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| 14-18 | Linköping | 2024-07-23 - 2024-08-12 | * Allra senaste nytt VT2024 <<allra-senaste-nytt>> +** 2024-06-01 +[[file:exams/2024/tenta-TATA54-20240601-losning.pdf][Lösningar]] till [[file:exams/2024/tenta-TATA54-20240601.pdf][dagens tenta]] finns nu att beskÃ¥da. Jag hoppas kunna rätta tentorna till pÃ¥ fredag nästa vecka. ** 2024-05-18 Ã…terstÃ¥ende lektion är inställd. Läs kursboken om Gaussiska heltal och summor av tvÃ¥ kvadrater, titta pÃ¥ föreläsningsanteckningarna om [[file:lectures/swelecture11.pdf][Gaussiska heltal]] @@ -407,6 +409,7 @@ De svenska versionerna är nyare. NÃ¥gra av föreläsningarna tar tvÃ¥ tillfäll | Datum | Examinator | Tentamen | Lösningar | |------------+-----------------+---------------------------+-----------------------------| +| 2024-06-01 | Jan Snellman | [[file:exams/2024/tenta-TATA54-20240601.pdf][TATA5420240601]] | [[file:exams/2024/tenta-TATA54-20240601-losning.pdf][TATA5420240601losn]] | | 2023-08-17 | Jan Snellman | [[file:exams/2023/tenta-TATA54-20230817.pdf][TATA5420230817]] | [[file:exams/2023/tenta-TATA54-20230817soln.pdf][TATA5420230817soln]] | | 2023-06-03 | Jan Snellman | [[file:exams/2023/tenta-TATA54-20230603.pdf][TATA5420230603]] | [[file:exams/2023/tenta-TATA54-20230603losn.pdf][TATA5420230603losn]] | | 2022-08-18 | Jan Snellman | [[file:exams/2022/tenta-TATA54-20220818.pdf][TATA5420220818]] | lösning saknas | diff --git a/homepage/sitemap.org b/homepage/sitemap.org index aa4e7f7..6e844cc 100644 --- a/homepage/sitemap.org +++ b/homepage/sitemap.org @@ -2,8 +2,6 @@ - [[file:newlectures/newlecture.org][Föreläsningar i Talteori]] - [[file:newlectures/new-lect-0.org][Talteori översiktsföreläsning]] -- [[file:lectures/Henselfaktorisering.org][Henselfaktorisering]] -- [[file:senaste-nytt.org][senaste-nytt]] - [[file:labs/lecture5.org][lecture5]] - [[file:labs/lecture4.org][lecture4]] - [[file:labs/lecture3.org][lecture3]] @@ -11,5 +9,7 @@ - [[file:labs/lecture1.org][lecture1]] - [[file:labs/lecture0.org][lecture0]] - [[file:index.org][TATA54 Talteori]] +- [[file:senaste-nytt.org][senaste-nytt]] - [[file:labs/kedjebraklab.org][Sagemath-övningar pÃ¥ kedjebrÃ¥k]] -- [[file:labs/HenselLyftLabHT2023.org][SageMath-övningar pÃ¥ Hensellyft, primitiva rötter, och KRS]] \ No newline at end of file +- [[file:labs/HenselLyftLabHT2023.org][SageMath-övningar pÃ¥ Hensellyft, primitiva rötter, och KRS]] +- [[file:lectures/Henselfaktorisering.org][Henselfaktorisering]] \ No newline at end of file diff --git a/public/exams/2024/tenta-TATA54-20240601-losning.pdf 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Talteori</title> @@ -63,148 +63,149 @@ <h2>Innehåll</h2> <div id="text-table-of-contents" role="doc-toc"> <ul> -<li><a href="#org8cf611f">Kurshemsida för TATA54, Talteori </a> +<li><a href="#org11cd8e4">Kurshemsida för TATA54, Talteori </a> <ul> -<li><a href="#orgd386ff5">ÄmnesomrÃ¥de</a></li> -<li><a href="#org5fa7c84">Poäng</a></li> -<li><a href="#org1941399">Examinator</a></li> -<li><a href="#orgd6f97a6">Schema</a></li> -<li><a href="#orgcbec67a">Examination</a></li> +<li><a href="#orgbf145e8">ÄmnesomrÃ¥de</a></li> +<li><a href="#orgbd10c80">Poäng</a></li> +<li><a href="#orgdf916de">Examinator</a></li> +<li><a href="#org0e97f91">Schema</a></li> +<li><a href="#org978acab">Examination</a></li> </ul> </li> -<li><a href="#orgda7b5cb">Allra senaste nytt VT2024 </a> +<li><a href="#orgc6ffe16">Allra senaste nytt VT2024 </a> <ul> -<li><a href="#orgb795cef">2024-05-18</a></li> -<li><a href="#orgef16020">2024-05-16</a></li> -<li><a href="#orgd3edf39">2024-05-13</a></li> -<li><a href="#orgbb2c19c">2024-05-06</a></li> -<li><a href="#org6916c72">2024-04-29</a></li> -<li><a href="#org2fc933f">2024-04-23</a></li> -<li><a href="#org0e96bfa">2024-04-22</a></li> -<li><a href="#org796ce06">2024-04-14</a> +<li><a href="#orgba4c7fd">2024-06-01</a></li> +<li><a href="#org2921027">2024-05-18</a></li> +<li><a href="#org580c3f6">2024-05-16</a></li> +<li><a href="#orgfb06446">2024-05-13</a></li> +<li><a href="#org36a5a6c">2024-05-06</a></li> +<li><a href="#orge2800f4">2024-04-29</a></li> +<li><a href="#org8296c85">2024-04-23</a></li> +<li><a href="#orgc936b6f">2024-04-22</a></li> +<li><a href="#org4dc177a">2024-04-14</a> <ul> -<li><a href="#org43f6ac2">Uppgifter att räkna till nästa gÃ¥ng</a></li> -<li><a href="#org87e8642">Datorlaboration</a></li> +<li><a href="#org55f3eec">Uppgifter att räkna till nästa gÃ¥ng</a></li> +<li><a href="#orgbc6c0fd">Datorlaboration</a></li> </ul> </li> -<li><a href="#orgff00c35">2024-04-07</a> +<li><a href="#org865cc31">2024-04-07</a> <ul> -<li><a href="#org1198084">Uppgifter att räkna till nästa gÃ¥ng</a></li> -<li><a href="#orgcb6d72a">Beviset för kvadratisk reciprocitet</a></li> +<li><a href="#org0f556e1">Uppgifter att räkna till nästa gÃ¥ng</a></li> +<li><a href="#org9f5a134">Beviset för kvadratisk reciprocitet</a></li> </ul> </li> -<li><a href="#org84ac4df">2024-04-02</a></li> -<li><a href="#orgecb5391">2024-03-11</a></li> -<li><a href="#orged53d50">2024-03-06</a></li> -<li><a href="#org69c699e">2024-03-05</a></li> -<li><a href="#org8b45b59">2024-02-29</a></li> -<li><a href="#org6ee578d">2024-02-20</a></li> -<li><a href="#org15914f2">2024-02-12</a></li> -<li><a href="#org445fa32">2024-02-07</a></li> -<li><a href="#org887cf9c">2024-01-30</a> +<li><a href="#org429e5d4">2024-04-02</a></li> +<li><a href="#orgfa53138">2024-03-11</a></li> +<li><a href="#org54eab67">2024-03-06</a></li> +<li><a href="#org73f95a7">2024-03-05</a></li> +<li><a href="#orgf0c9193">2024-02-29</a></li> +<li><a href="#org7f7d557">2024-02-20</a></li> +<li><a href="#org6fc379e">2024-02-12</a></li> +<li><a href="#org7b22a27">2024-02-07</a></li> +<li><a href="#orgbc98f91">2024-01-30</a> <ul> -<li><a href="#orge760dad">Tvillingfria primtal</a></li> +<li><a href="#org7ada8fb">Tvillingfria primtal</a></li> </ul> </li> -<li><a href="#org488e68b">2024-01-23</a></li> -<li><a href="#org96d1546">2024-01-16</a></li> +<li><a href="#org5081bbc">2024-01-23</a></li> +<li><a href="#orgec17e4b">2024-01-16</a></li> </ul> </li> -<li><a href="#org7fb0ecc">Kurslitteratur </a> +<li><a href="#org83cdbc2">Kurslitteratur </a> <ul> -<li><a href="#org1046eac">Kursbok</a></li> -<li><a href="#orgb1f71c0">Bredvidläsning</a> +<li><a href="#org969d2a9">Kursbok</a></li> +<li><a href="#orgfa4a7ab">Bredvidläsning</a> <ul> -<li><a