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<h1 class="title">TATA54 Talteori</h1>
</header><nav id="table-of-contents" role="doc-toc">
<h2>Inneh&aring;ll</h2>
<div id="text-table-of-contents" role="doc-toc">
<ul>
<li><a href="#org8cf611f">Kurshemsida för TATA54, Talteori  </a>
<ul>
<li><a href="#orgd386ff5">Ämnesområde</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>
</ul>
</li>
<li><a href="#org7fb0ecc">Kurslitteratur </a>
<ul>
<li><a href="#org1046eac">Kursbok</a></li>
<li><a href="#orgb1f71c0">Bredvidläsning</a>
<ul>
<li><a href="#org1304ec9">Fritt tillgängligt material</a></li>
<li><a href="#org156f528">Andra lämpliga böcker</a></li>
</ul>
</li>
</ul>
</li>
<li><a href="#org777e787">Kursinnehåll </a>
<ul>
<li><a href="#org8bd2546">Avsnitt av kursboken</a>
<ul>
<li><a href="#org2c630c7">Rekommenderade uppgifter</a></li>
</ul>
</li>
<li><a href="#orgf97dd5f">Kort beskrivning av kursinnehållet</a></li>
</ul>
</li>
<li><a href="#orgb1afa66">Föreläsningar </a></li>
<li><a href="#orgd9a1a3d">Tentor </a></li>
<li><a href="#orgaa8bfe8">Datorlaborationer </a>
<ul>
<li><a href="#org0e9470f">SageMath</a></li>
<li><a href="#org4e01f4d">Kod från vissa föreläsningar</a></li>
<li><a href="#org771ae33">Laborationer</a>
<ul>
<li><a href="#orge16b88e">Hensellyft, Primitiva rötter, Kinesiska restsatsen</a></li>
<li><a href="#org254ad94">Kedjebråk</a></li>
</ul>
</li>
</ul>
</li>
<li><a href="#org0fa4e59">Senaste nytt </a>
<ul>
<li><a href="#org0b03441">TATA54 Senaste nytt</a>
<ul>
<li><a href="#orgdfef631">2024</a></li>
<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>
</ul>
</li>
</ul>
</li>
<li><a href="#org27e935f">Index</a></li>
</ul>
</div>
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<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">
</div>
<div id="outline-container-orgd386ff5" class="outline-3">
<h3 id="orgd386ff5">Ämnesområde</h3>
<div class="outline-text-3" id="text-orgd386ff5">
<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">
<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">
<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">
<p>
Se <a href="https://cloud.timeedit.net/liu/web/schema/">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">
<p>
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<tr>
<td class="org-left">Utb. kod</td>
<td class="org-left">Kursnamn</td>
<td class="org-right">Datum</td>
<td class="org-right">Tid</td>
<td class="org-left">Ort</td>
<td class="org-left">Anmälningsperiod</td>
</tr>

<tr>
<td class="org-left">TATA54/TEN1</td>
<td class="org-left">Talteori</td>
<td class="org-right">2024-06-01</td>
<td class="org-right">8-12</td>
<td class="org-left">Linköping</td>
<td class="org-left">2024-05-02 - 2024-05-22</td>
</tr>

<tr>
<td class="org-left">TATA54/TEN1</td>
<td class="org-left">Talteori</td>
<td class="org-right">2024-08-22</td>
<td class="org-right">14-18</td>
<td class="org-left">Linköping</td>
<td class="org-left">2024-07-23 - 2024-08-12</td>
</tr>
</tbody>
</table>
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    </div>
</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">
</div>
<div id="outline-container-org1046eac" class="outline-3">
<h3 id="org1046eac">Kursbok</h3>
<div class="outline-text-3" id="text-org1046eac">
<p>
Kursbok är <a href="https://www.prisjakt.nu/produkt.php?p=8083662">Elementary Number Theory</a> av Kenneth Rosen.
</p>


<figure id="org2a1061a">
<img src="img/Rosen6ed.png" alt="Rosen6ed.png" width="40%">

<figcaption><span class="figure-number">Illustration 1 </span>Elementary Number Theory, Kenneth Rosen</figcaption>
</figure>

