3
-      content: |
-          Dimostrare il teorema di Cauchy
-      tags:
-          - 2024
-
-    - course: analisi-3
-      content: |
-          Dimostrare il teorema di Liouville
-      tags:
-          - 2023
-
-    - course: algebra-2
-      content: |
-          Dimostrare il teorema di struttura per i gruppi abeliani finiti
-      tags:
-          - 2024
-
-    - course: algebra-2
-      content: |
-          Dimostrare il teorema di struttura per i gruppi finiti
-      tags:
-          - 2023
-
-    - course: ricerca-operativa
-      content: |
-          Dimostrare il teorema di dualità per i problemi di programmazione lineare
-      tags:
-          - 2024
-
-    - course: geometria-topologia-differenziale
-      content: |
-          Dimostrare il teorema di Poincaré-Hopf
-      tags:
-          - 2024
-
-    - course: analisi-armonica
-      content: |
-          Dimostrare il teorema di Hahn-Banach
-      tags:
-          - 2024
-
-    - course: analisi-complessa
-      content: |
-          Dimostrare il teorema di Morera
-      tags:
-          - 2024
-
-    - course: analisi-complessa
-      content: |
-          Dimostrare il teorema degli zeri di Weierstrass
-      tags:
-          - 2023
-
-    - course: analisi-complessa
-      content: |
-          Dimostrare il teorema della mappa aperta
-      tags:
-          - 2022
-
-    - course: analisi-complessa
-      content: |
-          Dimostrare il teorema della mappa aperta
-      tags:
-          - 2021
-
-    - course: geometria-2
-      content: |
-          Dimostrare il teorema di Van Kampen
-      tags:
-          - 2024
-          - Frigerio
-
-    - course: geometria-2
-      content: |
-          Definizione di gruppo fondamentale
-      tags:
-          - 2023
-          - Frigerio
-
-    - course: geometria-2
-      content: |
-          Dimostrare il teorema Cauchy
-      tags:
-          - 2022
-          - Abate
+  - course: geometria-2
+    content: |
+      $\mathbb R^3$ meno due rette. Nei tre casi in cui sono incidenti, parallele o sghembe, chi è il $\pi_1$?
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Chi sono i biolomorfismi da $\mathbb C$ in $\mathbb C$?
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Zeri di funzioni olomorfe e Teorema di Rouché.
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Il gruppo $G$ delle rotazioni generato da quella di angolo $2\pi/7$ che agisce su $\mathbb R^2$. Calcolare il gruppo fondamentale di $\mathbb R^2/G$ e studiare il rivestimento dato dalla proiezione al quoziente di $\mathbb R^2\{0}$ su $\mathbb R^2\{0}/G$.
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Prodotto numerabile di metrizzabili è metrizzabile e controesempio quando il prodotto è più che numerabile
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Forme chiuse ed esatte, relazioni tra le due
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Esempio di funzione armonica che non sia la parte reale di una funzione olomorfa
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Riferimenti proiettivi e teorema fondamentale delle trasformazioni proiettive
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Retratti, in generale sono chiusi/aperti/nessuno dei due?
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Parlare delle singolarità, Weierstrass-Casorati
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Teorema di Brouwer, se levo il bordo a $D^2$ è ancora vero il teorema?
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Spazi separabili che implicazioni sai dirmi e dimostrazione
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Teorema di Liouville
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      In quale altro risultato che abbiamo visto si usano le stime di Cauchy sui coefficienti? (Voleva la caratterizzazione delle singolarità essenziali, io gli ho nominato il lemma di Schwarz e mi ha fatto fare la dimostrazione anche di quello)
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Differenzia (nel senso di dimostra che uno dei due non implica l'altro) due assiomi di separazione a scelta
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Cosa sai dire delle proprietà di separazione della topologia di Zariski?
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Un esempio di spazio $T_2$ con un quoziente non $T_2$ e un esempio in cui il quoziente è ottenuto per azioni di gruppo.
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Funzioni armoniche e parti reali di funzioni olomorfe.
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Proiettivo complesso è semplicemente connesso, e mappe dalla sfera complessa al proiettivo. Sono rivestimenti?
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Connesso non connesso per archi
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Archi $\implies$ connesso
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      $[0,1]$ connesso
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Olomorfa $\implies$ analitica
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Per quali $d$ interi esiste un rivestimento connesso della superficie di seconda specie di grado $d$
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Sottospazio compatto $\implies$ chiuso. Quando e perché. Controesempio se $X$ non è $T_2$.
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Metrico compatto $\implies$ limitato. Controesempio a metrico completo limitato $\implies$ compatto
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Definizione funzione olomorfa. Se abbiamo una funzione olomorfa su un disco aperto senza il centro, quando si può estendere nel punto?
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Il toro si retrae al toro senza un dischetto?
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Compattezza in spazi metrici. Compatto per successioni $\implies$ completo e totalmente limitato (Implicazione a scelta).
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Definizione di funzione analitica e criteri per stabilire se è identicamente nulla su un aperto connesso. Derivate nulle in un punto $\implies$ identicamente nulla nell'aperto connesso.
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Zeri di una funzione analitica, perché sono un insieme discreto. Come contarli con molteplicità?
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Definizione di semilocalmente semplicemente connesso + esempio di spazio senza tale proprietà
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Invertibilità locale di olomorfe dove la derivata è non nulla.
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Dove posso definire una funzione radice quadrata olomorfa?
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Gruppo fondamentale degli spazi proiettivi su $\mathbb R$ e su $\mathbb C$
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Punti in posizione generale, trasformazioni proiettive, scelta del punto unità - definizioni
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Teorema fondamentale trasformazioni proiettive
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      `O-O` è omotopicamente equivalente a `OO` ma non un suo retratto per deformazione + il loro $\pi_1$
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Definizione funzione armonica + ogni armonica è parte reale di una funzione olomorfa su di un semplicemente connesso.
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Connessione, connessione per archi e relazione tra le due.
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Funzioni meromorfe, poli di funzioni olomorfe. Dimostrazione teorema di Weierstrass
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Esempio di un connesso non connesso per archi
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      $Y$ connesso. $Y \subseteq Z \subseteq \bar{Y} \implies Z$ connesso
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Determinare chiusura dell'insieme $\{0\} \times [0,1] \cap \mathbb Q$ in $\mathbb R^2$, e di $\{0\} \times ]0,1[ \cap \mathbb Q$ in $\mathbb R^2$, chi sono i bordi in $\mathbb R^2$ di questi insiemi?
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Teorema di Liouville
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Birapporto: definizione, cosa succede se scambio $P_1$ e $P_2$, comportamento con trasf. proiettive
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Spazi contraibili: definizione, se $x_0 \in X$ contraibile allora $x_0$ ne è retratto per deformazione?
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Contraibile $\implies$ semplicemente connesso
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Definizione indice di avvolgimento.
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Rivestimento di grado due del wedge di due cerchi e sottogruppo associato nel $\pi_1$
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Relazione tra sottogruppi del $\pi_1$, rivestimenti e rivestimento universale.
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Quando ho un automorfismo di rivestimento che manda un punto di una fibra in un altro?
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Dimostrazione preferita del Teorema Fondamentale dell'Algebra
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Definizione di funzione olomorfa/analitica e relazione tra le due
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Olomorfa $\implies$ Analitica
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Definizione di rivestimento regolare, esibire un rivestimento non regolare.
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Un biolomorfismo dal disco unitario in sé con $f(0) = 0$
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Definizione di rivestimento regolare, esibire un rivestimento non regolare.
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Principio del massimo modulo
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Caratterizzazione degli zeri delle funzioni olomorfe e come contarli con molteplicità
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      $p_1 : \mathbb R^2 \to \mathbb R$ è aperta/chiusa/propria?
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Caratterizzare le funzioni intere e bigettive
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      In $\mathbb R^n$ aperto connesso sse connesso per archi
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Trovare uno spazio connesso ma non connesso per archi.
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Dimostrare che la chiusura di un connesso è connessa.
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Definizione di parte interna, chiusura e bordo di un insieme. Queste definizioni dipendono dallo spazio ambiente?
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Calcolare la chiusura di $(0,1)$ e dei razionali in $[0,1]$ immersi in $\mathbb R$ e $\mathbb R^2$.
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Enunciato e dimostrazione del teorema di Liouville.
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Calcolare $n$-proiettivo reale
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Olomorfa $\iff$ analitica
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Esercizio sul proiettivo del compito di luglio
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Spazio delle matrici $n \times n$ reali quozientate per azione di coniugio di $GL_n(\mathbb R)$. Lo spazio ottenuto è $T_1$, $T_2$?
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Curva affine in $\mathbb C^2$: $y^2=x^3-x$. Qual è la sua chiusura proiettiva? Il supporto affine è denso nel supporto proiettivo? Definizione di asintoto, calcolo degli asintoti e punti singolari di questa curva. Stima brutale del numero di asintoti di una curva di grado $d$.
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      $f(z)dz$ chiusa $\iff$ $f$ olomorfa
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Per quali "a" complessi esiste $f:\mathbb C^* \to \mathbb C$ olomorfa non identicamente nulla con $f'(z) = a*f(z)/z$?
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      $R^3$ meno due rette. Nei tre casi in cui sono incidenti, parallele o sghembe, chi è il $\pi_1$?
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Esempio di rivestimento non regolare
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Per un rivestimento dallo spazio $E$ connesso e localmente connesso per archi: gruppo degli automorfismi transitivo su una fibra $\iff$ l'immersione del $p_1(E)$ è normale
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Trovare tutte le funzioni olomorfe su $\mathbb C$ per cui esistono $k$ e $d$ tali che $|f(z)|<k|z|^d$
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Gruppo fondamentale di $P_n(\mathbb C)$
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Biolomorfismi di $\mathbb C$ e del disco aperto
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Parlare di retrazione e retrazione per deformazione, con le conseguenze sui gruppi fondamentali
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Teorema di Bezout
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Data $F$ irriducibile di grado $d$, quanti punti singolari può avere al massimo $F$? (una stima)
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Spazi metrici e caratterizzazione dei compatti per spazi metrici
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Formula di Cauchy
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      $f$ olomorfa in $U\{z}$ e limitata in un intorno di $z$, cosa possiamo dire?
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Definizione di gruppo fondamentale e perché è un gruppo