href="#org1304ec9">Fritt tillgängligt material</a></li> -<li><a href="#org156f528">Andra lämpliga böcker</a></li> +<li><a href="#orge4da471">Fritt tillgängligt material</a></li> +<li><a href="#org2169300">Andra lämpliga böcker</a></li> </ul> </li> </ul> </li> -<li><a href="#org777e787">KursinnehÃ¥ll </a> +<li><a href="#orgc6c0ef4">KursinnehÃ¥ll </a> <ul> -<li><a href="#org8bd2546">Avsnitt av kursboken</a> +<li><a href="#org43c7b85">Avsnitt av kursboken</a> <ul> -<li><a href="#org5c92b21">Rekommenderade uppgifter </a></li> +<li><a href="#org0c49604">Rekommenderade uppgifter </a></li> </ul> </li> -<li><a href="#orgf97dd5f">Kort beskrivning av kursinnehÃ¥llet</a></li> +<li><a href="#org33f6268">Kort beskrivning av kursinnehÃ¥llet</a></li> </ul> </li> -<li><a href="#orgb1afa66">Föreläsningar </a></li> -<li><a href="#orgd9a1a3d">Tentor </a></li> -<li><a href="#orgaa8bfe8">Datorlaborationer </a> +<li><a href="#org0e51919">Föreläsningar </a></li> +<li><a href="#orgf5fd67d">Tentor </a></li> +<li><a href="#orgac41624">Datorlaborationer </a> <ul> -<li><a href="#org0e9470f">SageMath</a></li> -<li><a href="#org4e01f4d">Kod frÃ¥n vissa föreläsningar</a></li> -<li><a href="#org771ae33">Laborationer</a> +<li><a href="#orgd0ccf06">SageMath</a></li> +<li><a href="#orgd3b0180">Kod frÃ¥n vissa föreläsningar</a></li> +<li><a href="#org85c34f4">Laborationer</a> <ul> -<li><a href="#orge16b88e">Hensellyft, Primitiva rötter, Kinesiska restsatsen</a></li> -<li><a href="#org254ad94">KedjebrÃ¥k</a></li> +<li><a href="#orga1be7da">Hensellyft, Primitiva rötter, Kinesiska restsatsen</a></li> +<li><a href="#org2528f16">KedjebrÃ¥k</a></li> </ul> </li> </ul> </li> -<li><a href="#orgcab2c84">Tidigare Ã¥r </a> +<li><a href="#org27d49bb">Tidigare Ã¥r </a> <ul> -<li><a href="#org5db15ec">TATA54 Anteckningar frÃ¥n tidigare Ã¥r</a> +<li><a href="#orga1fa650">TATA54 Anteckningar frÃ¥n tidigare Ã¥r</a> <ul> -<li><a href="#org2e74361">2023</a></li> -<li><a href="#org39f254e">2021</a></li> -<li><a href="#orgab915cd">2020</a></li> -<li><a href="#org51934a3">2019</a></li> -<li><a href="#org51909e4">2018</a></li> -<li><a href="#org50057cb">2017</a></li> +<li><a href="#orgd4aaf8a">2023</a></li> +<li><a href="#orgc39991d">2021</a></li> +<li><a href="#org6bff760">2020</a></li> +<li><a href="#org85cd779">2019</a></li> +<li><a href="#org21f5089">2018</a></li> +<li><a href="#org7ce4987">2017</a></li> </ul> </li> </ul> </li> -<li><a href="#org27e935f">Index</a></li> +<li><a href="#orga44ea53">Index</a></li> </ul> </div> </nav> -<section id="outline-container-org8cf611f" class="outline-2"> -<h2 id="org8cf611f">Kurshemsida för TATA54, Talteori <a id="org744b74f"></a></h2> -<div class="outline-text-2" id="text-org8cf611f"> +<section id="outline-container-org11cd8e4" class="outline-2"> +<h2 id="org11cd8e4">Kurshemsida för TATA54, Talteori <a id="orgebfa722"></a></h2> +<div class="outline-text-2" id="text-org11cd8e4"> </div> -<div id="outline-container-orgd386ff5" class="outline-3"> -<h3 id="orgd386ff5">ÄmnesomrÃ¥de</h3> -<div class="outline-text-3" id="text-orgd386ff5"> +<div id="outline-container-orgbf145e8" class="outline-3"> +<h3 id="orgbf145e8">ÄmnesomrÃ¥de</h3> +<div class="outline-text-3" id="text-orgbf145e8"> <p> Matematik </p> </div> </div> -<div id="outline-container-org5fa7c84" class="outline-3"> -<h3 id="org5fa7c84">Poäng</h3> -<div class="outline-text-3" id="text-org5fa7c84"> +<div id="outline-container-orgbd10c80" class="outline-3"> +<h3 id="orgbd10c80">Poäng</h3> +<div class="outline-text-3" id="text-orgbd10c80"> <p> 6 hp </p> </div> </div> -<div id="outline-container-org1941399" class="outline-3"> -<h3 id="org1941399">Examinator</h3> -<div class="outline-text-3" id="text-org1941399"> +<div id="outline-container-orgdf916de" class="outline-3"> +<h3 id="orgdf916de">Examinator</h3> +<div class="outline-text-3" id="text-orgdf916de"> <p> <a href="https://liu.se/medarbetare/jansn19">Jan Snellman</a> (se även min <a href="https://jansn19.gitlab-pages.liu.se/jan-snellman-hemsida/">hemsida</a>) </p> </div> </div> -<div id="outline-container-orgd6f97a6" class="outline-3"> -<h3 id="orgd6f97a6">Schema</h3> -<div class="outline-text-3" id="text-orgd6f97a6"> +<div id="outline-container-org0e97f91" class="outline-3"> +<h3 id="org0e97f91">Schema</h3> +<div class="outline-text-3" id="text-org0e97f91"> <p> Se <a href="https://cloud.timeedit.net/liu/web/schema/ri167XQQ538Z50Qm07065gZ6y2Y7306Q6Y43Y1.html">TimeEdit</a> </p> </div> </div> -<div id="outline-container-orgcbec67a" class="outline-3"> -<h3 id="orgcbec67a">Examination</h3> -<div class="outline-text-3" id="text-orgcbec67a"> +<div id="outline-container-org978acab" class="outline-3"> +<h3 id="org978acab">Examination</h3> +<div class="outline-text-3" id="text-org978acab"> <p> Skriftlig tentamen. </p> @@ -258,13 +259,21 @@ Skriftlig tentamen. </div> </section> -<section id="outline-container-orgda7b5cb" class="outline-2"> -<h2 id="orgda7b5cb">Allra senaste nytt VT2024 <a id="org53d52c1"></a></h2> -<div class="outline-text-2" id="text-orgda7b5cb"> +<section id="outline-container-orgc6ffe16" class="outline-2"> +<h2 id="orgc6ffe16">Allra senaste nytt VT2024 <a id="orgba15c0d"></a></h2> +<div class="outline-text-2" id="text-orgc6ffe16"> </div> -<div id="outline-container-orgb795cef" class="outline-3"> -<h3 id="orgb795cef">2024-05-18</h3> -<div class="outline-text-3" id="text-orgb795cef"> +<div id="outline-container-orgba4c7fd" class="outline-3"> +<h3 id="orgba4c7fd">2024-06-01</h3> +<div class="outline-text-3" id="text-orgba4c7fd"> +<p> +<a href="exams/2024/tenta-TATA54-20240601-losning.pdf">Lösningar</a> till <a href="exams/2024/tenta-TATA54-20240601.pdf">dagens tenta</a> finns nu att beskÃ¥da. Jag hoppas kunna rätta tentorna till pÃ¥ fredag nästa vecka. +</p> +</div> +</div> +<div id="outline-container-org2921027" class="outline-3"> +<h3 id="org2921027">2024-05-18</h3> +<div class="outline-text-3" id="text-org2921027"> <p> Ã…terstÃ¥ende lektion är inställd. Läs kursboken om Gaussiska heltal och summor av tvÃ¥ kvadrater, titta pÃ¥ föreläsningsanteckningarna om <a href="lectures/swelecture11.pdf">Gaussiska heltal</a> @@ -275,13 +284,13 @@ ingÃ¥r i kursen, som kongruenser modulo Gaussiska heltal. <p> Jag pÃ¥minner om att kursens innehÃ¥ll är specificerad som en lista av kapitel i -Rosen, finns <a href="#orgd3a32bb">längre ned pÃ¥ denna sida</a>. +Rosen, finns <a href="#org06fee11">längre ned pÃ¥ denna sida</a>. </p> </div> </div> -<div id="outline-container-orgef16020" class="outline-3"> -<h3 id="orgef16020">2024-05-16</h3> -<div class="outline-text-3" id="text-orgef16020"> +<div id="outline-container-org580c3f6" class="outline-3"> +<h3 id="org580c3f6">2024-05-16</h3> +<div class="outline-text-3" id="text-org580c3f6"> <p> Jag är inlagd pÃ¥ sjukhus… Det är väl osäkert om det gÃ¥r att hitta vikarier till lektionerna i morgon och pÃ¥ mÃ¥ndag. FrÃ¥ga nÃ¥gon av studierektorerna, eller proprefekt Jesper Thoren. @@ -292,35 +301,35 @@ Tentamen skall kunna bli av utan problem! </p> </div> </div> -<div id="outline-container-orgd3edf39" class="outline-3"> -<h3 id="orgd3edf39">2024-05-13</h3> -<div class="outline-text-3" id="text-orgd3edf39"> +<div id="outline-container-orgfb06446" class="outline-3"> +<h3 id="orgfb06446">2024-05-13</h3> +<div class="outline-text-3" id="text-orgfb06446"> <p> Till pÃ¥ fredag sÃ¥ tittar vi pÃ¥ 13.4.3abc, 13.4.5, 13.4.11. Till sista lektionen (mÃ¥ndag 20 maj) sÃ¥ tittar vi pÃ¥ 14.1.17ab, 14.1.23. </p> </div> </div> -<div id="outline-container-orgbb2c19c" class="outline-3"> -<h3 id="orgbb2c19c">2024-05-06</h3> -<div class="outline-text-3" id="text-orgbb2c19c"> +<div id="outline-container-org36a5a6c" class="outline-3"> +<h3 id="org36a5a6c">2024-05-06</h3> +<div class="outline-text-3" id="text-org36a5a6c"> <p> Till nästa gÃ¥ng sÃ¥ tittar vi pÃ¥ 13.1.15, 13.3.1.b, 13.3.2g, 13.3.6, 13.3.8. </p> </div> </div> -<div id="outline-container-org6916c72" class="outline-3"> -<h3 id="org6916c72">2024-04-29</h3> -<div class="outline-text-3" id="text-org6916c72"> +<div id="outline-container-orge2800f4" class="outline-3"> +<h3 id="orge2800f4">2024-04-29</h3> +<div class="outline-text-3" id="text-orge2800f4"> <p> Till nästa gÃ¥ng sÃ¥ tittar vi pÃ¥ 12.4.3b, 12.4.8, 13.1.2, 13.1.3. </p> </div> </div> -<div id="outline-container-org2fc933f" class="outline-3"> -<h3 id="org2fc933f">2024-04-23</h3> -<div class="outline-text-3" id="text-org2fc933f"> +<div id="outline-container-org8296c85" class="outline-3"> +<h3 id="org8296c85">2024-04-23</h3> +<div class="outline-text-3" id="text-org8296c85"> <p> Jag pratade om ”Eulers regel” som uttrycker kedjebrÃ¥kskonvergenterna q<sub>n</sub>/p<sub>n</sub> till [x<sub>0</sub>;x<sub>1,x</sub><sub>2,…</sub>] som rationella funktioner i @@ -333,9 +342,9 @@ beskrivningen kan visas med induktion. </p> </div> </div> -<div id="outline-container-org0e96bfa" class="outline-3"> -<h3 id="org0e96bfa">2024-04-22</h3> -<div class="outline-text-3" id="text-org0e96bfa"> +<div id="outline-container-orgc936b6f" class="outline-3"> +<h3 id="orgc936b6f">2024-04-22</h3> +<div class="outline-text-3" id="text-orgc936b6f"> <p> Vi har tvÃ¥ föreläsningar den kommande veckan, torsdag 24 april samt fredag 25 april. Till pÃ¥ torsdag tittar ni pÃ¥ 12.3.1c, 12.2.2a (nedskalad till första 4), 12.3.4 (nedskalat till första 5, approximationsfel < 1/100). @@ -343,21 +352,21 @@ Till pÃ¥ fredag 12.4.5b, 12.4.6b </p> </div> </div> -<div id="outline-container-org796ce06" class="outline-3"> -<h3 id="org796ce06">2024-04-14</h3> -<div class="outline-text-3" id="text-org796ce06"> +<div id="outline-container-org4dc177a" class="outline-3"> +<h3 id="org4dc177a">2024-04-14</h3> +<div class="outline-text-3" id="text-org4dc177a"> </div> -<div id="outline-container-org43f6ac2" class="outline-4"> -<h4 id="org43f6ac2">Uppgifter att räkna till nästa gÃ¥ng</h4> -<div class="outline-text-4" id="text-org43f6ac2"> +<div id="outline-container-org55f3eec" class="outline-4"> +<h4 id="org55f3eec">Uppgifter att räkna till nästa gÃ¥ng</h4> +<div class="outline-text-4" id="text-org55f3eec"> <p> 12.2.1bf, 12.2.2cd, 12.2.3c, 12.2.11 </p> </div> </div> -<div id="outline-container-org87e8642" class="outline-4"> -<h4 id="org87e8642">Datorlaboration</h4> -<div class="outline-text-4" id="text-org87e8642"> +<div id="outline-container-orgbc6c0fd" class="outline-4"> +<h4 id="orgbc6c0fd">Datorlaboration</h4> +<div class="outline-text-4" id="text-orgbc6c0fd"> <p> Titta pÃ¥ <a href="labs/kedjebraklabweb.html">kedjebrÃ¥kslabben</a> och använd den för att göra 12.2.3df. Hitta en formel för a(k,m) = [k;k,…,k] (längd m). Vad är @@ -366,21 +375,21 @@ gränsvärdet av a(k,m) dÃ¥ m gÃ¥r mot oändligheten? </div> </div> </div> -<div id="outline-container-orgff00c35" class="outline-3"> -<h3 id="orgff00c35">2024-04-07</h3> -<div class="outline-text-3" id="text-orgff00c35"> +<div id="outline-container-org865cc31" class="outline-3"> +<h3 id="org865cc31">2024-04-07</h3> +<div class="outline-text-3" id="text-org865cc31"> </div> -<div id="outline-container-org1198084" class="outline-4"> -<h4 id="org1198084">Uppgifter att räkna till nästa gÃ¥ng</h4> -<div class="outline-text-4" id="text-org1198084"> +<div id="outline-container-org0f556e1" class="outline-4"> +<h4 id="org0f556e1">Uppgifter att räkna till nästa gÃ¥ng</h4> +<div class="outline-text-4" id="text-org0f556e1"> <p> 11.1.1d, 11.1.4, 11.1.25ab, 11.2.1cd, 11.2.2, 11.2.3,11.2.4 </p> </div> </div> -<div id="outline-container-orgcb6d72a" class="outline-4"> -<h4 id="orgcb6d72a">Beviset för kvadratisk reciprocitet</h4> -<div class="outline-text-4" id="text-orgcb6d72a"> +<div id="outline-container-org9f5a134" class="outline-4"> +<h4 id="org9f5a134">Beviset för kvadratisk reciprocitet</h4> +<div class="outline-text-4" id="text-org9f5a134"> <p> Jag stakade mig lite vid bevist för kvadratisk reciprocitet. Speciellt sÃ¥ oroade jag mig över om det kunde finnas gitterpunkter (x,y) med x=(p-1)/2, (q-1)/2 < y <= (q/p)x. @@ -389,17 +398,17 @@ Men det är enkelt att visa att (p-1)/2*q < (q-1)2 +1, sÃ¥ det gÃ¥r inte. Bev </div> </div> </div> -<div id="outline-container-org84ac4df" class="outline-3"> -<h3 id="org84ac4df">2024-04-02</h3> -<div class="outline-text-3" id="text-org84ac4df"> +<div id="outline-container-org429e5d4" class="outline-3"> +<h3 id="org429e5d4">2024-04-02</h3> +<div class="outline-text-3" id="text-org429e5d4"> <p> PÃ¥ fredag sÃ¥ räknar vi de uppgifter om diskreta logaritmer vi inte hann med förra gÃ¥ngen. </p> </div> </div> -<div id="outline-container-orgecb5391" class="outline-3"> -<h3 id="orgecb5391">2024-03-11</h3> -<div class="outline-text-3" id="text-orgecb5391"> +<div id="outline-container-orgfa53138" class="outline-3"> +<h3 id="orgfa53138">2024-03-11</h3> +<div class="outline-text-3" id="text-orgfa53138"> <p> Jag