<p>
Den sjätte upplagan är den senaste, men det finns flera olika tryckningar,
vilket inte påverkar innehållet.
</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>
<div id="outline-container-org1304ec9" class="outline-4">
<h4 id="org1304ec9">Fritt tillgängligt material</h4>
<div class="outline-text-4" id="text-org1304ec9">
<p>
Följande böcker är fritt tillgängliga på nätet. Kursboken är väldigt grundlig
och täcker kursinnehållet, men det kan ändå vara bra att se olika
framställningar.
</p>
<ul class="org-ul">
<li><a href="https://wstein.org/ent/">Elementary Number Theory</a> av William Stein.</li>
<li><a href="https://hackmat.se/kurser/TATM54/booktot.pdf">Elementary Number Theory</a> av Peter Hackman.</li>
<li><a href="https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Elementary_Number_Theory_(Raji)">An introduction in elementary number theory</a> av Wissam Raji</li>
<li><a href="https://kconrad.math.uconn.edu/blurbs/ugradnumthy/Zinotes.pdf">The Gaussian integers</a> av <a href="https://kconrad.math.uconn.edu/blurbs/">Keith Conrad</a> behandlar just Gaussiska heltal, på ett
föredömligt sätt.</li>
<li>Jag hänvisar till <a href="https://arxiv.org/abs/0809.2139">Constructing the Primitive Roots of Prime Powers</a> av Nathan
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">
<ul class="org-ul">
<li>BAKER. A concise introduction to the theory of numbers.</li>
<li>DAVENPORT. The higher arithmetic.</li>
<li>DICKSON Introduction to the theory of numbers.</li>
<li>HARDY and WRIGHT. Introduction to the theory of numbers. En riktig klassiker,
som även behandlar analytisk talteori. Valda avsnitt är elementära.</li>
<li>IRELAND and ROSEN. A classical introduction to number theory. En lämplig
fortbildning efter denna kurs.</li>
<li>LEVEQUE. Topics in number theory.</li>
<li>SIERPINSKY. Elementary theory of numbers.</li>
<li>SILVERMAN. A friendly introduction to number theory.</li>
</ul>
</div>
</div>
</div>
</section>



<section id="outline-container-org777e787" class="outline-2">
<h2 id="org777e787">Kursinnehåll <a id="orgd3a32bb"></a></h2>
<div class="outline-text-2" id="text-org777e787">
</div>
<div id="outline-container-org8bd2546" class="outline-3">
<h3 id="org8bd2546">Avsnitt av kursboken</h3>
<div class="outline-text-3" id="text-org8bd2546">
<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
precis alla moment ovan, och jag kan komma att berätta om ämnen som inte
behandlas i dessa delar av kursboken. Tentamen kommer dock att testa kunskaper
från just dessa avsnitt.
</p>
</div>

<div id="outline-container-org2c630c7" class="outline-4">
<h4 id="org2c630c7">Rekommenderade uppgifter</h4>
<div class="outline-text-4" id="text-org2c630c7">
</div>
<ul class="org-ul">
<li><a id="org87a9a00"></a>Kap 3<br>
<ul class="org-ul">
<li><a id="org8d58eb7"></a>3.1<br>
<div class="outline-text-6" id="text-org8d58eb7">
<p>
1ab, 2f,6.
</p>
</div>
</li>
<li><a id="org7773607"></a>3.2<br>
<div class="outline-text-6" id="text-org7773607">
<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">
<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">
<p>
1bc, 19*, 20*.
</p>
</div>
</li>
<li><a id="org54380bd"></a>3.5<br>
<div class="outline-text-6" id="text-org54380bd">
<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">
<p>
1cd
</p>
</div>
</li>
</ul>
</li>
<li><a id="org3c52ecc"></a>Kap 4<br>
<ul class="org-ul">
<li><a id="org60d0871"></a>4.1<br>
<div class="outline-text-6" id="text-org60d0871">
<p>
4,5,7ab,9bc.
</p>
</div>
</li>
<li><a id="org6ccedb0"></a>4.2<br>
<div class="outline-text-6" id="text-org6ccedb0">
<p>
1df, 8c, 9d.
</p>
</div>
</li>
<li><a id="org89b0458"></a>4.3<br>
<div class="outline-text-6" id="text-org89b0458">
<p>
3,4.
</p>
</div>
</li>
<li><a id="orgce85497"></a>4.4<br>
<div class="outline-text-6" id="text-orgce85497">
<p>
2ab.
</p>
</div>
</li>
</ul>
</li>
<li><a id="orgce38e81"></a>Kap 5<br>
<ul class="org-ul">
<li><a id="org290a8f0"></a>5.1<br>
<div class="outline-text-6" id="text-org290a8f0">
<p>
4ab.
</p>
</div>
</li>
</ul>
</li>
<li><a id="org079c6dc"></a>Kap 6<br>
<ul class="org-ul">
<li><a id="org87f09e3"></a>6.1<br>
<div class="outline-text-6" id="text-org87f09e3">
<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">
<p>
2,8,12,16ab.
</p>
</div>
</li>