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Formula di Cauchy
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Derivata logaritmica
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Prodotto di due spazi compatti è compatto
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Se il prodotto di due spazi è compatto, è sempre vero che i due spazi sono compatti? (Sì, posso vederli entrambi come immagine continua tramite le proiezioni di $X \times Y$)
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Definire l'integrale di forme chiuse su curve continue, accenni di dimostrazione di "integrale su forme chiuse non cambia per curve omotope", un esercizio in cui di fatto serviva la definizione di indice di avvolgimento
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Un aperto di $\mathbb R^n$ connesso è connesso per archi, connesso+localmente connesso per archi implica connesso per archi, la connessione per archi è relazione di equivalenza
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Quanti asintoti può avere al massimo una curva di $P^2(\mathbb C)$?
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Automorfismi del disco
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Dato $S^1$ e $S^1$ ed il suo $\pi_1$ generato da $a,b$, trova il rivestimento associato ai sottogruppi $<a>$ e $N(<a>)$ (con quest'ultimo si intende il sottogruppo normale generato da $a$)
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Quando una funzione propria è chiusa e dimostrazione (più come esercizio che come teoria)
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Gruppo fondamentale del toro
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Una funzione olomorfa si può scrivere come serie di potenze
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Elencare gli assiomi di separazione, dimostrare le varie implicazioni. Dare un controesempio a scelta delle implicazioni metrizzabile -> normale -> regolare -> $T_2$
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Studiare $f$ olomorfa tale che $|f(z)|<k|z|^d$
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Teorema di Liouville (con dimostrazione)
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Un punto è singolare se e solo se il gradiente si annulla.
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Formula di Cauchy per funzioni olomorfe.
+    tags:
+      - 2021
+  - course: geometria-2
+    content: |
+      Trova un rivestimento di grado 3 del bouquet di due circonferenze
+    tags:
+      - 2021
+
+  - course: algebra-1
+    content: |
+      Trovare per quali $n$ esiste un’estensione di $\mathbb Q$ con discriminante (in modulo?) = $7^n$
+    tags:
+      - 2023
+  - course: algebra-1
+    content: |
+      Data un’estensione $L/K$ di grado $6$ e un primo $p$ di $K$, trovare tutti e soli i modi possibili in cui $p$ può fattorizzarsi in $L$, esibendo per ciascun modo un esempio.
+    tags:
+      - 2023
+  - course: algebra-1
+    content: |
+      Trovare la minima estensione ciclotomica di $\mathbb Q$ che contenga le radici quadrate di $3$, $5$ e $13$.
+    tags:
+      - 2023
+  - course: algebra-1
+    content: |
+      Determinare i primi che spezzano completamente in $\mathbb Q(\sqrt[5]{2})/\mathbb Q$
+    tags:
+      - 2023
+  - course: algebra-1
+    content: |
+      Definizione di discriminante e proprietà
+    tags:
+      - 2023
+  - course: algebra-1
+    content: |
+      Considera un’estensione di $\mathbb Q$ con gruppo di Galois $Z_2 \times Z_2$. E’ possibile che ramifichi esattamente un primo? $2$? $3$?
+    tags:
+      - 2023
+  - course: algebra-1
+    content: |
+      Gruppo delle classi, definizione e dimostrazione della finitezza (assumendo lambda con la giusta proprietà)
+    tags:
+      - 2023
+  - course: algebra-1
+    content: |
+      Determinare come spezzano i primi in $\mathbb Q(\sqrt[5]{3})$, in particolare se esistono primi che spezzano completamente e come spezza $5$.
+    tags:
+      - 2023
+
+  - course: aritmetica
+    content: |
+      Un polinomio $p \in \mathbb{Z}[x]$ può essere riducibile o irriducibile. Lo stesso polinomio, preso con coefficienti in $\mathbb{Z}/p\mathbb{Z}[x]$ può essere riducibile o irriducibile. Che relazione c’è tra queste due cose?
+      (Attenzione se su $\mathbb{Z}/p\mathbb{Z}$ la scomposizione diventa banale)
+    tags:
+      - 2015
+
+  - course: aritmetica
+    content: |
+      Capire se $-1$ è residuo quadratico modulo $p$. (Hint: si può dare per scontato che esista un generatore)
+    tags:
+      - 2015
+
+  - course: aritmetica
+    content: |
+      Sia $q \in \mathbb{Z}[x]$ un polinomio irriducibile. Si chiede se $\exists p \in P$ tale che $q$ modulo $p$ è riducibile?
+    tags:
+      - 2015
+
+  - course: aritmetica
+    content: |
+      Sia $G$ un gruppo abeliano finito e sia $H \triangleleft G$. Sappiamo che sia $H$ che $G/H$ sono ciclici. Si può dedurre che $G$ è ciclico? Se no, c’è una qualche altra ipotesi che mi permette di dedurlo? (Hint: pensare agli ordini di $H$ e $G/H$)
+    tags:
+      - 2015
+
+  - course: aritmetica
+    content: |
+      Fai un esempio di due anelli isomorfi come spazi vettoriali ma non come anelli.
+    tags:
+      - 2015
+
+  - course: aritmetica
+    content: |
+      Consideriamo $\sigma : \mathbb{N}^+ \to \mathbb{N}^+$ definita come $$\sigma(n) = \sum_{d \mid n} d.$$ Dimostrarne la moltiplicatività, ovvero che $\sigma(mn) = \sigma(m) \cdot \sigma(n)$ se $(n,m) = 1$.
+    tags:
+      - 2015
+
+  - course: aritmetica
+    content: |
+      Si consideri in $M(K, n, n)$ l’insieme delle matrici quadrate invertibili di ordine $n$ a coefficienti nel campo $K$. Dimostrare che è un gruppo.
+
+      Consideriamo $M(\mathbb{F}_{11}, 2, 2)$. Non è un gruppo abeliano ma mostriamo che esiste un sottogruppo normale. (Hint: prendiamo l’insieme delle matrici il cui determinante ...)
+
+      Sappiamo che ogni sottogruppo normale di un gruppo è $\ker$ di un omomorfismo. Sai trovare un omomorfismo $\varphi : M(\mathbb{F}_{11}, 2, 2) \to \mathbb{F}_{11}$ che abbia come $\ker$ il sottogruppo delle matrici con determinante che è un quadrato in $\mathbb{F}_{11}$?
+    tags:
+      - 2015
+
+  - course: aritmetica
+    content: |
+      Quanti sono i polinomi irriducibili di grado $n$ su $\mathbb{F}_p$? (Hint: può essere utile provare prima il caso dei polinomi di secondo grado. Hint: in alternativa si possono contare i polinomi riducibili.)
+      Hint: Altrimenti dimostrate che 
+      $$\prod_{p(x) \text{ irriducibile}, \deg(p(x)) | n} p(x) = x^{p^n} - x.$$
+    tags:
+      - 2015
+
+  - course: aritmetica
+    content: |
+      Sia $G = \langle x_1, x_2 \rangle$ un gruppo e $H < G$ un sottogruppo. È vero che anche $H$ è generato da al più due elementi? Se è falso trovare un controesempio. Provare prima il caso $H \triangleleft G$, poi il caso generale. (Hint: una volta è vero, l’altra è falsa)
+    tags:
+      - 2015
+
+  - course: aritmetica
+    content: |
+      Descrivere i sottogruppi di $G = \mathbb{Z}_{10} \times \mathbb{Z}_5$ e contare i sottogruppi $H \triangleleft V$ tali che $|H| = 1000$ e
+      $V = \mathbb{Z}_{1000} \times \mathbb{Z}_{500}$. E quanti sono i sottogruppi $H \triangleleft V$ tali che $|H| = 5$?
+    tags:
+      - 2015
+
+  - course: aritmetica
+    content: |
+      Considera l’insieme $W = \{p(x) \in \mathbb{Z}_5 [x]\}$. Ogni polinomio $p \in W$ lo posso vedere come funzione $f_p : \mathbb{Z}_5 \to \mathbb{Z}_5$ associando ad ogni polinomio la funzione valutazione sui suoi elementi.
+
+      Esistono polinomi distinti la cui funzione associata è la stessa?
+
+      Sia $\varphi$ l’omomorfismo che ad un polinomio associa la sua funzione polinomiale in $\mathbb{Z}/p\mathbb{Z}$. Qual è il $\ker$ di questa funzione? E l’immagine di $\varphi$ quanti elementi ha?
+    tags:
+      - 2015
+
+  - course: aritmetica
+    content: |
+      Siano $\alpha, \beta$ algebrici su $\mathbb{Q}$ tali che $\deg(\alpha) = m$ e $\deg(\beta) = n$. Quali sono i possibili valori per $\deg(\alpha + \beta)$?
+
+      Qual è il minimo $\deg(\alpha + \beta)$ fissati $m$ ed $n$?
+    tags:
+      - 2015
+
+  - course: aritmetica
+    content: |
+      $(\mathbb{Q}, +)$ è ciclico? Quanti generatori ha?
+      (Hint: considera le frazioni con numeratore uno e denominatore potenza di un primo) Dimostra che quelli che hai trovato generano.
+    tags:
+      - 2015
+
+  - course: aritmetica
+    content: |
+      Sia $H < G$, con $G$ gruppo ciclico finito. Dimostra che anche $H$ è ciclico. Vale anche nel caso $|G| = +\infty$?
+    tags:
+      - 2015
+
+  - course: aritmetica
+    content: |
+      $\forall n \in \mathbb{N}$ sia $z_n = e^{i 2\pi / n}$. Che cosa ottengo se aggiungo $z_n$ a $\mathbb{Q}$? E se aggiungo $z_n$ e $z_m$ con $m \neq n$?
+
+      Calcola il grado dell’estensione di campo $[\mathbb{Q}(z_n , z_m) : \mathbb{Q}]$ (Hint: $[\mathbb{Q}(z_n) : \mathbb{Q}] = \varphi(n)$)
+
+      Dimostra che se ho $(n,m) = 1$ allora $\mathbb{Q}(z_{nm}) = \mathbb{Q}(z_n , z_m)$.
+      Dimostra che $\sum_{j=0}^{p-1} x^j$ è irriducibile su $\mathbb{Q}[x]$.
+    tags:
+      - 2015
+
+  - course: aritmetica
+    content: |
+      Trova un $\mathbb{Z}/n\mathbb{Z} [x]$ in cui esiste un polinomio $p(x)$ tale che $\exists k \in \mathbb{N}$ con $p^k = 0$.
+      Esistono polinomi invertibili in $\mathbb{Z}/6\mathbb{Z} [x]$?
+
+      Sia $p(x) = \sum_{i=0}^{n} a_i x^i$ tale che $\exists k \in \mathbb{N}$ con $p^k = 0$. Dimostra che allora $a_i$ è nilpotente $\forall 0 \leq i \leq n$.
+    tags:
+      - 2015
+
+  - course: aritmetica
+    content: |
+      Sia $f (x) = x^{14} + 2 \in \mathbb{F}_{13} [x]$. Trova il suo campo di spezzamento.
+    tags:
+      - 2015
+
+  - course: aritmetica
+    content: |
+      Sia $G = (\mathbb{Z}/m\mathbb{Z})^*$ un gruppo e $f : G \to G$ definita come $f (x) = x^5$ una funzione. È un morfismo?
+
+      Quando è iniettiva e quando è suriettiva (al variare di $m$)?
+
+      Mostra che $\ker \varphi \cong \mathbb{Z}_5 \times \mathbb{Z}_5 \times \dots \times \mathbb{Z}_5$.
+
+      Trova un $G$ tale che $\ker \varphi \cong \mathbb{Z}_5 \times \mathbb{Z}_5$.
+    tags:
+      - 2015
+
+  - course: aritmetica
+    content: |
+      Dimostrare che $\forall p \in \mathbb{P}$ il polinomio $x^{p-1} + x^{p-2} + \dots + x + 1 \in \mathbb{Q}[x]$ è irriducibile.
+
+      Dimostra che $f (x)$ è irriducibile in $\mathbb{Q}[x]$ se e solo se $f (x + a)$ è irriducibile, con $a \in \mathbb{Q}$.
+
+      Per quali $n \in \mathbb{N}$ si ha $x^n + x^{n-1} + \dots + x + 1$ irriducibile?
+    tags:
+      - 2015
+  - course: aritmetica
+    content: |
+      Quando esiste $(3x+5)^{-1}$ in $Z_{100}$? (con x parametro).
+
+      So che $x^2 = a (p)$. Quando $\exists y$ t.c. $y^2 = (p^2)$?
+
+      (Hint: provare $y = x + bp$)
+      $\sqrt{2}+\sqrt{3}+\sqrt{5}$ è algebrico sui razionali? Trova un polinomio su cui si annulla e trova una base di
+
+      $\mathbb{Q}(\sqrt{2},\sqrt{3},\sqrt{5})$
+      Sia K un campo che contiene Q. Quando $K(\sqrt{a}) = K(\sqrt{6})$?
+    tags:
+      - 2015
+
+  - course: aritmetica
+    content: |
+      Qual è il campo di spezzamento di $x^7 - 2$ in $\mathbb{F}_{101}$?
+    tags:
+      - 2015
+
+  - course: ricerca-operativa
+    content: |
+      Definizione e caratterizzazione algebrica direzioni ammissibili e di crescita + considerazioni varie su Lemma di Farkas e la mutua esclusività dei due problemi.
+    tags:
+      - 2022-01
+
+  - course: ricerca-operativa
+    content: |
+      Formulazione in PL problema di flusso di costo minimo, variante se volessi minimizzare il flusso su ogni singolo arco.
+    tags:
+      - 2022-01
+
+  - course: ricerca-operativa
+    content: |
+      Trovare i piani di taglio di Gomory su un esempio pratico.
+    tags:
+      - 2022-01
+
+  - course: ricerca-operativa
+    content: |
+      Cosa succede nell’algoritmo del simplesso primale se $A_N \xi \leq 0$ e collegamento con il teorema fondamentale della PL.
+    tags:
+      - 2022-01
+
+  - course: ricerca-operativa
+    content: |
+      Data un’istanza del problema del flusso di costo minimo come stabilire se esistono flussi ammissibili.
+    tags:
+      - 2022-01
+
+  - course: ricerca-operativa
+    content: |
+      Modello PLI per il problema del commesso viaggiatore.
+    tags:
+      - 2022-01
+
+  - course: ricerca-operativa
+    content: |
+      Direzione di crescita del simplesso duale.
+    tags:
+      - 2022-01
+
+  - course: ricerca-operativa
+    content: |
+      Esercizio di modellazione con annessa una domanda sul flusso (scrivere come problema lineare uno dei problemi di flusso).
+    tags:
+      - 2022-01
+
+  - course: ricerca-operativa
+    content: |
+      L’algoritmo del rilassamento del TSP.
+    tags:
+      - 2022-01
+
+  - course: ricerca-operativa
+    content: |
+      Teorema forte della dualità e un esercizio di branch and bound per il TSP.
+    tags:
+      - 2022-01
+
+  - course: ricerca-operativa
+    content: |
+      Teorema forte della dualità.
+    tags:
+      - 2023
+
+  - course: ricerca-operativa
+    content: |
+      Caratterizzazione dell’ottimalità per il problema dei cammini minimi.
+    tags:
+      - 2023
+
+  - course: ricerca-operativa
+    content: |
+      Piani di taglio di Gomory.
+    tags:
+      - 2023
+
+  - course: ricerca-operativa
+    content: |
+      Caratterizzazione algebrica delle direzioni di ammissibilità e di crescita.
+    tags:
+      - 2023
+
+  - course: ricerca-operativa
+    content: |
