diff --git a/TATA54/TENTOR/#tenta-TATA54-20240822-skiss.org# b/TATA54/TENTOR/#tenta-TATA54-20240822-skiss.org# index fb6577bc98f1d0f82361afd70f64f8335ce90d4c..78b46aabe1a441043a536db1a1dac7a9a01d6df1 100644 --- a/TATA54/TENTOR/#tenta-TATA54-20240822-skiss.org# +++ b/TATA54/TENTOR/#tenta-TATA54-20240822-skiss.org# @@ -41,20 +41,19 @@ def H_L_tree(f, p: int, r: int): #+end_src -#+begin_src sage - :session - p = 5 - k = 4 - q = p^k - R.<x> = ZZ[] - f = x^4 + 2*x + 3 - [(s,f.roots(Integers(p^s),multiplicities=False)) for s in range(k+1)] - df = f.diff() - df, df(3) +#+begin_src sage :session + p = 5 + k = 4 + q = p^k + R.<x> = ZZ[] + f = x^4 + 2*x + 4 + [(s,f.roots(Integers(p^s),multiplicities=False)) for s in range(k+1)] + df = f.diff() + df, df(3) #+end_src #+RESULTS: -: [(0, [0]), (1, [3]), (2, []), (3, []), (4, [])] +: [(0, [0]), (1, []), (2, []), (3, []), (4, [])] : (4*x^3 + 2, 110) #+begin_src sage :session :results file :file "nu1.png" @@ -78,17 +77,16 @@ def H_L_tree(f, p: int, r: int): Parametrisera med lutning, rationell punkt (-1,0) -#+begin_src sage - :session - var('s,t,x,y') - kurva = x^2 + 2*y^2-1 - linje = y - t*(x+1) - soln = solve([kurva,linje],[x,y]) - soln - rp = soln[0] - rp - soln2 = solve([linje],[t]) - soln2 +#+begin_src sage :session +var('s,t,x,y') +kurva = x^2 + 2*y^2-1 +linje = y - t*(x+1) +soln = solve([kurva,linje],[x,y]) +soln +rp = soln[0] +rp +soln2 = solve([linje],[t]) +soln2 #+end_src #+RESULTS: @@ -106,12 +104,7 @@ parametric_plot((rp[0].rhs(),rp[1].rhs()), (t,+epsi,1/sqrt(7) -epsi) ) [[file:nu2.png]] ** U3 -#+begin_src sage :session - legendre_symbol(187,23) -#+end_src -#+RESULTS: -: 1 ** U4 #+begin_src latex @@ -122,8 +115,7 @@ parametric_plot((rp[0].rhs(),rp[1].rhs()), (t,+epsi,1/sqrt(7) -epsi) ) \] #+end_src -#+begin_s -rc sage :session +#+begin_src sage :session n=20 [(k,number_of_divisors(k),floor(n/k)) for k in range(1,n+1)] @@ -138,7 +130,6 @@ def w(n): #+end_src #+RESULTS: - #+begin_example [(1, 1, 20), (2, 2, 10), @@ -183,8 +174,6 @@ def w(n): #+end_example ** U5 - - #+begin_src latex #+end_src @@ -198,8 +187,7 @@ Hur mÃ¥nga har #+end_export -#+begin_src s -age :session +#+begin_src sage :session p = 23 a = 11*17 a @@ -210,6 +198,9 @@ f = x^2 -23 f.roots(Integers(187),multiplicities=False) f.roots(Integers(11),multiplicities=False) f.roots(Integers(17),multiplicities=False) + +g = x^2 -187 +g.roots(Integers(23),multiplicities=False) #+end_src #+RESULTS: @@ -218,6 +209,7 @@ f.roots(Integers(17),multiplicities=False) : [] : [10, 1] : [] +: [16, 7] ** U7 #+begin_src latex @@ -240,6 +232,7 @@ r=p/q cf = continued_fraction(r) cf best = cf.convergent(2) +best fel = abs(p/q - best) "kedjebrÃ¥kapprox fel", fel @@ -254,6 +247,7 @@ for j in range(2,q): #+RESULTS: #+begin_example [0; 1, 58, 2] +58/59 ('kedjebrÃ¥kapprox fel', 1/7021) 2 0.483193277310924 0.0168067226890756 0.000142429853297251 3 0.316526610644258 0.0168067226890756 0.000142429853297251 diff --git a/TATA54/TENTOR/.#tenta-TATA54-20240822-skiss.org b/TATA54/TENTOR/.#tenta-TATA54-20240822-skiss.org index 98366aef3653dfbec8bc58972ce3ac5fe43df19f..bf5a20e21c959bedba0523bb45bfed243411b667 120000 --- a/TATA54/TENTOR/.#tenta-TATA54-20240822-skiss.org +++ b/TATA54/TENTOR/.