<li><a id="orgffebf1d"></a>6.3<br>
<div class="outline-text-6" id="text-orgffebf1d">
<p>
1d,6,7,22*
</p>
</div>
</li>
</ul>
</li>

<li><a id="orgcfc4d04"></a>Kap 7<br>
<ul class="org-ul">
<li><a id="org614132a"></a>7.1<br>
<div class="outline-text-6" id="text-org614132a">
<p>
2bc,5,8.
</p>
</div>
</li>
<li><a id="org871658a"></a>7.2<br>
<div class="outline-text-6" id="text-org871658a">
<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">
<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">
<p>
1bd,2be,14,22,23,24,30,31.
</p>
</div>
</li>
</ul>
</li>

<li><a id="orgd9614bf"></a>Kap 9<br>
<ul class="org-ul">
<li><a id="org477479c"></a>9.1<br>
<div class="outline-text-6" id="text-org477479c">
<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">
<p>
1d, 2d, 3e, 6.
</p>
</div>
</li>
<li><a id="orgf6dd661"></a>9.3<br>
<div class="outline-text-6" id="text-orgf6dd661">
<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">
<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">
<p>
2,3,10.
</p>
</div>
</li>
<li><a id="orgf9dc898"></a>9.6<br>
<div class="outline-text-6" id="text-orgf9dc898">
<p>
1bcg, 4def, 13*, 14*.
</p>
</div>
</li>
</ul>
</li>

<li><a id="org2d75d4e"></a>Kap 11<br>
<ul class="org-ul">
<li><a id="org762f628"></a>11.1<br>
<div class="outline-text-6" id="text-org762f628">
<p>
1d, 4, 25.
</p>
</div>
</li>
<li><a id="orgd2d41f5"></a>11.2<br>
<div class="outline-text-6" id="text-orgd2d41f5">
<p>
1cd, 2, 4, 5.
</p>
</div>
</li>
<li><a id="orgc0bf6e6"></a>11.3<br>
<div class="outline-text-6" id="text-orgc0bf6e6">
<p>
1ef, 5, 6.
</p>
</div>
</li>
<li><a id="org53fd7ee"></a>11.4<br>
<div class="outline-text-6" id="text-org53fd7ee">
<p>
1, 2, 5, 6.
</p>
</div>
</li>
</ul>
</li>

<li><a id="org4de3188"></a>Kap 12<br>
<ul class="org-ul">
<li><a id="org7b01410"></a>12.2<br>
<div class="outline-text-6" id="text-org7b01410">
<p>
1bf, 2cd, 3c, 4c.
</p>
</div>
</li>
<li><a id="org1aa1c33"></a>12.3<br>
<div class="outline-text-6" id="text-org1aa1c33">
<p>
1c, 2a, 6*, 7.
</p>
</div>
</li>
<li><a id="orgccd3c06"></a>12.4<br>
<div class="outline-text-6" id="text-orgccd3c06">
<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">
<ol class="org-ol">
<li></li>
</ol>
</div>
</li>
</ul>
</li>

<li><a id="org919ec71"></a>Kap 13<br>
<ul class="org-ul">
<li><a id="org4beed34"></a>13.1<br>
<div class="outline-text-6" id="text-org4beed34">
<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">
<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">
<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">
<p>
1c,
  2a, 3def, 4ab, 6de, 8*.
</p>
</div>
</li>
</ul>
</li>