har nu bokat om föreläsningarna till Fredagar kl 13-15 (fortfarande i kompakta rummet) samt mÃ¥ndag 25 mars kl 13-15, @@ -408,9 +417,9 @@ Det blir 10 tillfällen totalt, vilket bör räcka. </p> </div> </div> -<div id="outline-container-orged53d50" class="outline-3"> -<h3 id="orged53d50">2024-03-06</h3> -<div class="outline-text-3" id="text-orged53d50"> +<div id="outline-container-org54eab67" class="outline-3"> +<h3 id="org54eab67">2024-03-06</h3> +<div class="outline-text-3" id="text-org54eab67"> <p> Det verkar som fredagar kl 13-15 inte kolliderar med andra kurser, sÃ¥ jag planerar att flytta lektioner till den tiden. Det är 8 sÃ¥dana fredagar under perioden, sÃ¥ helst skall jag schemalägga tre tillfällen till. @@ -419,9 +428,9 @@ Möjliga tider är mÃ¥ndag 25 mars kl 13-15, torsdag 25 april kl 13-15, mÃ¥ndag </p> </div> </div> -<div id="outline-container-org69c699e" class="outline-3"> -<h3 id="org69c699e">2024-03-05</h3> -<div class="outline-text-3" id="text-org69c699e"> +<div id="outline-container-org73f95a7" class="outline-3"> +<h3 id="org73f95a7">2024-03-05</h3> +<div class="outline-text-3" id="text-org73f95a7"> <p> Det har framförts önskemÃ¥l om att byta tid för lektionerna i period 4 för att undvika kollision med kursen i optimeringslära. @@ -442,9 +451,9 @@ Det rör sig om 11 tillfällen totalt. </p> </div> </div> -<div id="outline-container-org8b45b59" class="outline-3"> -<h3 id="org8b45b59">2024-02-29</h3> -<div class="outline-text-3" id="text-org8b45b59"> +<div id="outline-container-orgf0c9193" class="outline-3"> +<h3 id="orgf0c9193">2024-02-29</h3> +<div class="outline-text-3" id="text-orgf0c9193"> <p> Till nästa lektion sÃ¥ tittar ni pÃ¥ uppgifterna 9.1.1d, 9.1.2d, 9.1.5b, 9.1.6d, 9.1.10, 9.1.20. @@ -458,9 +467,9 @@ Till lektionen efter det (27 mars) sÃ¥ räknar ni </div> </div> -<div id="outline-container-org6ee578d" class="outline-3"> -<h3 id="org6ee578d">2024-02-20</h3> -<div class="outline-text-3" id="text-org6ee578d"> +<div id="outline-container-org7f7d557" class="outline-3"> +<h3 id="org7f7d557">2024-02-20</h3> +<div class="outline-text-3" id="text-org7f7d557"> <p> Till nästa lektion (27 feb) sÃ¥ tittar ni pÃ¥ uppgifterna 4.2.15, 4.2.16, 4.2.18, 4.4.2ab. Använd Hensels lemma vid behov. @@ -471,7 +480,7 @@ grad 5 eller 6. </p> <div class="org-src-container"> -<pre class="src src-sage" id="org2172c13">def H_L_tree(f, p: int, r: int): +<pre class="src src-sage" id="org4d90c6b">def H_L_tree(f, p: int, r: int): vert = [(0,0)] for j in range(1,r+1): @@ -500,25 +509,25 @@ H_L_tree(f,p,r).plot(layout='tree') </div> -<figure id="orgce8829f"> +<figure id="org0119fe4"> <img src="img/Henseluppgift.png" alt="Henseluppgift.png"> </figure> </div> </div> -<div id="outline-container-org15914f2" class="outline-3"> -<h3 id="org15914f2">2024-02-12</h3> -<div class="outline-text-3" id="text-org15914f2"> +<div id="outline-container-org6fc379e" class="outline-3"> +<h3 id="org6fc379e">2024-02-12</h3> +<div class="outline-text-3" id="text-org6fc379e"> <p> Till nästa lektion (20 feb) sÃ¥ tittar ni pÃ¥ uppgifterna 7.1.5, 7.2.1d, 7.2.8, 7.2.35, 7.4.23, 7.4.24 </p> </div> </div> -<div id="outline-container-org445fa32" class="outline-3"> -<h3 id="org445fa32">2024-02-07</h3> -<div class="outline-text-3" id="text-org445fa32"> +<div id="outline-container-org7b22a27" class="outline-3"> +<h3 id="org7b22a27">2024-02-07</h3> +<div class="outline-text-3" id="text-org7b22a27"> <p> Till nästa lektion (12 feb) sÃ¥ tittar ni pÃ¥ uppgifterna 4.1.5, 4.1.9b, 4.2.8c,4.3.3. @@ -528,9 +537,9 @@ att vara i Kompakta rummet. </div> </div> -<div id="outline-container-org887cf9c" class="outline-3"> -<h3 id="org887cf9c">2024-01-30</h3> -<div class="outline-text-3" id="text-org887cf9c"> +<div id="outline-container-orgbc98f91" class="outline-3"> +<h3 id="orgbc98f91">2024-01-30</h3> +<div class="outline-text-3" id="text-orgbc98f91"> <ul class="org-ul"> <li>Till nästa gÃ¥ng sÃ¥ tittar ni pÃ¥ uppgifterna 3.3.10, 3.4.1c,3.4.20, 3.5.32,3.7.1c</li> <li>Dessutom: visa att om \(m,n\) relativt prima, \(m|a\), \(n|a\), sÃ¥ \(mn|a\).</li> @@ -539,9 +548,9 @@ att vara i Kompakta rummet. </ul> </div> -<div id="outline-container-orge760dad" class="outline-4"> -<h4 id="orge760dad">Tvillingfria primtal</h4> -<div class="outline-text-4" id="text-orge760dad"> +<div id="outline-container-org7ada8fb" class="outline-4"> +<h4 id="org7ada8fb">Tvillingfria primtal</h4> +<div class="outline-text-4" id="text-org7ada8fb"> <p> Jag använde följande sagemath-kod för att hitta \((k,n)\) med sgd(k,n)=1, sgd(k-2,n) > 1, sgd(k+2,n) >1, sÃ¥ att Dirichlets sats @@ -549,7 +558,7 @@ garanterar oändligt mÃ¥nga primtal i nZ + k. </p> <div class="org-src-container"> -<pre class="src src-sage" id="org173cf70">def repr(n): +<pre class="src src-sage" id="org1e013cf">def repr(n): return [k for k in range(n) if gcd(k,n)==1] def isolated(n): @@ -580,17 +589,17 @@ Körning visar att n=15, k=7 är minsta exemplet. </div> </div> -<div id="outline-container-org488e68b" class="outline-3"> -<h3 id="org488e68b">2024-01-23</h3> -<div class="outline-text-3" id="text-org488e68b"> +<div id="outline-container-org5081bbc" class="outline-3"> +<h3 id="org5081bbc">2024-01-23</h3> +<div class="outline-text-3" id="text-org5081bbc"> <p> Till nästa gÃ¥ng sÃ¥ tittar ni pÃ¥ uppgifterna 1.5.18, 1.5.36, 3.1.6, 3.2.10. </p> </div> </div> -<div id="outline-container-org96d1546" class="outline-3"> -<h3 id="org96d1546">2024-01-16</h3> -<div class="outline-text-3" id="text-org96d1546"> +<div id="outline-container-orgec17e4b" class="outline-3"> +<h3 id="orgec17e4b">2024-01-16</h3> +<div class="outline-text-3" id="text-orgec17e4b"> <ul class="org-ul"> <li>Första föreläsningen, information om kursupplägget, kurslitteratur, tentamen.</li> <li>Pratade om <a href="lectures/swelecture0.pdf">talteori som matematisk disciplin</a>, mycket översiktligt.</li> @@ -598,7 +607,7 @@ Till nästa gÃ¥ng sÃ¥ tittar ni pÃ¥ uppgifterna 1.5.18, 1.5.36, 3.1.6, 3.2.10. <li>ÖnskemÃ¥l om information om vilka/vilket kapitel i kursboken en given föreläsning är kopplad till, skall ordna.</li> <li>Vi kommer att gÃ¥ igenom uppgifter -(hämtade frÃ¥n listan med <a href="#org9bd3039">rekommenderade uppgifter</a>) +(hämtade frÃ¥n listan med <a href="#orgd99cfc5">rekommenderade uppgifter</a>) pÃ¥ vissa av lektionstillfällena, kanske första 45 minuterna. Annonseras här.