#tenta-TATA54-20240822-skiss.org @@ -1 +1 @@ -jansn@jansn19-thinkpad.130192:1724236765 \ No newline at end of file +jansn@jansn19-thinkpad.315947:1724236765 \ No newline at end of file diff --git a/TATA54/TENTOR/tenta-TATA54-20240822-losning.log b/TATA54/TENTOR/tenta-TATA54-20240822-losning.log index e9be7f5ee43fd9a40629597210eda39e41fce46f..79a399caeb3a69a5c9af6328a2559d0c1bc12bc2 100644 --- a/TATA54/TENTOR/tenta-TATA54-20240822-losning.log +++ b/TATA54/TENTOR/tenta-TATA54-20240822-losning.log @@ -1,9 +1,12 @@ -This is pdfTeX, Version 3.141592653-2.6-1.40.25 (TeX Live 2023/Fedora 40) (preloaded format=pdflatex 2024.8.22) 22 AUG 2024 20:38 +This is pdfTeX, Version 3.141592653-2.6-1.40.25 (TeX Live 2023/Fedora 40) (preloaded format=pdflatex 2024.8.21) 23 AUG 2024 12:53 entering extended mode restricted \write18 enabled. + file:line:error style messages enabled. %&-line parsing enabled. -**\nonstopmode\input tenta-TATA54-20240822-losning.tex +**tenta-TATA54-20240822-losning.tex (./tenta-TATA54-20240822-losning.tex +LaTeX2e <2022-11-01> patch level 1 +L3 programming layer <2023-02-22> (/usr/share/texlive/texmf-dist/tex/latex/base/article.cls Document Class: article 2022/07/02 v1.4n Standard LaTeX document class (/usr/share/texlive/texmf-dist/tex/latex/base/size10.clo @@ -131,7 +134,7 @@ Package: inputenc 2021/02/14 v1.3d Input encoding file Package: babel 2023/02/13 3.86 The Babel package \babel@savecnt=\count271 \U@D=\dimen150 -\l@unhyphenated=\language3 +\l@unhyphenated=\language85 (/usr/share/texlive/texmf-dist/tex/generic/babel/txtbabel.def) \bbl@readstream=\read2 @@ -139,21 +142,13 @@ Package: babel 2023/02/13 3.86 The Babel package (/usr/share/texlive/texmf-dist/tex/generic/babel-swedish/swedish.ldf Language: swedish 2021/02/06 v2.3e Swedish support from the babel system - - -Package babel Warning: No hyphenation patterns were preloaded for -(babel) the language 'Swedish' into the format. -(babel) Please, configure your TeX system to add them and -(babel) rebuild the format. Now I will use the patterns -(babel) preloaded for \language=0 instead on input line 49. - -Package babel Info: Hyphen rules for 'swedish' set to \l@english -(babel) (\language0). Reported on input line 50. Package babel Info: Making " an active character on input line 90. -)) (/usr/share/texlive/texmf-dist/tex/generic/babel/locale/sv/babel-swedish.tex +)) +(/usr/share/texlive/texmf-dist/tex/generic/babel/locale/sv/babel-swedish.tex Package babel Info: Importing font and identification data for swedish (babel) from babel-sv.ini. Reported on input line 11. -) (/usr/share/texlive/texmf-dist/tex/latex/l3backend/l3backend-pdftex.def +) +(/usr/share/texlive/texmf-dist/tex/latex/l3backend/l3backend-pdftex.def File: l3backend-pdftex.def 2023-01-16 L3 backend support: PDF output (pdfTeX) \l__color_backend_stack_int=\count273 \l__pdf_internal_box=\box53 @@ -187,13 +182,13 @@ LaTeX Font Info: Trying to load font information for U+msb on input line 35. (/usr/share/texlive/texmf-dist/tex/latex/amsfonts/umsb.fd File: umsb.fd 2013/01/14 v3.01 AMS symbols B ) -Overfull \hbox (9.70393pt too wide) in paragraph at lines 89--94 -[]\OT1/cmr/bx/n/10 L[]osning: \OT1/cmr/m/n/10 Ked-je-br^^Waksutvecklingen []ar -$117\OML/cmm/m/it/10 =\OT1/cmr/m/n/10 118 = [0; 1\OML/cmm/m/it/10 ; \OT1/cmr/m/ -n/10 58\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 2]$ med kon-ver-gen-ter $0\OML/cmm/m/ -it/10 ; \OT1/cmr/m/n/10 1\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 58\OML/cmm/m/it/10 -=\OT1/cmr/m/n/10 59\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 117\OML/cmm/m/it/10 =\OT1 -/cmr/m/n/10 118$. +Overfull \hbox (9.70393pt too wide) in paragraph at lines 86--91 +[]\OT1/cmr/bx/n/10 L[]osning: \OT1/cmr/m/n/10 Ked-jebr^^Waksutvecklingen []ar $ +117\OML/cmm/m/it/10 =\OT1/cmr/m/n/10 118 = [0; 1\OML/cmm/m/it/10 ; \OT1/cmr/m/n +/10 58\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 2]$ med kon-ver-gen-ter $0\OML/cmm/m/i +t/10 ; \OT1/cmr/m/n/10 1\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 58\OML/cmm/m/it/10 = +\OT1/cmr/m/n/10 59\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 117\OML/cmm/m/it/10 =\OT1/ +cmr/m/n/10 118$. 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PDF statistics: 63 PDF objects out of 1000 (max. 8388607) 37 compressed objects within 1 object stream diff --git a/TATA54/TENTOR/tenta-TATA54-20240822-losning.pdf b/TATA54/TENTOR/tenta-TATA54-20240822-losning.pdf index 34f831aaf168f2a7b0660a02384565b351b6565c..02084b171957c977b9f32bab844b790b7a4fa52c 100644 Binary files a/TATA54/TENTOR/tenta-TATA54-20240822-losning.pdf and b/TATA54/TENTOR/tenta-TATA54-20240822-losning.pdf differ diff --git a/TATA54/TENTOR/tenta-TATA54-20240822-losning.tex b/TATA54/TENTOR/tenta-TATA54-20240822-losning.tex index 0c1a8b6a90798b77ca1b94f48d484fac3ba0e282..32038410948e530975f0ec404fef530bfc6e8009 100644 --- a/TATA54/TENTOR/tenta-TATA54-20240822-losning.tex +++ b/TATA54/TENTOR/tenta-TATA54-20240822-losning.tex @@ -36,11 +36,8 @@ Examinator: Jan Snellman} x^4 +2x +4 \equiv 0 \mod 625 ? \end{displaymath} - \soln Kalla polynomet för \(f(x)\). Modulo 5 finns den enda lösningen - \(x \equiv 3 \mod 5\). Eftersom \(f'(3)=110 \equiv 0 \mod 5\) - sÃ¥ lyfter inga eller alla av \(3 + 5s\), \(s=0,1,2,3,4\), - till lösningar modulo 25. Eftersom \(f(3)=110 \not \equiv 0\) - sÃ¥ finns inga lösningar modulo 25, och alltsÃ¥ inga modulo 625. + \soln Kalla polynomet för \(f(x)\). Modulo 5 finns + inga lösningar; alltsÃ¥ finns inga lösningar modulo \(5^4\). \item Hitta alla rationella punkter pÃ¥ kurvan \begin{displaymath} diff --git a/TATA54/TENTOR/tenta-TATA54-20240822-skiss.org b/TATA54/TENTOR/tenta-TATA54-20240822-skiss.org index 922d77621f673301ce4834871afbf2d5031851ca..5916c783d31f6e331aba14914029d0661e964f81 100644 --- a/TATA54/TENTOR/tenta-TATA54-20240822-skiss.org +++ b/TATA54/TENTOR/tenta-TATA54-20240822-skiss.org @@ -46,7 +46,7 @@ def H_L_tree(f, p: int, r: int): k = 4 q = p^k R.