<li><a id="org63d399d"></a>Kap 14<br>
<ul class="org-ul">
<li><a id="org85ae0e8"></a>14.1<br>
<div class="outline-text-6" id="text-org85ae0e8">
<p>
1ac, 12, 13, 17a.
</p>
</div>
</li>
<li><a id="org3dd76f9"></a>14.2<br>
<div class="outline-text-6" id="text-org3dd76f9">
<p>
16ab,
  17bc.
</p>
</div>
</li>
<li><a id="orgff2bf56"></a>14.3<br>
<div class="outline-text-6" id="text-orgff2bf56">
<p>
1bc, 2c
</p>
</div>
</li>
</ul>
</li>
</ul>
</div>
</div>

<div id="outline-container-orgf97dd5f" class="outline-3">
<h3 id="orgf97dd5f">Kort beskrivning av kursinnehållet</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">
<p>
Jag har föreläst enligt följande föreläsningsanteckningar, med vissa utsvävningar. De svenska versionerna är nyare. Några av föreläsningarna tar två tillfällen för att gå igenom.
</p>

<table>


<colgroup>
<col  class="org-right">

<col  class="org-left">

<col  class="org-left">
</colgroup>
<thead>
<tr>
<th scope="col" class="org-right">Nr</th>
<th scope="col" class="org-left">Föreläsning</th>
<th scope="col" class="org-left">Lecture</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-right">0</td>
<td class="org-left"><a href="lectures/swelecture0.pdf">Introduktion till talteori</a></td>
<td class="org-left"><a href="lectures/lecture0.pdf">Introduction to number theory</a></td>
</tr>

<tr>
<td class="org-right">1</td>
<td class="org-left"><a href="lectures/swelecture1.pdf">Heltal, delbarhet</a></td>
<td class="org-left"><a href="lectures/lecture1.pdf">Integers, divisibility</a></td>
</tr>

<tr>
<td class="org-right">2</td>
<td class="org-left"><a href="lectures/swelecture2.pdf">Kongruensräkning</a></td>
<td class="org-left"><a href="lectures/lecture2.pdf">Congruences</a></td>
</tr>

<tr>
<td class="org-right">2b</td>
<td class="org-left"><a href="lectures/swelectureALG.pdf">Fermats och Eulers satser</a></td>
<td class="org-left"><a href="lectures/lecture2b.pdf">Fermat&rsquo;s and Eulers&rsquo;s theorems</a></td>
</tr>

<tr>
<td class="org-right">3</td>
<td class="org-left"><a href="lectures/swelecture3.pdf">Aritmetiska funktioner</a></td>
<td class="org-left"><a href="lectures/lecture3.pdf">Arithmetical functions</a></td>
</tr>

<tr>
<td class="org-right">4</td>
<td class="org-left"><a href="lectures/swelecture4.pdf">Hensel-lyft</a></td>
<td class="org-left"><a href="lectures/lecture4.pdf">Hensel lifting</a></td>
</tr>

<tr>
<td class="org-right">4</td>
<td class="org-left"><a href="lectures/Henselfaktorisering.html">Hensel-faktorisering</a></td>
<td class="org-left">not translated</td>
</tr>

<tr>
<td class="org-right">5</td>
<td class="org-left"><a href="lectures/swelecture5.pdf">Primitiva rötter</a></td>
<td class="org-left"><a href="lectures/lecture5.pdf">Primitive roots</a></td>
</tr>

<tr>
<td class="org-right">6</td>
<td class="org-left"><a href="lectures/swelecture6.pdf">Kvadratiska residyer</a></td>
<td class="org-left"><a href="lectures/lecture6.pdf">Quadratic residues</a></td>
</tr>

<tr>
<td class="org-right">7</td>
<td class="org-left"><a href="lectures/kedjebrakinledning.pdf">Kedjebråk, inledande exempel</a></td>
<td class="org-left">not translated</td>
</tr>

<tr>
<td class="org-right">7</td>
<td class="org-left"><a href="lectures/swelecture7.pdf">Kedjebråk</a></td>
<td class="org-left"><a href="lectures/lecture7.pdf">Continued fractions</a></td>
</tr>