+      (DR) ha soluzione, che posso dire della soluzione duale?
+    tags:
+      - 2023
+
+  - course: ricerca-operativa
+    content: |
+      Esempio geometrico di soluzione primale unica e duale degenere.
+    tags:
+      - 2023
+
+  - course: ricerca-operativa
+    content: |
+      Formulazione di TSP in PLI con rilassamento MST.
+    tags:
+      - 2023
+
+  - course: ricerca-operativa
+    content: |
+      Se so che $3x_1 + 6x_2 + 9x_3 \leq 13$ è un piano di taglio, posso dire che anche $x_1 + 2x_2 + 3x_3 \leq 4$ è un piano di taglio?
+    tags:
+      - 2023
+
+  - course: ricerca-operativa
+    content: |
+      Cosa si può dire se $A_N \xi \leq 0$?
+    tags:
+      - 2023
+
+  - course: ricerca-operativa
+    content: |
+      Formulazione di CSP in PLI con rilassamento.
+    tags:
+      - 2023
+
+  - course: ricerca-operativa
+    content: |
+      Discutere l’ottimalità di CSP al variare del parametro $L$.
+    tags:
+      - 2023
+
+  - course: ricerca-operativa
+    content: |
+      Discutere l’esistenza di una soluzione ammissibile per CSP (trovare un algoritmo: cammini minimi con costi=lunghezze).
+    tags:
+      - 2023
+
+  - course: ricerca-operativa
+    content: |
+      Verificare mediante scarti complementari se una soluzione del duale è ottima.
+    tags:
+      - 2023
+
+  - course: ricerca-operativa
+    content: |
+      Relazione tra flusso massimo e taglio minimo.
+    tags:
+      - 2023
+
+  - course: ricerca-operativa
+    content: |
+      Esempio di grafo con più tagli di capacità minima.
+    tags:
+      - 2023
+
+  - course: ricerca-operativa
+    content: |
+      Rilassamento convessificato di un problema di programmazione lineare intera.
+    tags:
+      - 2023
+
+  - course: ricerca-operativa
+    content: |
+      Caratterizzazione direzioni ammissibili e di crescita.
+    tags:
+      - 2023
+
+  - course: ricerca-operativa
+    content: |
+      Piani di taglio di Gomory.
+    tags:
+      - 2023
+
+  - course: ricerca-operativa
+    content: |
+      È possibile che il problema di flusso massimo sia vuoto? Può essere che il valore del flusso massimo sia zero? Quando è possibile?
+    tags:
+      - 2023
+
+  - course: ricerca-operativa
+    content: |
+      Esegui un’iterazione del simplesso duale.
+    tags:
+      - 2023
+
+  - course: ricerca-operativa
+    content: |
+      Definisci piani di taglio di Gomory e trovane uno per il problema precedente.
+    tags:
+      - 2023
+
+  - course: ricerca-operativa
+    content: |
+      Dato un grafo, esibire dei bilanci, costi e capacità tali che il problema di flusso di costo minimo ammetta più di una soluzione (e dire quante).
+    tags:
+      - 2023
+
+  - course: ricerca-operativa
+    content: |
+      Dato il problema $\max (x_1 + 2x_2)$ soggetto ai vincoli:  
+      $$
+      \begin{cases}
+      x_2 \leq 4 \\
+      x_1 \leq 2 \\
+      x_1 - 2x_2 \leq 10 \\
+      2x_1 + x_2 \leq 4 \\
+      -x_1 \leq -4
+      \end{cases}
+      $$
+      come decidere da $B = \{4, 5\}$ quale algoritmo utilizzare?
+    tags:
+      - 2023
+
+  - course: ricerca-operativa
+    content: |
+      Dimostrare che $y(\theta)$ è una direzione di decrescita nell’algoritmo del simplesso duale.
+    tags:
+      - 2023
+
+  - course: ricerca-operativa
+    content: |
+      Flusso massimo - Taglio minimo con dimostrazione.
+    tags:
+      - 2023
+
+  - course: ricerca-operativa
+    content: |
+      Data una rete, fornire un algoritmo per trovare il cammino minimo dal nodo $s$ al nodo $t$ supponendo che ogni nodo costi $T$, con tempi di percorrenza degli archi $t_{ij}$, $t_{i'j'}$.
+    tags:
+      - 2023
+
+  - course: ricerca-operativa
+    content: |
+      Modello PL del problema di flusso di costo minimo.
+    tags:
+      - 2023
+
+  - course: ricerca-operativa
+    content: |
+      Un flusso ammissibile è di costo minimo se e solo se non esistono cicli aumentanti negativi.
+    tags:
+      - 2023
+
+  - course: ricerca-operativa
+    content: |
+      Modellazione di un problema di cammino minimo "doppio", con due coppie sorgente-destinazione.
+    tags:
+      - 2023
+
+  - course: ricerca-operativa
+    content: |
+      Come cambia il modello se impongo che i cammini (da $s_1$ a $t_1$, da $s_2$ a $t_2$) non abbiano archi in comune?
+    tags:
+      - 2023
+
+  - course: istituzioni-di-geometria
+    content: |
+      Definizione di gruppo fondamentale e perché è un gruppo
+    tags:
+      - 2023
+
+  - course: istituzioni-di-geometria
+    content: |
+      Hopf-Rinow
+    tags:
+      - 2024
+  - course: istituzioni-di-geometria
+    content: |
+      Mayer-Vietoris a supporto cpt
+    tags:
+      - 2024
+  - course: istituzioni-di-geometria
+    content: |
+      M cpt => X cv sempre completo (in realtà poi ha chiesto “se vivi almeno epsilon ecc”)
+    tags:
+      - 2024
+  - course: istituzioni-di-geometria
+    content: |
+      Frobenius
+    tags:
+      - 2024
+  - course: istituzioni-di-geometria
+    content: |
+      Invarianza omotopica (non ha chiesto l'uguaglianza con la derivata di lie, gli è bastata la frase "per definizione di derivata di Lie")
+    tags:
+      - 2024
+  - course: istituzioni-di-geometria
+    content: |
+      Connessione di Levi-Civita (definizione praticamente)
+    tags:
+      - 2024
+  - course: istituzioni-di-geometria
+    content: |
+      Connessione compatibile (proposizione dei fatti equivalenti)
+    tags:
+      - 2024
+  - course: istituzioni-di-geometria
+    content: |
+      Isotopia tra sottovarietà e isotopia ambiente, che relazioni ci sono
+    tags:
+      - 2024
+  - course: istituzioni-di-geometria
+    content: |
+      Differenziale di una $k$-forma (ha chiesto di dim che il differenziale su $R^n$ è unico)
+    tags:
+      - 2024
+  - course: istituzioni-di-geometria
+    content: |
+      Trasporto parallelo
+    tags:
+      - 2024
+  - course: istituzioni-di-geometria
+    content: |
+      Meyer-Vietoris
+    tags:
+      - 2024
+  - course: istituzioni-di-geometria
+    content: |
+      Orientazione; perché mobius e klein non sono orientabili
+    tags:
+      - 2024
+  - course: istituzioni-di-geometria
+    content: |
+      Relazione tra euclidea e piatta
+    tags:
+      - 2024
+  - course: istituzioni-di-geometria
+    content: |
+      Dualità di poincare
+    tags:
+      - 2024
+  - course: istituzioni-di-geometria
+    content: |
+      Definizione gruppo di Lie e sottogruppo di Lie
+    tags:
+      - 2024
+  - course: istituzioni-di-geometria
+    content: |
+      Esempio di immersione iniettiva che non è embedding(?)
+    tags:
+      - 2024
+  - course: istituzioni-di-geometria
+    content: |
+      Algebra di Lie, distribuzione (?) Non ho capito, qualcosa in cui si applica Frobenius. Ah forse la bigezione tra sottogruppi connessi e algebre di lie.
+    tags:
+      - 2024
+  - course: istituzioni-di-geometria
+    content: |
+      Definizione derivata di lie.
+    tags:
+      - 2024
+  - course: istituzioni-di-geometria
+    content: |
+      Perché le geodetiche sono curve minimizzanti
+    tags:
+      - 2024
+  - course: istituzioni-di-geometria
+    content: |
+      Definizione bracket di Lie di due campi vettoriali, cos'è che bisogna dimostrare? Se metto un + funziona lo stesso? (Verificare le proprietà delle derivazioni)
+    tags:
+      - 2024
+  - course: istituzioni-di-geometria
+    content: |
+      Rigidità isometrie
+    tags:
+      - 2024
+  - course: istituzioni-di-geometria
+    content: |
+      Stokes
+    tags:
+      - 2024
+  - course: istituzioni-di-geometria
+    content: |
+      Embedding compatto
+    tags:
+      - 2024
+  - course: istituzioni-di-geometria
+    content: |
+      compatta $\implies$ geodeticamente completa
+    tags:
+      - 2024
+  - course: istituzioni-di-geometria
+    content: |
+      Formula magica di Cartan (idea)
+    tags:
+      - 2024
+
+  - course: eti
+    content: |
+      Dimostrare Cantor-Bernstein
+    tags:
+      - Mamino
+  - course: eti
+    content: |
+      Esistenza ed unicità della differenza fra ordinali
+    tags:
+      - Mamino
+  - course: eti
+    content: |
+      Esercizio su cardinalità di certe funzioni reali
+    tags:
+      - Mamino
+  - course: eti
+    content: |
+      assioma di scelta ed enunciati equivalenti
+    tags:
+      - Mamino
+  - course: eti
+    content: |
+      AC $\implies$ Lemma di Zorn
+    tags:
+      - Mamino
+  - course: eti
+    content: |
+      Teorema di Hartogs e robe sugli ordinali
+    tags:
+      - Mamino
+  - course: eti
+    content: |
+      Verificare che la definizione di esponenziale tra buoni ordini è ben data
+    tags:
+      - Mamino
+  - course: eti
+    content: |
+      Teorema di cantor-bendixon, la dimostrazione
+    tags:
+      - Mamino
+  - course: eti
+    content: |
+      Se prendendo un ordinale, ne faccio la forma normale di cantor, poi sugli esponenti che compaiono che non sono epsilon-number fare la forma normale e cosi via, dire se mi fermo dopo un numero finito di passi o no. (La risposta è si e si ragiona sulla forma normale di cantor che può avere il minimo controesempio, ossia il minimo ordinale per cui questa operazione non termina in un numero finito di passi)
+    tags:
+      - Mamino
+  - course: eti
+    content: |
+      Dimostrare Cantor-Bernstein
+    tags:
+      - Mamino
+  - course: eti
+    content: |
+      Esercizio: qual è la cardinalità dei polinomi a coefficienti in $\mathbb Z / 7$ che hanno per radici tutti gli elementi di $\mathbb Z / 7$?
+    tags:
+      - Mamino
+  - course: eti
+    content: |
+      Cosa si può dire della cofinalità di cardinali regolari e limite? Dimostralo
+    tags:
+      - Mamino
+  - course: eti
+    content: |
+      Dimostrare $\aleph_\alpha^2$ = $\aleph_alpha$ (prima mi aveva chiesto se secondo me per dimostrarlo serviva la scelta)
+    tags:
+      - Mamino
+  - course: eti
+    content: |
+      Con la scelta cosa si può dire a riguardo? (Tarsky, non me lo ha fatto dimostrare)
+    tags:
+      - Mamino
+  - course: eti
+    content: |
+      Esistenza ed unicità del numero di hartogs
+    tags:
+      - Mamino
+  - course: eti
+    content: |
+      Unicità dell'ordinale isomorfo ad un b.o.
+    tags:
+      - Mamino
+  - course: eti
+    content: |
+      Definire i $V_{\alpha}$, che cardinalità hanno, e punti fissi dell'associazione $\alpha \implies |V_{\alpha}|$, mostrare che i punti fissi sono una classe, l'$(\omega+1)$-esimo punto fisso che cofinalità ha, esistono punti fissi non regolari
+    tags:
+      - Mamino
+
+  - course: istituzioni-di-algebra
+    content: |
+      Domanda 5 (Artin-Rees & Krull Intersection)
+      - A corollary of Artin-Rees (exactness of completion for f.g. modules over Noe rings)
+      - Why Artinian Local implies Complete (w.r. to $P$) [$P^n$ stabilizes]
+      - Example of Artinian Local which is not a field (e.g. $K[x]/(x^n), n>1$)
+    tags:
+      - Tamas
+  - course: istituzioni-di-algebra
+    content: |
+      Domanda 13 (Equivalence between $D^-(A)$ and $K^-(P)$)
+      - What do the intermediate lemmas tell us in the case of $R$-Mod?
+      - Where did we use this theorem?
+    tags:
+      - Tamas
+  - course: istituzioni-di-algebra
+    content: |
+      Domanda 12
+      - Definition and properties of exact triangles
+    tags:
+      - Tamas
+  - course: istituzioni-di-algebra
+    content: |
+      Domanda 14
+      - Base change for $\text{Tor}$ tensor a flat object
+    tags:
+      - Tamas
+
+  - course: meccanica-razionale
+    content: |
+      Equazioni di Eulero
+    tags:
+      - 2023
+
+  - course: meccanica-razionale
+    content: |
+      Moto per inerzia (una panoramica di tutti i risultati)
+    tags:
+      - 2023
+
+  - course: meccanica-razionale
+    content: |
+      Definizione di stabilità
+    tags:
+      - 2023
+
+  - course: meccanica-razionale
+    content: |
+      Instabilità della seconda rotazione stazionaria tramite la linearizzazione (pseudo-esercizio)
+    tags:
+      - 2023
+
+  - course: meccanica-razionale
+    content: |
+      Riduzione di Routh
+    tags:
+      - 2023
+
+  - course: meccanica-razionale
+    content: |
+      Se passando al sistema ridotto trovo una soluzione stazionaria, posso con-
+      cludere che ho una soluzione stazionaria del sistema di partenza? (No,
+      l'esempio è il moto circolare che ha $\rho$ costante)
+    tags:
+      - 2023
+
+  - course: meccanica-razionale
+    content: |
+      Equazioni Cardinali della Dinamica
+    tags:
+      - 2023
+
+  - course: meccanica-razionale
+    content: |
+      Scrivere le equazioni del moto di una bicicletta (con una coppia di forze
+      applicata sulla ruota posteriore) che rotola senza strisciare lungo Ox e
+      calcolarne le componenti tangenziali delle reazioni vincolari sui punti di
+      contatto
+    tags:
+      - 2023
+
+  - course: meccanica-razionale
+    content: |
+      Dire qualitativamente quale equazione e quale polo è conveniente usare
+      per calcolare le componenti tangenziali delle reazioni vincolari nel caso
+      in cui la stessa bicicletta sia vincolata ad una guida circolare e spiegare
+      perché
+    tags:
+      - 2023
+
+  - course: meccanica-razionale
+    content: |
+      Dire quali sono le forze in gioco di un' asta appesa all'origine di un piano
+      $Oxy$ (con gravità) che ruota in modo uniforme intorno all'asse y, e dare
+      un'idea di calcolo dell'energia potenziale di tali forze
+    tags:
+      - 2023
+