</li> <li>Jag glömde att framföra följande förmaning: även om kursen examineras med en enda skriftlig tentamen i juni sÃ¥ är det viktigt att studera kontinuerligt, och räkna uppgifter. @@ -612,19 +621,19 @@ till, nu med fokus pÃ¥ att förstÃ¥ bevisen.</li> </div> </section> -<section id="outline-container-org7fb0ecc" class="outline-2"> -<h2 id="org7fb0ecc">Kurslitteratur <a id="org43c1e74"></a></h2> -<div class="outline-text-2" id="text-org7fb0ecc"> +<section id="outline-container-org83cdbc2" class="outline-2"> +<h2 id="org83cdbc2">Kurslitteratur <a id="org47e9684"></a></h2> +<div class="outline-text-2" id="text-org83cdbc2"> </div> -<div id="outline-container-org1046eac" class="outline-3"> -<h3 id="org1046eac">Kursbok</h3> -<div class="outline-text-3" id="text-org1046eac"> +<div id="outline-container-org969d2a9" class="outline-3"> +<h3 id="org969d2a9">Kursbok</h3> +<div class="outline-text-3" id="text-org969d2a9"> <p> Kursbok är <a href="https://www.prisjakt.nu/produkt.php?p=8083662">Elementary Number Theory</a> av Kenneth Rosen. </p> -<figure id="org2a1061a"> +<figure id="orgc8a4fed"> <img src="img/Rosen6ed.png" alt="Rosen6ed.png" width="40%"> <figcaption><span class="figure-number">Illustration 1 </span>Elementary Number Theory, Kenneth Rosen</figcaption> @@ -636,13 +645,13 @@ vilket inte pÃ¥verkar innehÃ¥llet. </p> </div> </div> -<div id="outline-container-orgb1f71c0" class="outline-3"> -<h3 id="orgb1f71c0">Bredvidläsning</h3> -<div class="outline-text-3" id="text-orgb1f71c0"> +<div id="outline-container-orgfa4a7ab" class="outline-3"> +<h3 id="orgfa4a7ab">Bredvidläsning</h3> +<div class="outline-text-3" id="text-orgfa4a7ab"> </div> -<div id="outline-container-org1304ec9" class="outline-4"> -<h4 id="org1304ec9">Fritt tillgängligt material</h4> -<div class="outline-text-4" id="text-org1304ec9"> +<div id="outline-container-orge4da471" class="outline-4"> +<h4 id="orge4da471">Fritt tillgängligt material</h4> +<div class="outline-text-4" id="text-orge4da471"> <p> Följande böcker är fritt tillgängliga pÃ¥ nätet. Kursboken är väldigt grundlig och täcker kursinnehÃ¥llet, men det kan ändÃ¥ vara bra att se olika @@ -660,9 +669,9 @@ Jolly för en metod att hitta primitiva rötter.</li> </ul> </div> </div> -<div id="outline-container-org156f528" class="outline-4"> -<h4 id="org156f528">Andra lämpliga böcker</h4> -<div class="outline-text-4" id="text-org156f528"> +<div id="outline-container-org2169300" class="outline-4"> +<h4 id="org2169300">Andra lämpliga böcker</h4> +<div class="outline-text-4" id="text-org2169300"> <ul class="org-ul"> <li>BAKER. A concise introduction to the theory of numbers.</li> <li>DAVENPORT. The higher arithmetic.</li> @@ -682,13 +691,13 @@ fortbildning efter denna kurs.</li> -<section id="outline-container-org777e787" class="outline-2"> -<h2 id="org777e787">KursinnehÃ¥ll <a id="orgd3a32bb"></a></h2> -<div class="outline-text-2" id="text-org777e787"> +<section id="outline-container-orgc6c0ef4" class="outline-2"> +<h2 id="orgc6c0ef4">KursinnehÃ¥ll <a id="org06fee11"></a></h2> +<div class="outline-text-2" id="text-orgc6c0ef4"> </div> -<div id="outline-container-org8bd2546" class="outline-3"> -<h3 id="org8bd2546">Avsnitt av kursboken</h3> -<div class="outline-text-3" id="text-org8bd2546"> +<div id="outline-container-org43c7b85" class="outline-3"> +<h3 id="org43c7b85">Avsnitt av kursboken</h3> +<div class="outline-text-3" id="text-org43c7b85"> <p> Kursen omfattar följande delar/kapitel av kursboken: 1.5, 2.1, 3, 4.1-4.4, 5.1, 6, 7.1-7.4, 9, 11.1-11.4, 12, 13.1-13.4,14. Jag kommer inte att föreläsa om @@ -698,15 +707,15 @@ frÃ¥n just dessa avsnitt. </p> </div> -<div id="outline-container-org5c92b21" class="outline-4"> -<h4 id="org5c92b21">Rekommenderade uppgifter <a id="org9bd3039"></a></h4> -<div class="outline-text-4" id="text-org5c92b21"> +<div id="outline-container-org0c49604" class="outline-4"> +<h4 id="org0c49604">Rekommenderade uppgifter <a id="orgd99cfc5"></a></h4> +<div class="outline-text-4" id="text-org0c49604"> </div> <ul class="org-ul"> -<li><a id="org180341a"></a>Kap 1<br> +<li><a id="org1cc7e3a"></a>Kap 1<br> <ul class="org-ul"> -<li><a id="org7ad84d9"></a>1.5<br> -<div class="outline-text-6" id="text-org7ad84d9"> +<li><a id="org978ec51"></a>1.5<br> +<div class="outline-text-6" id="text-org978ec51"> <p> 8a,9b,18,36,37 </p> @@ -714,46 +723,46 @@ frÃ¥n just dessa avsnitt. </li> </ul> </li> -<li><a id="org87a9a00"></a>Kap 3<br> +<li><a id="org0585282"></a>Kap 3<br> <ul class="org-ul"> -<li><a id="org8d58eb7"></a>3.1<br> -<div class="outline-text-6" id="text-org8d58eb7"> +<li><a id="orgba991bb"></a>3.1<br> +<div class="outline-text-6" id="text-orgba991bb"> <p> 1ab, 2f,6. </p> </div> </li> -<li><a id="org7773607"></a>3.2<br> -<div class="outline-text-6" id="text-org7773607"> +<li><a id="org1d83cec"></a>3.2<br> +<div class="outline-text-6" id="text-org1d83cec"> <ol class="org-ol"> <li></li> </ol> </div> </li> -<li><a id="orgd200f28"></a>3.3<br> -<div class="outline-text-6" id="text-orgd200f28"> +<li><a id="org1f58297"></a>3.3<br> +<div class="outline-text-6" id="text-org1f58297"> <p> 1df,2ef,10,24,30,31 </p> </div> </li> -<li><a id="org5f021b7"></a>3.4<br> -<div class="outline-text-6" id="text-org5f021b7"> +<li><a id="org658bec3"></a>3.4<br> +<div class="outline-text-6" id="text-org658bec3"> <p> 1bc, 19*, 20*. </p> </div> </li> -<li><a id="org54380bd"></a>3.5<br> -<div class="outline-text-6" id="text-org54380bd"> +<li><a id="orgb0fdc9e"></a>3.5<br> +<div class="outline-text-6" id="text-orgb0fdc9e"> <p> 1il, 2, 4c, 29cd, 32*, 34, 58ac. </p> </div> </li> -<li><a id="orge8d3c38"></a>3.7<br> -<div class="outline-text-6" id="text-orge8d3c38"> +<li><a id="org45b4d99"></a>3.7<br> +<div class="outline-text-6" id="text-org45b4d99"> <p> 1cd </p> @@ -761,31 +770,31 @@ frÃ¥n just dessa avsnitt. </li> </ul> </li> -<li><a id="org3c52ecc"></a>Kap 4<br> +<li><a id="orgbb7b14d"></a>Kap 4<br> <ul class="org-ul"> -<li><a id="org60d0871"></a>4.1<br> -<div class="outline-text-6" id="text-org60d0871"> +<li><a id="org06c1fef"></a>4.1<br> +<div class="outline-text-6" id="text-org06c1fef"> <p> 4,5,7ab,9bc. </p> </div> </li> -<li><a id="org6ccedb0"></a>4.2<br> -<div class="outline-text-6" id="text-org6ccedb0"> +<li><a id="org53f1544"></a>4.2<br> +<div class="outline-text-6" id="text-org53f1544"> <p> 1df, 8c, 9d. </p> </div> </li> -<li><a id="org89b0458"></a>4.3<br> -<div