<tr>
<td class="org-right">8</td>
<td class="org-left"><a href="lectures/swelecture8.pdf">Pytagoriska tripplar</a></td>
<td class="org-left"><a href="lectures/lecture8.pdf">Pythagorean triples</a></td>
</tr>

<tr>
<td class="org-right">9</td>
<td class="org-left"><a href="lectures/swelecture9.pdf">Summor av kvadrater</a></td>
<td class="org-left"><a href="lectures/lecture9.pdf">Sums of squares</a></td>
</tr>

<tr>
<td class="org-right">10</td>
<td class="org-left"><a href="lectures/swelecture10.pdf">Pells ekvation</a></td>
<td class="org-left"><a href="lectures/lecture10.pdf">Pell&rsquo;s equation</a></td>
</tr>

<tr>
<td class="org-right">11</td>
<td class="org-left"><a href="lectures/swelecture11.pdf">Gaussiska heltal</a></td>
<td class="org-left"><a href="lectures/lecture11.pdf">The Gaussian Integers</a></td>
</tr>

<tr>
<td class="org-right">12</td>
<td class="org-left">ej översatt</td>
<td class="org-left"><a href="lectures/lecture12.pdf">RSA, Mersenne primes, integer part function, decimal expansion</a></td>
</tr>

<tr>
<td class="org-right">13</td>
<td class="org-left">ej översatt</td>
<td class="org-left"><a href="lectures/lecture13.pdf">Repetition</a></td>
</tr>

<tr>
<td class="org-right">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
</tr>
</tbody>
</table>
</div>
</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">
<table>


<colgroup>
<col  class="org-right">

<col  class="org-left">

<col  class="org-left">

<col  class="org-left">
</colgroup>
<thead>
<tr>
<th scope="col" class="org-right">Datum</th>
<th scope="col" class="org-left">Examinator</th>
<th scope="col" class="org-left">Tentamen</th>
<th scope="col" class="org-left">Lösningar</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-right">2023-08-17</td>
<td class="org-left">Jan Snellman</td>
<td class="org-left"><a href="exams/2023/tenta-TATA54-20230817.pdf">TATA5420230817</a></td>
<td class="org-left"><a href="exams/2023/tenta-TATA54-20230817soln.pdf">TATA5420230817soln</a></td>
</tr>

<tr>
<td class="org-right">2023-06-03</td>
<td class="org-left">Jan Snellman</td>
<td class="org-left"><a href="exams/2023/tenta-TATA54-20230603.pdf">TATA5420230603</a></td>
<td class="org-left"><a href="exams/2023/tenta-TATA54-20230603losn.pdf">TATA5420230603losn</a></td>
</tr>

<tr>
<td class="org-right">2022-08-18</td>
<td class="org-left">Jan Snellman</td>
<td class="org-left"><a href="exams/2022/tenta-TATA54-20220818.pdf">TATA5420220818</a></td>
<td class="org-left">lösning saknas</td>
</tr>

<tr>
<td class="org-right">2021-06-03</td>
<td class="org-left">Jan Snellman</td>
<td class="org-left"><a href="exams/2021/tenta-TATA54-20210603.pdf">TATA5420210603sv</a></td>
<td class="org-left"><a href="exams/2021/tenta-TATA54-20230817soln.pdf">TATA5420210603soln</a></td>
</tr>

<tr>
<td class="org-right">2021-06-03</td>
<td class="org-left">Jan Snellman</td>
<td class="org-left"><a href="exams/2021/tenta-TATA54-20210603_en.pdf">TATA5420210603en</a></td>
<td class="org-left"><a href="exams/2021/tenta-TATA54-20230817soln.pdf">TATA5420210603soln</a></td>
</tr>

<tr>
<td class="org-right">2021-08-19</td>
<td class="org-left">Jan Snellman</td>
<td class="org-left"><a href="exams/2021/tenta-TATA54-20210819.pdf">TATA5420210819</a></td>
<td class="org-left"><a href="exams/2021/tenta-TATA54-20210819soln.pdf">TATA54202108119soln</a></td>
</tr>