+  - course: meccanica-razionale
+    content: |
+      Dimostrare che, se un sistema ha trinomio invariante è nullo e la risultante
+      è non nulla, allora è equivalente al sistema composto dalla sola risultante
+      applicata ad un punto dell'asse centrale
+    tags:
+      - 2023
+
+  - course: meccanica-razionale
+    content: |
+      Definizione di forze interne di tipo classico e prime proprietà
+    tags:
+      - 2023
+
+  - course: meccanica-razionale
+    content: |
+      Definizione di operatore di inerzia e prime proprietà, cosa sono i momenti
+      principali di inerzia e in cosa è utile per lo studio del moto di un corpo
+      rigido
+    tags:
+      - 2023
+
+  - course: meccanica-razionale
+    content: |
+      Scomposizione di momento angolare in cui compare il momento di inerzia
+      e scomposizione rispetto al baricentro
+    tags:
+      - 2023
+
+  - course: meccanica-razionale
+    content: |
+      Modi normali di oscillazione cosa sono e scrivere il sistema linearizzato a
+      cui ci si riduce per studiare la stabilità
+    tags:
+      - 2023
+
+  - course: meccanica-razionale
+    content: |
+      Definizione di velocità angolare, formule di Poisson, derivata in diversi
+      sistemi di riferimento
+    tags:
+      - 2023
+
+  - course: meccanica-razionale
+    content: |
+      Velocità angolare di un corpo rigido ed esercizio sul calcolo di una velocità
+      angolare (guida rotola senza strisciare e disco r.s.s. Sulla guida)
+    tags:
+      - 2023
+
+  - course: meccanica-razionale
+    content: |
+      Equivalenza tra equazioni di Lagrange di prima specie ed eq. di D'Alembert
+
+    tags:
+      - 2023
+
+  - course: meccanica-razionale
+    content: |
+      equilibri, Lagrange-Dirichlet (x2)
+    tags:
+      - 2023
+
+  - course: meccanica-razionale
+    content: |
+      integrale di Jacobi
+    tags:
+      - 2023
+
+  - course: meccanica-razionale
+    content: |
+      asse istantaneo di rotazione
+    tags:
+      - 2023
+
+  - course: meccanica-razionale
+    content: |
+      energia potenziale generalizzata delle forze apparenti, lagrangiana per il
+      problema dei tre corpi in un riferimento rotante, perché è utile in questo
+      riferimento
+    tags:
+      - 2023
+
+  - course: meccanica-razionale
+    content: |
+      Teorema di Noether: premesse, enunciato, dimostrazione, applicazione
+      nel caso con una variabile ciclica (ritrovare che il momento coniugato si
+      conserva), applicazione nel caso dei moti centrali (invarianza per rotazione,
+      ritrovare che il momento angolare si conserva)
+    tags:
+      - 2023
+
+  - course: meccanica-razionale
+    content: |
+      Moti centrali: fare la storia del potenziale efficace, mostrare che sono
+      integrabili, quando un'orbita è periodica?
+    tags:
+      - 2023
+
+  - course: meccanica-razionale
+    content: |
+      Forze conservative e energia potenziale; forze interne di tipo classico; i
+      sistemi di forze di tipo classico hanno risultante nulla; energia potenziale
+      delle forze di tipo classico.
+    tags:
+      - 2023
+
+  - course: meccanica-razionale
+    content: |
+      Teorema di König, versione per sistemi di N punti e versione per corpo
+      rigido
+    tags:
+      - 2023
+
+  - course: meccanica-razionale
+    content: |
+      Le forze interne ammettono potenziale
+    tags:
+      - 2023
+
+  - course: meccanica-razionale
+    content: |
+      Trovare gli equilibri di un sistema di 3 corpi soggetti all interazione gravi-
+      tazionale (che si risolve con il teorema di Eulero sulle omogene enunciato)
+    tags:
+      - 2023
+
+  - course: meccanica-razionale
+    content: |
+      Discorsi generali sui vincoli, esempio di vinvolo olonomo
+    tags:
+      - 2023
+
+  - course: meccanica-razionale
+    content: |
+      In presenza di vincoli olonomi cosa si può dire dell energia cinetica
+    tags:
+      - 2023
+
+  - course: meccanica-razionale
+    content: |
+      Vincoli ideali
+    tags:
+      - 2023
+
+  - course: meccanica-razionale
+    content: |
+      Potenziale delle forze apparenti
+    tags:
+      - 2023
+
+  - course: meccanica-razionale
+    content: |
+      definizione di operatore di inerzia e prima proprietà fino al teorema di
+      scomposizione. Huygens-Steiner e un esempio di applicazione
+    tags:
+      - 2023
+
+  - course: meccanica-razionale
+    content: |
+      principio di d'Alembert e definizione di forze generalizzate. Calcolo di
+      quest'ultime nel caso dell'asta ruotante
+    tags:
+      - 2023
+
+  - course: meccanica-razionale
+    content: |
+      definizione di equilibrio stabile; come interpreti questa definizione per gli
+      equilibri stabili della lagrangiana?
+    tags:
+      - 2023
+
+  - course: meccanica-razionale
+    content: |
+      Dimostrare che il vincolo di rigidità di un corpo rigido è un vincolo olonomo
+      e ideale
+    tags:
+      - 2023
+
+  - course: meccanica-razionale
+    content: |
+      Lagrangiana ridotta. Che cosa puoi dire sulla stabilitá/instabilità del sis-
+      tema di partenza se trovi un equilibrio stabile/instabile per la Lagrangiana
+      di Routh?
+    tags:
+      - 2023
+
+  - course: meccanica-razionale
+    content: |
+      Esercizio 2 10 Maggio 2018 (Matematica)
+    tags:
+      - 2023
+
+  - course: meccanica-razionale
+    content: |
+      Operatore di inerzia
+    tags:
+      - 2023
+
+  - course: meccanica-razionale
+    content: |
+      Basi principali di un sistema di 8 punti disposti ai vertici di un cubo
+    tags:
+      - 2023
+
+  - course: meccanica-razionale
+    content: |
+      Potenziali generalizzati
+    tags:
+      - 2023
+
+  - course: meccanica-razionale
+    content: |
+      Potenziale generalizzato della forza di Coriolis
+    tags:
+      - 2023
+
+  - course: meccanica-razionale
+    content: |
+      Problema inverso di Keplero
+    tags:
+      - 2023
+
+  - course: meccanica-razionale
+    content: |
+      Lagrange-Dirichlet
+    tags:
+      - 2023
+
+  - course: meccanica-razionale
+    content: |
+      Parlare dei sistemi equivalenti di vettori applicati
+    tags:
+      - 2023
+
+  - course: meccanica-razionale
+    content: |
+      Problema dei due corpi e problema di keplero
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      Dimostrazione del teorema di divergenza?
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      Definire la misura di Lebesgue nei due modi
+      (Misura esterna+Caratheodory e modo costruttivo tramite aperti e compatti)
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      E un esempio di insieme non misurabile
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      Insiemi frattali e la loro dimensione e moltiplicatori di Lagrange
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      Weierstrass in $\mathbb{R}^n$
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      Definizione di compatto
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      Gauss Green con dimostrazione
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      e conseguenze (formula dell’area)
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      Enunciato del teorema di divergenza in $\mathbb{R}^n$
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      Definizione di flusso di un campo attraverso una superficie
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      Scrivere sviluppo in serie di Fourier di $f(x)=|x|$ su $[-\pi,\pi]$ estesa per periodicità su $\mathbb{R}$
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      Risultati di convergenza serie di Fourier e dimostrazione della convergenza in $L^2$
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      Teorema di Cauchy
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      Controesempio di esistenza ma non unicità
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      Teorema di Peano (solo idea della dim)
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      Cauchy-Lipschitz
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      Banach-Caccioppoli
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      Forme differenziali chiuse e esatte definizione e quando chiusa implica esatta e viceversa
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      Definizione di serie numerica; cosa significa che converge/diverge; definizione equivalente di convergenza (criterio di Cauchy)
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      Criterio di condensazione di Cauchy
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      Dimostrare che $\mathbb{R}$ è completo per successioni
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      Enunciato del Teorema Fondamentale del Calcolo
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      Teorema di esistenza degli zeri
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      Teorema dei valori intermedi
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      Una funzione che soddisfa la proprietà di Darboux è continua?
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      Enunciato Teorema Fondamentale del Calcolo
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      Teorema di Weierstrass
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      Dimostrare che esiste una successione dentro E che tende a sup E
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      Teorema della Media Integrale
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      Funzioni continue sono integrabili
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      Dimostrazione di Heine-Cantor
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      Cos'è una successione di Cauchy
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      Dimostrare che una successione di Cauchy reale converge
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      Teorema di Darboux
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      Esempio di funzione con derivata non continua
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      Caratterizzare i punti di discontinuità di una derivata
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      Teorema di Lagrange; conseguenze sulla monotonia di Lagrange
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      Dimostrazione Polinomio di Taylor con resto di Peano e di Lagrange
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      Criterio di Leibniz per le serie
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      Enunciato criterio di Dirichlet; applicazione alla serie $\sum \frac{\sin n}{n^\alpha}$ con $\alpha>0$
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      Perché $\sin n$ non ha limite a $+\infty$ (e $e^{in}$ denso nella circonferenza unitaria)
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      Due definizioni equivalenti di $e$
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      dimostrazione lagrange
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      dimostrazione rolle
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      qualche implicazione di lagrange
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      definizione di funzione analitica
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      esempio di funzione non analitica
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      teoria dei massimi e dei minimi con taylor oppure con le derivate successive
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      teorema di esistenza e unicità
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      definizione di equazione differenziale ordinaria
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      mostrare come si risolvono equazioni lineari
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      mostrare che lo spazio delle soluzioni omogenee è uno spazio vettoriale
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      Esempio di funzione continua solo in un punto. F continua manda compatti in compatti. Definizione di integrale e teorema della media.
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      ha chiesto di dimostrare che la funzione integrale è continua e se ingenerale è qualcosa di più che continua (è uniformemente continua)
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      E di definire cos’è l’integrale di riemann
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      Teorema di Rolle,Lagrange.
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      Una funzione con derivata nulla è costante.
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      Una funzione con derivata seconda nulla è una retta (varie dimostrazionei  via Lagrange, Taylor, con problema di Cauchy)
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      Cosa è una serie e dimostrazione criterio di Cauchy (via completezza di $\mathbb{R}$)
+    tags:
+      - 2023
+
+  - course: analisi-2
+    content: |
+      Se f derivabile, f' manda intervalli in intervalli. Se f' può avere discontinuità a salto, baffo di Peano
+    tags:
+      - 2023
diff --git a/src/pages/domande-esami/index.astro b/src/pages/domande-esami/index.astro
index 0429116..bcda123 100644
--- a/src/pages/domande-esami/index.astro
+++ b/src/pages/domande-esami/index.astro
@@ -10,7 +10,7 @@ const courseQuestionCounts = Object.fromEntries(
     database.questions.reduce((acc, question) => {
         acc.set(question.course, (acc.get(question.course) || 0) + 1)
         return acc
-    }, new Map())
+    }, new Map()),
 )
 ---
 