<x> = ZZ[] - f = x^4 + 2*x + 3 + f = x^4 + 2*x + 4 [(s,f.roots(Integers(p^s),multiplicities=False)) for s in range(k+1)] df = f.diff() df, df(3) diff --git a/homepage/exams/2024/tenta-TATA54-20240822-losning.pdf b/homepage/exams/2024/tenta-TATA54-20240822-losning.pdf index 34f831aaf168f2a7b0660a02384565b351b6565c..02084b171957c977b9f32bab844b790b7a4fa52c 100644 Binary files a/homepage/exams/2024/tenta-TATA54-20240822-losning.pdf and b/homepage/exams/2024/tenta-TATA54-20240822-losning.pdf differ diff --git a/homepage/sitemap.org b/homepage/sitemap.org index 89f01736841522bb59ce8f53b542657d9adff995..c1e5cb859f16e9669b647fa5cb9e82129c8944a0 100644 --- a/homepage/sitemap.org +++ b/homepage/sitemap.org @@ -1,8 +1,10 @@ #+TITLE: Kurshemsida +- [[file:newlectures/newlecture.org][Föreläsningar i Talteori]] +- [[file:newlectures/new-lect-0.org][Talteori översiktsföreläsning]] - [[file:index.org][TATA54 Talteori]] -- [[file:senaste-nytt.org][senaste-nytt]] - [[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]] @@ -10,6 +12,4 @@ - [[file:labs/lecture1.org][lecture1]] - [[file:labs/lecture0.org][lecture0]] - [[file:labs/kedjebraklab.org][Sagemath-övningar pÃ¥ kedjebrÃ¥k]] -- [[file:labs/HenselLyftLabHT2023.org][SageMath-övningar pÃ¥ Hensellyft, primitiva rötter, och KRS]] -- [[file:newlectures/newlecture.org][Föreläsningar i Talteori]] -- [[file:newlectures/new-lect-0.org][Talteori översiktsföreläsning]] \ No newline at end of file +- [[file:labs/HenselLyftLabHT2023.org][SageMath-övningar pÃ¥ Hensellyft, primitiva rötter, och KRS]] \ No newline at end of file diff --git a/public/exams/2024/tenta-TATA54-20240822-losning.pdf b/public/exams/2024/tenta-TATA54-20240822-losning.pdf index 34f831aaf168f2a7b0660a02384565b351b6565c..02084b171957c977b9f32bab844b790b7a4fa52c 100644 Binary files a/public/exams/2024/tenta-TATA54-20240822-losning.pdf and b/public/exams/2024/tenta-TATA54-20240822-losning.pdf differ diff --git a/public/index.html b/public/index.html index cdfbbecdfbab232bd1613a451bec8cce85e66290..aabbb11a77237462e93106ef777fdbf4397d7e2d 100644 --- a/public/index.html +++ b/public/index.html @@ -1,7 +1,7 @@ <!DOCTYPE html> <html lang="sv"> <head> -<!-- 2024-08-22 --> +<!-- 2024-08-23 --> <meta charset="utf-8" /> <meta name="viewport" content="width=device-width, initial-scale=1" /> <title>TATA54 Talteori</title> @@ -63,151 +63,151 @@ <h2>Innehåll</h2> <div id="text-table-of-contents" role="doc-toc"> <ul> -<li><a href="#orgb8be38a">Kurshemsida för TATA54, Talteori </a> +<li><a href="#org8cf611f">Kurshemsida för TATA54, Talteori </a> <ul> -<li><a href="#org46c8838">ÄmnesomrÃ¥de</a></li> -<li><a href="#org0536e03">Poäng</a></li> -<li><a href="#org483cd31">Examinator</a></li> -<li><a href="#org79caf1d">Schema</a></li> -<li><a href="#org3280174">Examination</a></li> +<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> </ul> </li> -<li><a href="#orge4d1d7b">Allra senaste nytt VT2024 </a> +<li><a href="#orgda7b5cb">Allra senaste nytt VT2024 </a> <ul> -<li><a href="#org79df182">2024-08-22</a></li> -<li><a href="#org4de2404">2024-06-05</a></li> -<li><a href="#org7866ed4">2024-06-01</a></li> -<li><a href="#org896f14e">2024-05-18</a></li> -<li><a href="#org016a4e1">2024-05-16</a></li> -<li><a href="#org4232b8e">2024-05-13</a></li> -<li><a href="#org95a2714">2024-05-06</a></li> -<li><a href="#orgcae408e">2024-04-29</a></li> -<li><a href="#org9f9d6f3">2024-04-23</a></li> -<li><a href="#orgb23df4f">2024-04-22</a></li> -<li><a href="#org6bf16cd">2024-04-14</a> +<li><a href="#org3caa1c9">2024-08-22</a></li> +<li><a href="#org5787ffb">2024-06-05</a></li> +<li><a href="#org820103f">2024-06-01</a></li> +<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> <ul> -<li><a