<tr>
<td class="org-right">2021-10-22</td>
<td class="org-left">Jan Snellman</td>
<td class="org-left"><a href="exams/2021/tenta-TATA54-20211022.pdf">TATA5420212022</a></td>
<td class="org-left"><a href="exams/2021/tenta-TATA54-20211022soln.pdf">TATA5420211022soln</a></td>
</tr>

<tr>
<td class="org-right">2020-06-04</td>
<td class="org-left">Jan Snellman</td>
<td class="org-left"><a href="exams/2020/tenta-TATA54-20200604.pdf">TATA5420200604</a></td>
<td class="org-left"><a href="exams/2020/tenta-TATA54-20200604soln.pdf">TATA5420200604soln</a></td>
</tr>

<tr>
<td class="org-right">2019-06-04</td>
<td class="org-left">Jan Snellman</td>
<td class="org-left"><a href="exams/2019/tenta-TATA54-20190604.pdf">TATA5420190604</a></td>
<td class="org-left"><a href="exams/2019/tenta-TATA54-20190604soln.pdf">TATA5420190604soln</a></td>
</tr>

<tr>
<td class="org-right">2019-11-01</td>
<td class="org-left">Jan Snellman</td>
<td class="org-left"><a href="exams/2019/tenta-TATA54-20191101.pdf">TATA5420191101</a></td>
<td class="org-left"><a href="exams/2019/tenta-TATA54-20191101soln.pdf">TATA5420191101soln</a></td>
</tr>

<tr>
<td class="org-right">2018-06-07</td>
<td class="org-left">Jan Snellman</td>
<td class="org-left"><a href="exams/2018/tenta-TATA54-20180607.pdf">TATA5420180607</a></td>
<td class="org-left"><a href="exams/2018/tenta-TATA54-20180607soln.pdf">TATA5420180607soln</a></td>
</tr>

<tr>
<td class="org-right">2018-03-12</td>
<td class="org-left">Jan Snellman</td>
<td class="org-left"><a href="exams/2018/tenta-TATA54-20180312.pdf">TATA5420180312</a></td>
<td class="org-left"><a href="exams/2018/tenta-TATA54-20180312soln.pdf">TATA5420180312soln</a></td>
</tr>

<tr>
<td class="org-right">2017-03-13</td>
<td class="org-left">Jan Snellman</td>
<td class="org-left"><a href="exams/2017/tenta-TATA54-20170313.pdf">TATA5420170313</a></td>
<td class="org-left"><a href="exams/2017/tenta-TATA54-20170313soln.pdf">TATA5420170313soln</a></td>
</tr>

<tr>
<td class="org-right">2017-06-08</td>
<td class="org-left">Jan Snellman</td>
<td class="org-left"><a href="exams/2017/tenta-TATA54-20170608.pdf">TATA5420170608</a></td>
<td class="org-left"><a href="exams/2017/tenta-TATA54-20170608soln.pdf">TATA5420170608soln</a></td>
</tr>

<tr>
<td class="org-right">2017-08-26</td>
<td class="org-left">Jan Snellman</td>
<td class="org-left"><a href="exams/2017/tenta-TATA54-20170826.pdf">TATA5420170826</a></td>
<td class="org-left"><a href="exams/2017/tenta-TATA54-20170826soln.pdf">TATA5420170826soln</a></td>
</tr>

<tr>
<td class="org-right">2016</td>
<td class="org-left">Leif Melkersson</td>
<td class="org-left"><a href="exams/2016/tam.pdf">exams/2016/tam.pdf</a></td>
<td class="org-left"><a href="exams/2016/stam.pdf">exams/2016/stam.pdf</a></td>
</tr>

<tr>
<td class="org-right">2016</td>
<td class="org-left">Leif Melkersson</td>
<td class="org-left"><a href="exams/2016/tau.pdf">exams/2016/tau.pdf</a></td>
<td class="org-left"><a href="exams/2016/stau.pdf">exams/2016/stau.pdf</a></td>
</tr>

<tr>
<td class="org-right">2016</td>
<td class="org-left">Leif Melkersson</td>
<td class="org-left"><a href="exams/2016/taj.pdf">exams/2016/taj.pdf</a></td>
<td class="org-left"><a href="exams/2016/staj.pdf">exams/2016/staj.pdf</a></td>
</tr>