@@ -33,16 +33,18 @@ const courseQuestionCounts = Object.fromEntries(
                         </h2>
                     </summary>
                     <div class="wide-card-list">
-                        {group.items.map(course => (
-                            <a href={`/domande-esami/${course}`}>
-                                <div class="card">
-                                    <h2>{database.names[course]}</h2>
-                                    <div class="text">
-                                        <p>{courseQuestionCounts[course] || 0} domande</p>
+                        {group.items
+                            .filter(course => courseQuestionCounts[course] > 0)
+                            .map(course => (
+                                <a href={`/domande-esami/${course}`}>
+                                    <div class="card">
+                                        <h2>{database.names[course]}</h2>
+                                        <div class="text">
+                                            <p>{courseQuestionCounts[course] || 0} domande</p>
+                                        </div>
                                     </div>
-                                </div>
-                            </a>
-                        ))}
+                                </a>
+                            ))}
                     </div>
                 </details>
             ))
diff --git a/src/styles/components.scss b/src/styles/components.scss
index dc3874d..c7fd776 100644
--- a/src/styles/components.scss
+++ b/src/styles/components.scss
@@ -33,7 +33,11 @@
         place-content: center;
 
         font-size: 24px;
-        font-variation-settings: 'FILL' 0, 'wght' 300, 'GRAD' 0, 'opsz' 24;
+        font-variation-settings:
+            'FILL' 0,
+            'wght' 300,
+            'GRAD' 0,
+            'opsz' 24;
 