class="outline-text-6" id="text-org89b0458"> +<li><a id="org490796e"></a>4.3<br> +<div class="outline-text-6" id="text-org490796e"> <p> 3,4. </p> </div> </li> -<li><a id="orgce85497"></a>4.4<br> -<div class="outline-text-6" id="text-orgce85497"> +<li><a id="orgb4590fd"></a>4.4<br> +<div class="outline-text-6" id="text-orgb4590fd"> <p> 2ab. </p> @@ -793,10 +802,10 @@ frÃ¥n just dessa avsnitt. </li> </ul> </li> -<li><a id="orgce38e81"></a>Kap 5<br> +<li><a id="org8aea6f0"></a>Kap 5<br> <ul class="org-ul"> -<li><a id="org290a8f0"></a>5.1<br> -<div class="outline-text-6" id="text-org290a8f0"> +<li><a id="org34987f8"></a>5.1<br> +<div class="outline-text-6" id="text-org34987f8"> <p> 4ab. </p> @@ -804,26 +813,26 @@ frÃ¥n just dessa avsnitt. </li> </ul> </li> -<li><a id="org079c6dc"></a>Kap 6<br> +<li><a id="org44c4796"></a>Kap 6<br> <ul class="org-ul"> -<li><a id="org87f09e3"></a>6.1<br> -<div class="outline-text-6" id="text-org87f09e3"> +<li><a id="org5467c3d"></a>6.1<br> +<div class="outline-text-6" id="text-org5467c3d"> <p> 4,5,6,9,10,14,18,19,22,24,24,28,36,38*,41,48*,52. </p> </div> </li> -<li><a id="orgbc16a8c"></a>6.2<br> -<div class="outline-text-6" id="text-orgbc16a8c"> +<li><a id="orgcb44edd"></a>6.2<br> +<div class="outline-text-6" id="text-orgcb44edd"> <p> 2,8,12,16ab. </p> </div> </li> -<li><a id="orgffebf1d"></a>6.3<br> -<div class="outline-text-6" id="text-orgffebf1d"> +<li><a id="orga80d292"></a>6.3<br> +<div class="outline-text-6" id="text-orga80d292"> <p> 1d,6,7,22* </p> @@ -832,31 +841,31 @@ frÃ¥n just dessa avsnitt. </ul> </li> -<li><a id="orgcfc4d04"></a>Kap 7<br> +<li><a id="orgdcdc40f"></a>Kap 7<br> <ul class="org-ul"> -<li><a id="org614132a"></a>7.1<br> -<div class="outline-text-6" id="text-org614132a"> +<li><a id="org90dcdab"></a>7.1<br> +<div class="outline-text-6" id="text-org90dcdab"> <p> 2bc,5,8. </p> </div> </li> -<li><a id="org871658a"></a>7.2<br> -<div class="outline-text-6" id="text-org871658a"> +<li><a id="org39c711c"></a>7.2<br> +<div class="outline-text-6" id="text-org39c711c"> <p> 1bd,2cd,8,34*,35,38*. </p> </div> </li> -<li><a id="org122f2e6"></a>7.3<br> -<div class="outline-text-6" id="text-org122f2e6"> +<li><a id="org2d9e7af"></a>7.3<br> +<div class="outline-text-6" id="text-org2d9e7af"> <p> 3b,4,7,8,10,18,22**,28*,29cd. </p> </div> </li> -<li><a id="org9ba696a"></a>7.4<br> -<div class="outline-text-6" id="text-org9ba696a"> +<li><a id="org01dd2e1"></a>7.4<br> +<div class="outline-text-6" id="text-org01dd2e1"> <p> 1bd,2be,14,22,23,24,30,31. </p> @@ -865,47 +874,47 @@ frÃ¥n just dessa avsnitt. </ul> </li> -<li><a id="orgd9614bf"></a>Kap 9<br> +<li><a id="org22e6c42"></a>Kap 9<br> <ul class="org-ul"> -<li><a id="org477479c"></a>9.1<br> -<div class="outline-text-6" id="text-org477479c"> +<li><a id="org3171b1b"></a>9.1<br> +<div class="outline-text-6" id="text-org3171b1b"> <p> 1ad, 2cd, 5b, 6df, 8, 10, 20*, 22*. </p> </div> </li> -<li><a id="orga68111e"></a>9.2<br> -<div class="outline-text-6" id="text-orga68111e"> +<li><a id="org9d9f07a"></a>9.2<br> +<div class="outline-text-6" id="text-org9d9f07a"> <p> 1d, 2d, 3e, 6. </p> </div> </li> -<li><a id="orgf6dd661"></a>9.3<br> -<div class="outline-text-6" id="text-orgf6dd661"> +<li><a id="orgf0b7847"></a>9.3<br> +<div class="outline-text-6" id="text-orgf0b7847"> <p> 2,3c, 5c,6c, 8b, 10. </p> </div> </li> -<li><a id="org37dfb2a"></a>9.4<br> -<div class="outline-text-6" id="text-org37dfb2a"> +<li><a id="org9f8fe1f"></a>9.4<br> +<div class="outline-text-6" id="text-org9f8fe1f"> <p> 1, 2b, 3a, 4, 9, 10, 19, 20*. </p> </div> </li> -<li><a id="org29656a1"></a>9.5<br> -<div class="outline-text-6" id="text-org29656a1"> +<li><a id="org99d1763"></a>9.5<br> +<div class="outline-text-6" id="text-org99d1763"> <p> 2,3,10. </p> </div> </li> -<li><a id="orgf9dc898"></a>9.6<br> -<div class="outline-text-6" id="text-orgf9dc898"> +<li><a id="orgfa55cb8"></a>9.6<br> +<div class="outline-text-6" id="text-orgfa55cb8"> <p> 1bcg, 4def, 13*, 14*. </p> @@ -914,31 +923,31 @@ frÃ¥n just dessa avsnitt. </ul> </li> -<li><a id="org2d75d4e"></a>Kap 11<br> +<li><a id="org94cf781"></a>Kap 11<br> <ul class="org-ul"> -<li><a id="org762f628"></a>11.1<br> -<div class="outline-text-6" id="text-org762f628"> +<li><a id="org7d092f2"></a>11.1<br> +<div class="outline-text-6" id="text-org7d092f2"> <p> 1d, 4, 25. </p> </div> </li> -<li><a id="orgd2d41f5"></a>11.2<br> -<div class="outline-text-6" id="text-orgd2d41f5"> +<li><a id="org88bf99e"></a>11.2<br> +<div class="outline-text-6" id="text-org88bf99e"> <p> 1cd, 2, 4, 5. </p> </div> </li> -<li><a id="orgc0bf6e6"></a>11.3<br> -<div class="outline-text-6" id="text-orgc0bf6e6"> +<li><a id="org01d2881"></a>11.3<br> +<div class="outline-text-6" id="text-org01d2881"> <p> 1ef, 5, 6. </p> </div> </li> -<li><a id="org53fd7ee"></a>11.4<br> -<div class="outline-text-6" id="text-org53fd7ee"> +<li><a id="orgad3a1ae"></a>11.4<br> +<div class="outline-text-6" id="text-orgad3a1ae"> <p> 1, 2, 5, 6. </p> @@ -947,32 +956,32 @@ frÃ¥n just dessa avsnitt. </ul> </li> -<li><a id="org4de3188"></a>Kap 12<br> +<li><a id="org44aa093"></a>Kap 12<br> <ul class="org-ul"> -<li><a id="org7b01410"></a>12.2<br> -<div class="outline-text-6" id="text-org7b01410"> +<li><a id="org936a20d"></a>12.2<br> +<div class="outline-text-6" id="text-org936a20d"> <p> 1bf, 2cd, 3c, 4c. </p> </div> </li> -<li><a id="org1aa1c33"></a>12.3<br> -<div class="outline-text-6" id="text-org1aa1c33"> +<li><a id="org30d8efe"></a>12.3<br> +<div class="outline-text-6" id="text-org30d8efe"> <p> 1c, 2a, 6*, 7. </p> </div> </li> -<li><a id="orgccd3c06"></a>12.4<br> -<div class="outline-text-6" id="text-orgccd3c06"> +<li><a id="orgc28fd4b"></a>12.4<br> +<div class="outline-text-6" id="text-orgc28fd4b"> <p> 1c, 2c, 3b, 4a, 5b, 6b, 7b, 8, 10, 17. </p> </div> </li> -<li><a id="org1a8a715"></a>12.5<br> -<div class="outline-text-6" id="text-org1a8a715"> +<li><a id="org6fe52f2"></a>12.5<br> +<div class="outline-text-6" id="text-org6fe52f2"> <ol class="org-ol"> <li></li> </ol> @@ -981,32 +990,32 @@ frÃ¥n just dessa avsnitt. </ul> </li> -<li><a id="org919ec71"></a>Kap 13<br> +<li><a id="org3f74cbe"></a>Kap 13<br> <ul class="org-ul"> -<li><a id="org4beed34"></a>13.1<br> -<div class="outline-text-6" id="text-org4beed34"> +<li><a id="orgd9fc89a"></a>13.1<br> +<div class="outline-text-6" id="text-orgd9fc89a"> <p> 1, 2, 3, 8, 16. </p> </div> </li> -<li><a