<tr>
<td class="org-right">2015</td>
<td class="org-left">Leif Melkersson</td>
<td class="org-left"><a href="exams/2015/tja.pdf">exams/2015/tja.pdf</a></td>
<td class="org-left"><a href="exams/2015/tjas.pdf">exams/2015/tjas.pdf</a></td>
</tr>

<tr>
<td class="org-right">2015</td>
<td class="org-left">Leif Melkersson</td>
<td class="org-left"><a href="exams/2015/tju.pdf">exams/2015/tju.pdf</a></td>
<td class="org-left"><a href="exams/2015/tjus.pdf">exams/2015/tjus.pdf</a></td>
</tr>

<tr>
<td class="org-right">2015</td>
<td class="org-left">Leif Melkersson</td>
<td class="org-left"><a href="exams/2015/tma.pdf">exams/2015/tma.pdf</a></td>
<td class="org-left"><a href="exams/2015/tmas.pdf">exams/2015/tmas.pdf</a></td>
</tr>

<tr>
<td class="org-right">2014</td>
<td class="org-left">Leif Melkersson</td>
<td class="org-left"><a href="exams/2014/rieja.pdf">exams/2014/rieja.pdf</a></td>
<td class="org-left"><a href="exams/2014/sv1408.pdf">exams/2014/sv1408.pdf</a></td>
</tr>

<tr>
<td class="org-right">2013</td>
<td class="org-left">Leif Melkersson</td>
<td class="org-left"><a href="exams/2013/tenta.pdf">exams/2013/tenta.pdf</a></td>
<td class="org-left"><a href="exams/2013/tentasv.pdf">exams/2013/tentasv.pdf</a></td>
</tr>

<tr>
<td class="org-right">2013</td>
<td class="org-left">Leif Melkersson</td>
<td class="org-left"><a href="exams/2013/tena.pdf">exams/2013/tena.pdf</a></td>
<td class="org-left"><a href="exams/2013/sv1308.pdf">exams/2013/sv1308.pdf</a></td>
</tr>

<tr>
<td class="org-right">2012</td>
<td class="org-left">Leif Melkersson</td>
<td class="org-left"><a href="exams/2012/numm.pdf">exams/2012/numm.pdf</a></td>
<td class="org-left"><a href="exams/2013/numms.pdf">exams/2013/numms.pdf</a></td>
</tr>
</tbody>
</table>
</div>
</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">
</div>
<div id="outline-container-org0e9470f" class="outline-3">
<h3 id="org0e9470f">SageMath</h3>
<div class="outline-text-3" id="text-org0e9470f">
<p>
Jag kommer att använda datoralgebraprogrammet <a href="https://www.sagemath.org/">SageMath</a> för att beräkna lite större exempel.
Om ni vill experimentera på egen hand kan ni enkelt <a href="https://doc.sagemath.org/html/en/installation/index.html">installera programmet på er dator</a>,
och köra de kodsnuttar nedan som jag utvunnit från mina föreläsningsanteckningar.
</p>

<p>
Man kan också köra SageMath på nätet via <a href="https://cocalc.com/">CoCalc</a>.
</p>

<p>
Ett tredje alternativ, enkelt och flärdfritt, är att mata in sin kod till <a href="https://sagecell.sagemath.org/">SageCell</a>.
</p>
</div>
</div>
<div id="outline-container-org4e01f4d" class="outline-3">
<h3 id="org4e01f4d">Kod från vissa föreläsningar</h3>
<div class="outline-text-3" id="text-org4e01f4d">
<ul class="org-ul">
<li><a href="labs/lecture0.html">Föreläsning 0</a></li>
<li><a href="labs/lecture1.html">Föreläsning 1</a></li>
<li><a href="labs/lecture2.html">Föreläsning 2</a></li>
<li><a href="labs/lecture3.html">Föreläsning 3</a></li>
<li><a href="labs/lecture4.html">Föreläsning 4</a></li>
<li><a href="labs/lecture5.html">Föreläsning 5</a></li>
</ul>
</div>
</div>
<div id="outline-container-org771ae33" class="outline-3">
<h3 id="org771ae33">Laborationer</h3>
<div class="outline-text-3" id="text-org771ae33">
    Show full blame