         max-width: 32px;
     }
@@ -900,11 +904,17 @@
         width: 100%;
 
         justify-content: center;
+        // align-items: start;
 
         .text > * {
             max-width: none;
         }
 
+        .card {
+            display: grid;
+            grid-template-rows: 1fr auto;
+        }
+
         @media screen and (max-width: $screen-desktop-min) {
             grid-template-columns: 1fr;
 

From ae70cfc5e3888327a899b0888df09b7d3e4c58cb Mon Sep 17 00:00:00 2001
From: Antonio De Lucreziis <antonio.delucreziis@gmail.com>
Date: Sun, 9 Feb 2025 20:24:39 +0100
Subject: [PATCH 5/7] last checks

---
 src/client/DomandeEsamiCourse.tsx      | 18 ++++--
 src/client/lib/debug-console.js        | 27 +++++++++
 src/components/Header.astro            |  1 +
 src/data/domande-esami.yaml            | 83 ++++++++++++++++++++++++--
 src/pages/domande-esami/[course].astro |  2 +-
 src/pages/domande-esami/index.astro    |  5 +-
 src/styles/components.scss             |  7 ++-
 src/styles/main.scss                   |  2 +
 8 files changed, 131 insertions(+), 14 deletions(-)
 create mode 100644 src/client/lib/debug-console.js

diff --git a/src/client/DomandeEsamiCourse.tsx b/src/client/DomandeEsamiCourse.tsx
index 356693e..09ea675 100644
--- a/src/client/DomandeEsamiCourse.tsx
+++ b/src/client/DomandeEsamiCourse.tsx
@@ -9,7 +9,6 @@ marked.use(
     extendedLatex({
         lazy: false,
         render: (formula: string, display: boolean) => {
-            console.log('rendering', formula)
             return display ? '$$' + formula + '$$' : '$' + formula + '$'
         },
     }),
@@ -20,10 +19,13 @@ import type { Database } from '@/data/domande-esami.yaml'
 const useRemoteValue = <T,>(url: string): T | null => {
     const [value, setValue] = useState<T | null>(null)
 
+    console.log('fetching', url, value)
+
     useEffect(() => {
         fetch(url)
             .then(response => response.json())
             .then(value => setValue(value))
+            .catch(error => console.error(error))
     }, [url])
 
     return value
@@ -39,10 +41,13 @@ export const DomandeEsamiCourse = ({ course }: Props) => {
         return <>Loading...</>
     }
 
-    // @ts-ignore
-    requestIdleCallback(() => window.renderMath())
-
-    console.log(database)
+    if ('requestIdleCallback' in window) {
+        // @ts-ignore
+        requestIdleCallback(() => window.renderMath())
+    } else {
+        // @ts-ignore
+        setTimeout(() => window.renderMath(), 100)
+    }
 
     const courseTags = [
         ...new Set(
@@ -56,6 +61,8 @@ export const DomandeEsamiCourse = ({ course }: Props) => {
         .filter(question => question.course === course)
         .filter(question => selectedTags.length === 0 || selectedTags.every(tag => question.tags.includes(tag)))
 
+    console.log('filteredQuestions', filteredQuestions)
+
     return (
         <>
             <div class="grid-center">
@@ -97,6 +104,7 @@ export const DomandeEsamiCourse = ({ course }: Props) => {
                 {filteredQuestions.length === 0 ? (
                     <div class="grid-center">
                         <em>No questions found</em>
+                        <button onClick={() => setSelectedTags([])}>Rimuovi i filtri</button>
                     </div>
                 ) : (
                     filteredQuestions.map(question => (
diff --git a/src/client/lib/debug-console.js b/src/client/lib/debug-console.js
new file mode 100644
index 0000000..82205a4
--- /dev/null
+++ b/src/client/lib/debug-console.js
@@ -0,0 +1,27 @@
+const $debugConsole = document.createElement('div')
+
+$debugConsole.style.position = 'fixed'
+$debugConsole.style.bottom = '0'
+$debugConsole.style.left = '0'
+$debugConsole.style.width = '100%'
+$debugConsole.style.height = '25vh'
+$debugConsole.style.backgroundColor = 'black'
+$debugConsole.style.color = 'white'
+$debugConsole.style.overflow = 'auto'
+$debugConsole.style.padding = '10px'
+$debugConsole.style.boxSizing = 'border-box'
+$debugConsole.style.fontFamily = 'monospace'
+$debugConsole.style.zIndex = '9999'
+$debugConsole.style.fontSize = '15px'
+$debugConsole.style.opacity = '0.8'
+
+document.body.appendChild($debugConsole)
+
+function logDebugConsole(...args) {
+    $debugConsole.innerHTML += args.join(' ') + '<br>'
+}
+
+console.error = logDebugConsole
+console.warn = logDebugConsole
+console.log = logDebugConsole
+console.debug = logDebugConsole
diff --git a/src/components/Header.astro b/src/components/Header.astro
index ea04268..922ed11 100644
--- a/src/components/Header.astro
+++ b/src/components/Header.astro
@@ -5,6 +5,7 @@ const links = [
     // { href: '/appunti', text: 'Appunti' },
     { href: '/notizie', text: 'Notizie' },
     { href: '/guide', text: 'Guide' },
+    { href: '/domande-esami', text: 'Domande Esami' },
     { href: '/storia', text: 'Storia' },
     // { href: '/login', text: 'Login' },
 ]
diff --git a/src/data/domande-esami.yaml b/src/data/domande-esami.yaml
index e849968..07e4b31 100644
--- a/src/data/domande-esami.yaml
+++ b/src/data/domande-esami.yaml
@@ -131,7 +131,7 @@ questions:
       - 2021
   - course: geometria-2
     content: |
-      Il gruppo $G$ delle rotazioni generato da quella di angolo $2\pi/7$ che agisce su $\mathbb R^2$. Calcolare il gruppo fondamentale di $\mathbb R^2/G$ e studiare il rivestimento dato dalla proiezione al quoziente di $\mathbb R^2\{0}$ su $\mathbb R^2\{0}/G$.
+      Il gruppo $G$ delle rotazioni generato da quella di angolo $2\pi/7$ che agisce su $\mathbb R^2$. Calcolare il gruppo fondamentale di $\mathbb R^2/G$ e studiare il rivestimento dato dalla proiezione al quoziente di $\mathbb R^2 \setminus {0}$ su $\mathbb R^2 \setminus {0}/G$.
     tags:
       - 2021
   - course: geometria-2
@@ -652,7 +652,7 @@ questions:
       - 2023
   - course: algebra-1
     content: |
-      Data un’estensione $L/K$ di grado $6$ e un primo $p$ di $K$, trovare tutti e soli i modi possibili in cui $p$ può fattorizzarsi in $L$, esibendo per ciascun modo un esempio.
+      Data un'estensione $\mathbb L / \mathbb K$ di grado $6$ e un primo $p$ di $\mathbb K$, trovare tutti e soli i modi possibili in cui $p$ può fattorizzarsi in $\mathbb L$, esibendo per ciascun modo un esempio.
     tags:
       - 2023
   - course: algebra-1
@@ -672,7 +672,7 @@ questions:
       - 2023
   - course: algebra-1
     content: |
-      Considera un’estensione di $\mathbb Q$ con gruppo di Galois $Z_2 \times Z_2$. E’ possibile che ramifichi esattamente un primo? $2$? $3$?
+      Considera un’estensione di $\mathbb Q$ con gruppo di Galois $\mathbb{Z}_2 \times \mathbb{Z}_2$. E’ possibile che ramifichi esattamente un primo? $2$? $3$?
     tags:
       - 2023
   - course: algebra-1
@@ -686,6 +686,71 @@ questions:
     tags:
       - 2023
 
+  # Domande 2021 da Fra
+
+  - course: algebra-1
+    content: |
+      Come si classificano gli ideali primi in $\mathbb Z[i]$ + fare una lista
+    tags:
+      - 2021
+  - course: algebra-1
+    content: |
+      Calcolare min n tale che $A_n$ (o $S_n$) contenga un gruppo di ordine $21$
+    tags:
+      - 2021
+  - course: algebra-1
+    content: |
+      Anelli speciali
+    tags:
+      - 2021
+  - course: algebra-1
+    content: |
+      $A_n$ è semplice quando... (per ogni $n>=5$) + classi di coniugio e elementi
+    tags:
+      - 2021
+  - course: algebra-1
+    content: |
+      Discorso generale sulle permutazioni + scrittura in cicli -> ogni permutazione si scrive in modo “unico” come prodotto di cicli disgiunti
+    tags:
+      - 2021
+  - course: algebra-1
+    content: |
+      Quante scritture diverse può avere un k ciclo?
+    tags:
+      - 2021
+  - course: algebra-1
+    content: |
+      Come posso dare una definizione più formale della decomposizione di cicli? Con un’azione da quale gruppo a quale gruppo?
+    tags:
+      - 2021
+  - course: algebra-1
+    content: |
+      Segno delle permutazioni
+    tags:
+      - 2021
+  - course: algebra-1
+    content: |
+      Teorema di Cayley -> caso in cui $G = S_3$ (chi è l’immagine? Dove va un ciclo $(1,2)$?)
+    tags:
+      - 2021
+  - course: algebra-1
+    content: |
+      Perché i sottogruppi normali corrispondono alle sottoestensioni normali
+    tags:
+      - 2021
+  - course: algebra-1
+    content: |
+      Esempio particolare
+    tags:
+      - 2021
+  - course: algebra-1
+    content: |
+      Elementi di Galois
+    tags:
+      - 2021
+
+  # Domande di Aritmetica da una raccolta di Luca Bruni
+
   - course: aritmetica
     content: |
       Un polinomio $p \in \mathbb{Z}[x]$ può essere riducibile o irriducibile. Lo stesso polinomio, preso con coefficienti in $\mathbb{Z}/p\mathbb{Z}[x]$ può essere riducibile o irriducibile. Che relazione c’è tra queste due cose?
@@ -737,7 +802,7 @@ questions:
     content: |
       Quanti sono i polinomi irriducibili di grado $n$ su $\mathbb{F}_p$? (Hint: può essere utile provare prima il caso dei polinomi di secondo grado. Hint: in alternativa si possono contare i polinomi riducibili.)
       Hint: Altrimenti dimostrate che 
-      $$\prod_{p(x) \text{ irriducibile}, \deg(p(x)) | n} p(x) = x^{p^n} - x.$$
+      $$\prod_{\mathclap{\substack{p(x) \text{irriducibile} \\ \deg(p(x)) | n}}} p(x) = x^{p^n} - x.$$
     tags:
       - 2015
 
@@ -852,6 +917,8 @@ questions:
     tags:
       - 2015
 
+  # Ricerca Operativa dal sito di Fra
+
   - course: ricerca-operativa
     content: |
       Definizione e caratterizzazione algebrica direzioni ammissibili e di crescita + considerazioni varie su Lemma di Farkas e la mutua esclusività dei due problemi.
@@ -1102,6 +1169,8 @@ questions:
     tags:
       - 2023
 
+  # Raccolta di Istituzioni di Geometria da Fra
+
   - course: istituzioni-di-geometria
     content: |
       Definizione di gruppo fondamentale e perché è un gruppo
@@ -1234,6 +1303,8 @@ questions:
     tags:
       - 2024
 