id="org670cfbe"></a>13.2<br> -<div class="outline-text-6" id="text-org670cfbe"> +<li><a id="org80effe7"></a>13.2<br> +<div class="outline-text-6" id="text-org80effe7"> <p> 3, 4, 6*, 8, 10, 11*, 20. </p> </div> </li> -<li><a id="org9de6939"></a>13.3<br> -<div class="outline-text-6" id="text-org9de6939"> +<li><a id="orgc699f00"></a>13.3<br> +<div class="outline-text-6" id="text-orgc699f00"> <p> 1b, 2gh,3cd, 6, 7, 9c, 10ef. </p> </div> </li> -<li><a id="org3183550"></a>13.4<br> -<div class="outline-text-6" id="text-org3183550"> +<li><a id="orgb9e9b7b"></a>13.4<br> +<div class="outline-text-6" id="text-orgb9e9b7b"> <p> 1c, 2a, 3def, 4ab, 6de, 8*. @@ -1016,25 +1025,25 @@ frÃ¥n just dessa avsnitt. </ul> </li> -<li><a id="org63d399d"></a>Kap 14<br> +<li><a id="org1a1cc94"></a>Kap 14<br> <ul class="org-ul"> -<li><a id="org85ae0e8"></a>14.1<br> -<div class="outline-text-6" id="text-org85ae0e8"> +<li><a id="org8bd881e"></a>14.1<br> +<div class="outline-text-6" id="text-org8bd881e"> <p> 1ac, 12, 13, 17a. </p> </div> </li> -<li><a id="org3dd76f9"></a>14.2<br> -<div class="outline-text-6" id="text-org3dd76f9"> +<li><a id="org659103e"></a>14.2<br> +<div class="outline-text-6" id="text-org659103e"> <p> 16ab, 17bc. </p> </div> </li> -<li><a id="orgff2bf56"></a>14.3<br> -<div class="outline-text-6" id="text-orgff2bf56"> +<li><a id="org20cf5b1"></a>14.3<br> +<div class="outline-text-6" id="text-org20cf5b1"> <p> 1bc, 2c </p> @@ -1046,15 +1055,15 @@ frÃ¥n just dessa avsnitt. </div> </div> -<div id="outline-container-orgf97dd5f" class="outline-3"> -<h3 id="orgf97dd5f">Kort beskrivning av kursinnehÃ¥llet</h3> +<div id="outline-container-org33f6268" class="outline-3"> +<h3 id="org33f6268">Kort beskrivning av kursinnehÃ¥llet</h3> </div> </section> -<section id="outline-container-orgb1afa66" class="outline-2"> -<h2 id="orgb1afa66">Föreläsningar <a id="org0da9d7f"></a></h2> -<div class="outline-text-2" id="text-orgb1afa66"> +<section id="outline-container-org0e51919" class="outline-2"> +<h2 id="org0e51919">Föreläsningar <a id="org025d360"></a></h2> +<div class="outline-text-2" id="text-org0e51919"> <p> Jag har föreläst enligt följande föreläsningsanteckningar, med vissa utsvävningar. De svenska versionerna är nyare. NÃ¥gra av föreläsningarna tar tvÃ¥ tillfällen för att gÃ¥ igenom. @@ -1233,9 +1242,9 @@ De svenska versionerna är nyare. NÃ¥gra av föreläsningarna tar tvÃ¥ tillfäll </section> -<section id="outline-container-orgd9a1a3d" class="outline-2"> -<h2 id="orgd9a1a3d">Tentor <a id="org113b7d1"></a></h2> -<div class="outline-text-2" id="text-orgd9a1a3d"> +<section id="outline-container-orgf5fd67d" class="outline-2"> +<h2 id="orgf5fd67d">Tentor <a id="org64fbaef"></a></h2> +<div class="outline-text-2" id="text-orgf5fd67d"> <table> @@ -1257,6 +1266,13 @@ De svenska versionerna är nyare. NÃ¥gra av föreläsningarna tar tvÃ¥ tillfäll </tr> </thead> <tbody> +<tr> +<td class="org-right">2024-06-01</td> +<td class="org-left">Jan Snellman</td> +<td class="org-left"><a href="exams/2024/tenta-TATA54-20240601.pdf">TATA5420240601</a></td> +<td class="org-left"><a href="exams/2024/tenta-TATA54-20240601-losning.pdf">TATA5420240601losn</a></td> +</tr> + <tr> <td class="org-right">2023-08-17</td> <td class="org-left">Jan Snellman</td> @@ -1437,13 +1453,13 @@ De svenska versionerna är nyare. NÃ¥gra av föreläsningarna tar tvÃ¥ tillfäll </section> -<section id="outline-container-orgaa8bfe8" class="outline-2"> -<h2 id="orgaa8bfe8">Datorlaborationer <a id="orgd7ec18a"></a></h2> -<div class="outline-text-2" id="text-orgaa8bfe8"> +<section id="outline-container-orgac41624" class="outline-2"> +<h2 id="orgac41624">Datorlaborationer <a id="org2d2cfa4"></a></h2> +<div class="outline-text-2" id="text-orgac41624"> </div> -<div id="outline-container-org0e9470f" class="outline-3"> -<h3 id="org0e9470f">SageMath</h3> -<div class="outline-text-3" id="text-org0e9470f"> +<div id="outline-container-orgd0ccf06" class="outline-3"> +<h3 id="orgd0ccf06">SageMath</h3> +<div class="outline-text-3" id="text-orgd0ccf06"> <p> Jag kommer att använda datoralgebraprogrammet <a href="https://www.sagemath.org/">SageMath</a> för att beräkna lite större exempel. Om ni vill experimentera pÃ¥ egen hand kan ni enkelt <a href="https://doc.sagemath.org/html/en/installation/index.html">installera programmet pÃ¥ er dator</a>, @@ -1459,9 +1475,9 @@ Ett tredje alternativ, enkelt och flärdfritt, är att mata in sin kod till <a h </p> </div> </div> -<div id="outline-container-org4e01f4d" class="outline-3"> -<h3 id="org4e01f4d">Kod frÃ¥n vissa föreläsningar</h3> -<div class="outline-text-3" id="text-org4e01f4d"> +<div id="outline-container-orgd3b0180" class="outline-3"> +<h3 id="orgd3b0180">Kod frÃ¥n vissa föreläsningar</h3> +<div class="outline-text-3" id="text-orgd3b0180"> <ul class="org-ul"> <li><a href="labs/lecture0.html">Föreläsning 0</a></li> <li><a href="labs/lecture1.html">Föreläsning 1</a></li> @@ -1472,21 +1488,21 @@ Ett tredje alternativ, enkelt och flärdfritt, är att mata in sin kod till <a h </ul> </div> </div> -<div id="outline-container-org771ae33" class="outline-3"> -<h3 id="org771ae33">Laborationer</h3> -<div class="outline-text-3" id="text-org771ae33"> +<div id="outline-container-org85c34f4" class="outline-3"> +<h3 id="org85c34f4">Laborationer</h3> +<div class="outline-text-3" id="text-org85c34f4"> </div> -<div id="outline-container-orge16b88e" class="outline-4"> -<h4 id="orge16b88e">Hensellyft, Primitiva rötter, Kinesiska restsatsen</h4> -<div class="outline-text-4" id="text-orge16b88e"> +<div id="outline-container-orga1be7da" class="outline-4"> +<h4 id="orga1be7da">Hensellyft, Primitiva rötter, Kinesiska restsatsen</h4> +<div class="outline-text-4" id="text-orga1be7da"> <p> Finns att <a href="labs/HenselLyftLabHT2023.html">läsa direkt</a> eller som <a href="labs/HenselLyftLabHT2023.ipynb">Jupyter notebook</a> eller som <a href="labs/HenselLyftLabHT2023web.html">webapp</a>. </p> </div> </div> -<div id="outline-container-org254ad94" class="outline-4"> -<h4 id="org254ad94">KedjebrÃ¥k</h4> -<div class="outline-text-4" id="text-org254ad94"> +<div id="outline-container-org2528f16" class="outline-4"> +<h4 id="org2528f16">KedjebrÃ¥k</h4> +<div class="outline-text-4" id="text-org2528f16"> <p> Finns att <a href="labs/kedjebraklab.html">läsa direkt</a> eller som <a href="labs/kedjebraklab.ipynb">Jupyter notebook</a> eller som <a