+  # Raccolta di ETI da Fra
+
   - course: eti
     content: |
       Dimostrare Cantor-Bernstein
@@ -1348,6 +1419,8 @@ questions:
     tags:
       - Tamas
 
+  # Raccolta di MR di Fra
+
   - course: meccanica-razionale
     content: |
       Equazioni di Eulero
@@ -1659,6 +1732,8 @@ questions:
     tags:
       - 2023
 
+  # Raccolta di Analisi 2
+
   - course: analisi-2
     content: |
       Dimostrazione del teorema di divergenza?
diff --git a/src/pages/domande-esami/[course].astro b/src/pages/domande-esami/[course].astro
index 65bc2b3..465368f 100644
--- a/src/pages/domande-esami/[course].astro
+++ b/src/pages/domande-esami/[course].astro
@@ -22,7 +22,7 @@ const { course } = Astro.params
 <BaseLayout title="Domande Esami | PHC" pageTags={'domande-esami'}>
     <Header />
     <main>
-        <DomandeEsamiCourse client:load course={course} />
+        <DomandeEsamiCourse client:only="preact" course={course} />
     </main>
     <Footer />
 </BaseLayout>
diff --git a/src/pages/domande-esami/index.astro b/src/pages/domande-esami/index.astro
index bcda123..70b5553 100644
--- a/src/pages/domande-esami/index.astro
+++ b/src/pages/domande-esami/index.astro
@@ -53,7 +53,10 @@ const courseQuestionCounts = Object.fromEntries(
         <h3>Come Contribuire</h3>
         <div class="card large">
             <div class="text">
-                <p>Se hai raccolte di domande da condividere, puoi...</p>
+                <p>
+                    Se hai raccolto delle domande da un orale, puoi inviarcele per email all'indirizzo
+                    <a href="mailto:macchinisti@lists.dm.unipi.it"> macchinisti@lists.dm.unipi.it</a>.
+                </p>
             </div>
         </div>
     </main>
diff --git a/src/styles/components.scss b/src/styles/components.scss
index c7fd776..a2e0034 100644
--- a/src/styles/components.scss
+++ b/src/styles/components.scss
@@ -604,7 +604,8 @@
         place-content: center;
         place-items: center;
 
-        background: #0003;
+        color: #111;
+        background: #0004;
 
         padding: 0 0.25rem;
         border-radius: 0.25rem;
@@ -619,7 +620,7 @@
         }
 
         &.disabled {
-            color: #0005;
+            color: #0004;
             background: #0002;
         }
     }
@@ -897,7 +898,7 @@
 
     .wide-card-list {
         display: grid;
-        grid-template-columns: repeat(auto-fit, minmax(auto, 30rem));
+        grid-template-columns: repeat(auto-fit, minmax(auto, 28rem));
         gap: 2rem;
         padding: 2rem;
 
diff --git a/src/styles/main.scss b/src/styles/main.scss
index 46ceb26..165d33c 100644
--- a/src/styles/main.scss
+++ b/src/styles/main.scss
@@ -122,6 +122,8 @@ body {
                 font-weight: 500;
                 letter-spacing: 1px;
                 color: #333;
+
+                padding: 0.25rem 1.325rem;
             }
 
             @media screen and (max-width: $screen-desktop-min) {

From fa564754f24110e5801bf5e0b307ed44b781df10 Mon Sep 17 00:00:00 2001
From: Antonio De Lucreziis <antonio.delucreziis@gmail.com>
Date: Sun, 9 Feb 2025 20:39:28 +0100
Subject: [PATCH 6/7] simplified tagging selection

---
 src/client/DomandeEsamiCourse.tsx | 59 +++++++++++++------------------
 1 file changed, 25 insertions(+), 34 deletions(-)

diff --git a/src/client/DomandeEsamiCourse.tsx b/src/client/DomandeEsamiCourse.tsx
index 09ea675..d61d1b6 100644
--- a/src/client/DomandeEsamiCourse.tsx
+++ b/src/client/DomandeEsamiCourse.tsx
@@ -19,8 +19,6 @@ import type { Database } from '@/data/domande-esami.yaml'
 const useRemoteValue = <T,>(url: string): T | null => {
     const [value, setValue] = useState<T | null>(null)
 
-    console.log('fetching', url, value)
-
     useEffect(() => {
         fetch(url)
             .then(response => response.json())
@@ -55,13 +53,11 @@ export const DomandeEsamiCourse = ({ course }: Props) => {
         ),
     ]
 
-    const [selectedTags, setSelectedTags] = useState<string[]>([])
+    const [selectedTag, setSelectedTag] = useState<string | null>(null)
 
     const filteredQuestions = database.questions
         .filter(question => question.course === course)
-        .filter(question => selectedTags.length === 0 || selectedTags.every(tag => question.tags.includes(tag)))
-
-    console.log('filteredQuestions', filteredQuestions)
+        .filter(question => (selectedTag ? question.tags.includes(selectedTag) : true))
 
     return (
         <>
@@ -72,39 +68,34 @@ export const DomandeEsamiCourse = ({ course }: Props) => {
                 <h1>{database.names[course]}</h1>
             </div>
 
-            <div class="card filter">
-                <div class="grid-h">
-                    <Funnel />
-                    <strong>Filtra Tag</strong>
-                </div>
-                <div class="flex-row-wrap">
-                    {selectedTags.length === 0
-                        ? courseTags.map(tag => (
-                              <div class="chip clickable" onClick={() => setSelectedTags([tag])}>
-                                  {tag}
-                              </div>
-                          ))
-                        : courseTags.map(tag => (
-                              <div
-                                  class={selectedTags.includes(tag) ? 'chip clickable' : 'chip clickable disabled'}
-                                  onClick={() =>
-                                      setSelectedTags(
-                                          selectedTags.includes(tag)
-                                              ? selectedTags.filter(t => t !== tag)
-                                              : [...selectedTags, tag],
-                                      )
-                                  }
-                              >
-                                  {tag}
-                              </div>
-                          ))}
+            {courseTags.length > 1 && (
+                <div class="card filter">
+                    <div class="grid-h">
+                        <Funnel />
+                        <strong>Filtra Tag</strong>
+                    </div>
+                    <div class="flex-row-wrap">
+                        {!selectedTag
+                            ? courseTags.map(tag => (
+                                  <div class="chip clickable" onClick={() => setSelectedTag(tag)}>
+                                      {tag}
+                                  </div>
+                              ))
+                            : courseTags.map(tag => (
+                                  <div
+                                      class={tag === selectedTag ? 'chip clickable' : 'chip clickable disabled'}
+                                      onClick={() => setSelectedTag(tag === selectedTag ? null : tag)}
+                                  >
+                                      {tag}
+                                  </div>
+                              ))}
+                    </div>
                 </div>
-            </div>
+            )}
             <div class="wide-card-list" id="questions">
                 {filteredQuestions.length === 0 ? (
                     <div class="grid-center">
                         <em>No questions found</em>
-                        <button onClick={() => setSelectedTags([])}>Rimuovi i filtri</button>
                     </div>
                 ) : (
                     filteredQuestions.map(question => (

From db083e20c24fd240900155f3986f79e410025ac8 Mon Sep 17 00:00:00 2001
From: Antonio De Lucreziis <antonio.delucreziis@gmail.com>
Date: Sun, 9 Feb 2025 20:54:15 +0100
Subject: [PATCH 7/7] updated questions and style

---
 src/data/domande-esami.yaml | 100 +++++++++---------------------------
 src/styles/pages.scss       |   6 +--
 2 files changed, 26 insertions(+), 80 deletions(-)

diff --git a/src/data/domande-esami.yaml b/src/data/domande-esami.yaml
index 07e4b31..10821fd 100644
--- a/src/data/domande-esami.yaml
+++ b/src/data/domande-esami.yaml
@@ -59,60 +59,6 @@ groups:
       - elementi-di-analisi-complessa
       - eti
 
-# Gruppo fondamentale dei proiettivi reali o complessi.
-# Compattezza in spazi metrici.
-# “Esercizio”: caratterizzare le funzioni intere olomorfe iniettive.
-
-# Domande 20/6/2022
-
-# Primo enunciato di Riemann-Weierstrass
-# • Calcolare il π1(S1). (∼= Z)
-# • Formula di Cauchy per funzioni olomorfe.
-# • π1(P^n(R)) (discorso generale).
-# • Come ottenere Pn(R) da Dn (dettagliata).
-# • Equazione di Cauchy-Riemann.
-# • Esempio di funzione continua differenziabile non olomorfa [ f(z) = \bar{z} ]
-# • Cos’è un punto singolare di una curva proiettiva.
-# • Conica singolare => degenere con K = C.
-# • il toro è omeomorfo al toro meno un punto?
-# • Chi è il rivestimento universale del toro?
-
-# Marzenta Giovanni:
-# Caratterizzazione dei rivestimenti regolari tramite il 1; un esempio di rivestimento regolare e uno di un rivestimento non regolare per il bouquet di due circonferenze.
-# Caratterizzare le funzioni olomorfe intere (da C in C) tali che |f(z)||z|d .
-
-# • X = [0; 1), topologia di base: (a; b), con a > 0, e [0; a)U(b; 1), con 0 < a < b < 1.
-# E più o meno fine della topologia Euclidea? Assiomi di topologia? Connesso? ` E`
-# compatto? Conosci un compatto famoso che ne è omeomorfo? (S1) Un esempio di tale
-# omeomorfismo? (t -> e^2πit).
-# • Gruppo fondamentale degli spazi proiettivi complessi
-
-# 21/6/2022
-
-# Che relazione c'è tra connessione e connessione per archi? Connesso per archi => Connesso
-# (dimostrazione) e Connesso non implica Connesso per archi (dimostrazione).
-# • Data f : U \{z0} → C, punti di singolarità? A riguardo, cosa succede a lim z→z0 |f(z)|?
-# Esempio di funzione con singolarità`a essenziale? [f(z) = e^(1/z) ]
-# Dimostrazione del secondo enunciato di Riemann-Weierstrass
-# • X topologico e Y sottoinsieme, se Y e compatto e chiuso, che relazioni ci sono tra compattezza e chiusura?
-# • Come calcolare Zeri e Poli di una funzione, eventualmente con molteplicità?
-# • Consideriamo la striscia in R2 tra le rette x = 0 e x = 1 comprese e quozientiamolo con la
-# relazione (0; y) ∼ (1; -y) . Come ti immagini questo quoziente? E una varietà topologica? `
-# Togliendo il segmento [0; 1], il quoziente è connesso per archi? Qual è il suo gruppo fondamentale? (Calcolarlo).
-# • Si può retrarre il nastro di Mobius sul suo bordo?
-# • Quanti punti di intersezione può avere al massimo una curva C = [F] in C con una retta?
-# • Come costruiresti uno spazio topologico con gruppo fondamentale Z/3?
-# • Prendiamo due triple di rette in P2(C), quando è possibile mandare le prime tre nelle seconde
-# tre?
-# • Definizione di Topologia Quoziente. Caratterizzazione degli aperti. Prendiamo X = R, x ∼
-# y sse x - y \in Q: la topologia quoziente si può descrivere facilmente... Chi sono gli aperti di
-# questa topologia quoziente? (Topologia indiscreta).
-# • Definizione di Rivestimento.
-# Condizione su E affinché qualunque rivestimento sia di grado finito.
-# • Teorema fondamentale dell’Algebra.
-# • Una cubica C = [p], può avere una retta tangente in due punti? Se invece ha grado 4?
-# • Teorema di Riemann-Weierstrass.
-
 questions:
   - course: geometria-2
     content: |
@@ -131,7 +77,7 @@ questions:
       - 2021
   - course: geometria-2
     content: |
-      Il gruppo $G$ delle rotazioni generato da quella di angolo $2\pi/7$ che agisce su $\mathbb R^2$. Calcolare il gruppo fondamentale di $\mathbb R^2/G$ e studiare il rivestimento dato dalla proiezione al quoziente di $\mathbb R^2 \setminus {0}$ su $\mathbb R^2 \setminus {0}/G$.
+      Il gruppo $G$ delle rotazioni generato da quella di angolo $2\pi/7$ che agisce su $\mathbb R^2$. Calcolare il gruppo fondamentale di $\mathbb R^2/G$ e studiare il rivestimento dato dalla proiezione al quoziente di $\mathbb R^2 \setminus \{0\}$ su $\mathbb R^2 \setminus \{0\}/G$.
     tags:
       - 2021
   - course: geometria-2
@@ -216,7 +162,7 @@ questions:
       - 2021
   - course: geometria-2
     content: |
-      Archi $\implies$ connesso
+      Archi $\Rightarrow$ connesso
     tags:
       - 2021
   - course: geometria-2
@@ -226,7 +172,7 @@ questions:
       - 2021
   - course: geometria-2
     content: |
-      Olomorfa $\implies$ analitica
+      Olomorfa $\Rightarrow$ analitica
     tags:
       - 2021
   - course: geometria-2
@@ -236,12 +182,12 @@ questions:
       - 2021
   - course: geometria-2
     content: |
-      Sottospazio compatto $\implies$ chiuso. Quando e perché. Controesempio se $X$ non è $T_2$.
+      Sottospazio compatto $\Rightarrow$ chiuso. Quando e perché. Controesempio se $X$ non è $T_2$.
     tags:
       - 2021
   - course: geometria-2
     content: |
-      Metrico compatto $\implies$ limitato. Controesempio a metrico completo limitato $\implies$ compatto
+      Metrico compatto $\Rightarrow$ limitato. Controesempio a metrico completo limitato $\Rightarrow$ compatto
     tags:
       - 2021
   - course: geometria-2
@@ -256,12 +202,12 @@ questions:
       - 2021
   - course: geometria-2
     content: |
-      Compattezza in spazi metrici. Compatto per successioni $\implies$ completo e totalmente limitato (Implicazione a scelta).
+      Compattezza in spazi metrici. Compatto per successioni $\Rightarrow$ completo e totalmente limitato (Implicazione a scelta).
     tags:
       - 2021
   - course: geometria-2
     content: |
-      Definizione di funzione analitica e criteri per stabilire se è identicamente nulla su un aperto connesso. Derivate nulle in un punto $\implies$ identicamente nulla nell'aperto connesso.
+      Definizione di funzione analitica e criteri per stabilire se è identicamente nulla su un aperto connesso. Derivate nulle in un punto $\Rightarrow$ identicamente nulla nell'aperto connesso.
     tags:
       - 2021
   - course: geometria-2
@@ -326,12 +272,12 @@ questions:
       - 2021
   - course: geometria-2
     content: |
-      $Y$ connesso. $Y \subseteq Z \subseteq \bar{Y} \implies Z$ connesso
+      $Y$ connesso. $Y \subseteq Z \subseteq \overline{Y} \Rightarrow Z$ connesso
     tags:
       - 2021
   - course: geometria-2
     content: |
-      Determinare chiusura dell'insieme $\{0\} \times [0,1] \cap \mathbb Q$ in $\mathbb R^2$, e di $\{0\} \times ]0,1[ \cap \mathbb Q$ in $\mathbb R^2$, chi sono i bordi in $\mathbb R^2$ di questi insiemi?
+      Determinare chiusura dell'insieme $\{0\} \times [0,1] \cap \mathbb Q$ in $\mathbb R^2$, e di $\{0\} \times \,]0,1[ \,\cap\, \mathbb Q$ in $\mathbb R^2$, chi sono i bordi in $\mathbb R^2$ di questi insiemi?
     tags:
       - 2021
   - course: geometria-2
@@ -351,7 +297,7 @@ questions:
       - 2021
   - course: geometria-2
     content: |
-      Contraibile $\implies$ semplicemente connesso
+      Contraibile $\Rightarrow$ semplicemente connesso
     tags:
       - 2021
   - course: geometria-2
@@ -386,7 +332,7 @@ questions:
       - 2021
   - course: geometria-2
     content: |
-      Olomorfa $\implies$ Analitica
+      Olomorfa $\Rightarrow$ Analitica
     tags:
       - 2021
   - course: geometria-2
@@ -461,7 +407,7 @@ questions:
       - 2021
   - course: geometria-2
     content: |
-      Olomorfa $\iff$ analitica
+      Olomorfa $\Leftrightarrow$ analitica
     tags:
       - 2021
   - course: geometria-2
@@ -481,12 +427,12 @@ questions:
       - 2021
   - course: geometria-2
     content: |
-      $f(z)dz$ chiusa $\iff$ $f$ olomorfa
+      $f(z)\,\mathrm d z$ chiusa $\Leftrightarrow$ $f$ olomorfa
     tags:
       - 2021
   - course: geometria-2
     content: |
-      Per quali "a" complessi esiste $f:\mathbb C^* \to \mathbb C$ olomorfa non identicamente nulla con $f'(z) = a*f(z)/z$?
+      Per quali "a" complessi esiste $f:\mathbb C^\times \to \mathbb C$ olomorfa non identicamente nulla con $f'(z) = a*f(z)/z$?
     tags:
       - 2021
   - course: geometria-2
@@ -501,7 +447,7 @@ questions:
       - 2021
   - course: geometria-2
     content: |
-      Per un rivestimento dallo spazio $E$ connesso e localmente connesso per archi: gruppo degli automorfismi transitivo su una fibra $\iff$ l'immersione del $p_1(E)$ è normale
+      Per un rivestimento dallo spazio $E$ connesso e localmente connesso per archi: gruppo degli automorfismi transitivo su una fibra $\Leftrightarrow$ l'immersione del $p_1(E)$ è normale
     tags:
       - 2021
   - course: geometria-2
@@ -511,7 +457,7 @@ questions:
       - 2021
   - course: geometria-2
     content: |
-      Gruppo fondamentale di $P_n(\mathbb C)$
+      Gruppo fondamentale di $\mathbb P^n(\mathbb C)$
     tags:
       - 2021
   - course: geometria-2
@@ -546,7 +492,7 @@ questions:
       - 2021
   - course: geometria-2
     content: |
-      $f$ olomorfa in $U\{z}$ e limitata in un intorno di $z$, cosa possiamo dire?
+      $f$ olomorfa in $U \setminus \{z\}$ e limitata in un intorno di $z$, cosa possiamo dire?
     tags:
       - 2021
   - course: geometria-2
@@ -586,7 +532,7 @@ questions:
       - 2021
   - course: geometria-2
     content: |
-      Quanti asintoti può avere al massimo una curva di $P^2(\mathbb C)$?
+      Quanti asintoti può avere al massimo una curva di $\mathbb P^2(\mathbb C)$?
     tags:
       - 2021
   - course: geometria-2
@@ -596,7 +542,7 @@ questions:
       - 2021
   - course: geometria-2
     content: |
-      Dato $S^1$ e $S^1$ ed il suo $\pi_1$ generato da $a,b$, trova il rivestimento associato ai sottogruppi $<a>$ e $N(<a>)$ (con quest'ultimo si intende il sottogruppo normale generato da $a$)
+      Dato $S^1$ e $S^1$ ed il suo $\pi_1$ generato da $a,b$, trova il rivestimento associato ai sottogruppi $\langle a \rangle$ e $N(\langle a \rangle)$ (con quest'ultimo si intende il sottogruppo normale generato da $a$)
     tags:
       - 2021
   - course: geometria-2
@@ -621,7 +567,7 @@ questions:
       - 2021
   - course: geometria-2
     content: |
-      Studiare $f$ olomorfa tale che $|f(z)|<k|z|^d$
+      Studiare $f$ olomorfa tale che $|f(z)| \lt k|z|^d$.
     tags:
       - 2021
   - course: geometria-2
@@ -1294,7 +1240,7 @@ questions:
       - 2024
   - course: istituzioni-di-geometria
     content: |
-      compatta $\implies$ geodeticamente completa
+      compatta $\Rightarrow$ geodeticamente completa
     tags:
       - 2024
   - course: istituzioni-di-geometria
@@ -1327,7 +1273,7 @@ questions:
       - Mamino
   - course: eti
     content: |
-      AC $\implies$ Lemma di Zorn
+      AC $\Rightarrow$ Lemma di Zorn
     tags:
       - Mamino
   - course: eti
@@ -1387,7 +1333,7 @@ questions:
       - Mamino
   - course: eti
     content: |
-      Definire i $V_{\alpha}$, che cardinalità hanno, e punti fissi dell'associazione $\alpha \implies |V_{\alpha}|$, mostrare che i punti fissi sono una classe, l'$(\omega+1)$-esimo punto fisso che cofinalità ha, esistono punti fissi non regolari
+      Definire i $V_{\alpha}$, che cardinalità hanno, e punti fissi dell'associazione $\alpha \Rightarrow |V_{\alpha}|$, mostrare che i punti fissi sono una classe, l'$(\omega+1)$-esimo punto fisso che cofinalità ha, esistono punti fissi non regolari
     tags:
       - Mamino
 
diff --git a/src/styles/pages.scss b/src/styles/pages.scss
index b83e059..605b601 100644
--- a/src/styles/pages.scss
+++ b/src/styles/pages.scss
@@ -438,8 +438,8 @@
     }
 
     .domande-esami {
-        background: hsl(45, 100%, 95%);
-        --card-base: hsl(45, 100%, 80%);
+        background: hsl(180, 100%, 95%);
+        --card-base: hsl(180, 100%, 85%);
 
         main {
             justify-self: center;
@@ -457,7 +457,7 @@
             }
 
             button {
-                background: hsl(45, 100%, 72%);
+                background: hsl(180, 100%, 72%);
             }
 
             .card a {