href="labs/kedjebraklabweb.html">webapp</a>. </p> @@ -1497,20 +1513,20 @@ Finns att <a href="labs/kedjebraklab.html">läsa direkt</a> eller som <a href="l -<section id="outline-container-orgcab2c84" class="outline-2"> -<h2 id="orgcab2c84">Tidigare Ã¥r <a id="org0573e61"></a></h2> -<div class="outline-text-2" id="text-orgcab2c84"> +<section id="outline-container-org27d49bb" class="outline-2"> +<h2 id="org27d49bb">Tidigare Ã¥r <a id="orgb17e462"></a></h2> +<div class="outline-text-2" id="text-org27d49bb"> </div> -<div id="outline-container-org5db15ec" class="outline-3"> -<h3 id="org5db15ec">TATA54 Anteckningar frÃ¥n tidigare Ã¥r</h3> -<div class="outline-text-3" id="text-org5db15ec"> +<div id="outline-container-orga1fa650" class="outline-3"> +<h3 id="orga1fa650">TATA54 Anteckningar frÃ¥n tidigare Ã¥r</h3> +<div class="outline-text-3" id="text-orga1fa650"> </div> -<div id="outline-container-org2e74361" class="outline-4"> -<h4 id="org2e74361">2023</h4> -<div class="outline-text-4" id="text-org2e74361"> +<div id="outline-container-orgd4aaf8a" class="outline-4"> +<h4 id="orgd4aaf8a">2023</h4> +<div class="outline-text-4" id="text-orgd4aaf8a"> <ul class="org-ul"> <li>2023-12-21: Gjorde klart <a href="index.html">denna nya kurshemsida</a>.</li> <li>2023-06-05: Jag har rättat tentan; en @@ -1564,9 +1580,9 @@ tryckfel (skall vara w(d)). 7.2.38 är komplicerad och kan skippas.</li> </div> -<div id="outline-container-org39f254e" class="outline-4"> -<h4 id="org39f254e">2021</h4> -<div class="outline-text-4" id="text-org39f254e"> +<div id="outline-container-orgc39991d" class="outline-4"> +<h4 id="orgc39991d">2021</h4> +<div class="outline-text-4" id="text-orgc39991d"> <ul class="org-ul"> <li>2021-20-26: Alla klarade omtentan, trots att uppgift 5 kanske var oklar, jag menade periodLÄNGD för decimalutvecklingen, den kan @@ -1614,9 +1630,9 @@ nÃ¥gon inbjudan, sÃ¥ mejla mig.</li> </div> </div> -<div id="outline-container-orgab915cd" class="outline-4"> -<h4 id="orgab915cd">2020</h4> -<div class="outline-text-4" id="text-orgab915cd"> +<div id="outline-container-org6bff760" class="outline-4"> +<h4 id="org6bff760">2020</h4> +<div class="outline-text-4" id="text-org6bff760"> <ul class="org-ul"> <li><p> 2020-12-12: Kursen kommer att ges VT2021, med start den 19e januari. @@ -1669,9 +1685,9 @@ someone else (perhaps </div> </div> -<div id="outline-container-org51934a3" class="outline-4"> -<h4 id="org51934a3">2019</h4> -<div class="outline-text-4" id="text-org51934a3"> +<div id="outline-container-org85cd779" class="outline-4"> +<h4 id="org85cd779">2019</h4> +<div class="outline-text-4" id="text-org85cd779"> <ul class="org-ul"> <li>2019-11-01: The course will not be given spring 2020.</li> @@ -1686,9 +1702,9 @@ available.</li> </div> </div> -<div id="outline-container-org51909e4" class="outline-4"> -<h4 id="org51909e4">2018</h4> -<div class="outline-text-4" id="text-org51909e4"> +<div id="outline-container-org21f5089" class="outline-4"> +<h4 id="org21f5089">2018</h4> +<div class="outline-text-4" id="text-org21f5089"> <ul class="org-ul"> <li>2018-06-08: <a href="exams/2018/tentaTATA5420180607soln.pdf">Solutions</a> to <a href="exams/2018/tenta20180607.pdf">the exam on June 7</a> are now @@ -1701,9 +1717,9 @@ available.</li> </div> </div> -<div id="outline-container-org50057cb" class="outline-4"> -<h4 id="org50057cb">2017</h4> -<div class="outline-text-4" id="text-org50057cb"> +<div id="outline-container-org7ce4987" class="outline-4"> +<h4 id="org7ce4987">2017</h4> +<div class="outline-text-4" id="text-org7ce4987"> <ul class="org-ul"> <li>2017-08-28: <a href="exams/2017/tentaTATA54170826soln.pdf">Solutions</a> to <a href="exams/2017/tenta170826.pdf">the exam on Saturday 26</a> are now @@ -1726,7 +1742,7 @@ Another text is <a href="https://wstein.org/ent/">Elementary Number Theory</a> a </ul> -<figure id="org2c3b0e5"> +<figure id="orgd0c0b37"> <img src="img/sieveE.jpg" alt="sieveE.jpg"> </figure> @@ -1736,9 +1752,9 @@ Another text is <a href="https://wstein.org/ent/">Elementary Number Theory</a> a </section> -<section id="outline-container-org27e935f" class="outline-2"> -<h2 id="org27e935f">Index</h2> -<div class="outline-text-2" id="text-org27e935f"> +<section id="outline-container-orga44ea53" class="outline-2"> +<h2 id="orga44ea53">Index</h2> +<div class="outline-text-2" id="text-orga44ea53"> <p> <a href="sitemap.html">Samtliga nÃ¥bara filer</a> </p> @@ -1747,7 +1763,7 @@ Another text is <a href="https://wstein.org/ent/">Elementary Number Theory</a> a </main> <footer id="postamble" class="status"> <p class="author">Författare: Jan Snellman Jan Snellman</p> -<p class="date">Created: 2024-05-18</p> +<p class="date">Created: 2024-06-01</p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> </footer> </body> diff --git a/public/sitemap.html b/public/sitemap.html index 9ff29f5..2f164d9 100644 --- a/public/sitemap.html +++ b/public/sitemap.html @@ -1,7 +1,7 @@ <!DOCTYPE html> <html lang="en"> <head> -<!-- 2024-05-18 --> +<!-- 2024-06-01 --> <meta charset="utf-8" /> <meta name="viewport" content="width=device-width, initial-scale=1" /> <title>Kurshemsida</title> @@ -208,8 +208,6 @@ </header><ul class="org-ul"> <li><a href="newlectures/newlecture.html">Föreläsningar i Talteori</a></li> <li><a href="newlectures/new-lect-0.html">Talteori översiktsföreläsning</a></li> -<li><a href="lectures/Henselfaktorisering.html">Henselfaktorisering</a></li> -<li><a href="senaste-nytt.html">senaste-nytt</a></li> <li><a href="labs/lecture5.html">lecture5</a></li> <li><a href="labs/lecture4.html">lecture4</a></li> <li><a href="labs/lecture3.html">lecture3</a></li> @@ -217,13 +215,15 @@ <li><a href="labs/lecture1.html">lecture1</a></li> <li><a href="labs/lecture0.html">lecture0</a></li> <li><a href="index.html">TATA54 Talteori</a></li> +<li><a href="senaste-nytt.html">senaste-nytt</a></li> <li><a href="labs/kedjebraklab.html">Sagemath-övningar pÃ¥ kedjebrÃ¥k</a></li> <li><a href="labs/HenselLyftLabHT2023.html">SageMath-övningar pÃ¥ Hensellyft, primitiva rötter, och KRS</a></li> +<li><a href="lectures/Henselfaktorisering.html">Henselfaktorisering</a></li> </ul> </main> <footer id="postamble" class="status"> <p class="author">Author: Jan Snellman</p> -<p class="date">Created: 2024-05-18</p> +<p class="date">Created: 2024-06-01</p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> </footer> </body> -- GitLab