href="#orgfb7845d">Uppgifter att räkna till nästa gÃ¥ng</a></li> -<li><a href="#orgef7eb4d">Datorlaboration</a></li> +<li><a href="#org1198084">Uppgifter att räkna till nästa gÃ¥ng</a></li> +<li><a href="#org87e8642">Datorlaboration</a></li> </ul> </li> -<li><a href="#org4a80012">2024-04-07</a> +<li><a href="#orgff00c35">2024-04-07</a> <ul> -<li><a href="#org3f1c3a4">Uppgifter att räkna till nästa gÃ¥ng</a></li> -<li><a href="#orgd77ff3b">Beviset för kvadratisk reciprocitet</a></li> +<li><a href="#org10c6215">Uppgifter att räkna till nästa gÃ¥ng</a></li> +<li><a href="#orgcb6d72a">Beviset för kvadratisk reciprocitet</a></li> </ul> </li> -<li><a href="#orgb250740">2024-04-02</a></li> -<li><a href="#orged4ff0b">2024-03-11</a></li> -<li><a href="#org0de71ab">2024-03-06</a></li> -<li><a href="#org84eda8d">2024-03-05</a></li> -<li><a href="#orgea6ed65">2024-02-29</a></li> -<li><a href="#org823f5e2">2024-02-20</a></li> -<li><a href="#org1c24ff1">2024-02-12</a></li> -<li><a href="#org499023d">2024-02-07</a></li> -<li><a href="#orgf683b42">2024-01-30</a> +<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> <ul> -<li><a href="#org53dcc9b">Tvillingfria primtal</a></li> +<li><a href="#orge760dad">Tvillingfria primtal</a></li> </ul> </li> -<li><a href="#orgd22b4e6">2024-01-23</a></li> -<li><a href="#org5900f63">2024-01-16</a></li> +<li><a href="#org488e68b">2024-01-23</a></li> +<li><a href="#org96d1546">2024-01-16</a></li> </ul> </li> -<li><a href="#org4f543bd">Kurslitteratur </a> +<li><a href="#org7fb0ecc">Kurslitteratur </a> <ul> -<li><a href="#org09cac9a">Kursbok</a></li> -<li><a href="#orgdf2c024">Bredvidläsning</a> +<li><a href="#org1046eac">Kursbok</a></li> +<li><a href="#orgb1f71c0">Bredvidläsning</a> <ul> -<li><a href="#org9934079">Fritt tillgängligt material</a></li> -<li><a href="#org486a906">Andra lämpliga böcker</a></li> +<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="#org83d546e">KursinnehÃ¥ll </a> +<li><a href="#org777e787">KursinnehÃ¥ll </a> <ul> -<li><a href="#org34795a7">Avsnitt av kursboken</a> +<li><a href="#org8bd2546">Avsnitt av kursboken</a> <ul> -<li><a href="#org10138de">Rekommenderade uppgifter </a></li> +<li><a href="#org5c92b21">Rekommenderade uppgifter </a></li> </ul> </li> -<li><a href="#orgab0c2e2">Kort beskrivning av kursinnehÃ¥llet</a></li> +<li><a href="#orgf97dd5f">Kort beskrivning av kursinnehÃ¥llet</a></li> </ul> </li> -<li><a href="#org67ef94b">Föreläsningar </a></li> -<li><a href="#org9e66246">Tentor </a></li> -<li><a href="#orgf236219">Datorlaborationer </a> +<li><a href="#orgb1afa66">Föreläsningar </a></li> +<li><a href="#orgd9a1a3d">Tentor </a></li> +<li><a href="#orgaa8bfe8">Datorlaborationer </a> <ul> -<li><a href="#org7a98c02">SageMath</a></li> -<li><a href="#org38724a4">Kod frÃ¥n vissa föreläsningar</a></li> -<li><a href="#org80ba8f8">Laborationer</a> +<li><a href="#org0e9470f">SageMath</a></li> +<li><a href="#org4e01f4d">Kod frÃ¥n vissa föreläsningar</a></li> +<li><a href="#org771ae33">Laborationer</a> <ul> -<li><a href="#org4bb0ea2">Hensellyft, Primitiva rötter, Kinesiska restsatsen</a></li> -<li><a href="#org4f8b714">KedjebrÃ¥k</a></li> +<li><a href="#orge16b88e">Hensellyft, Primitiva rötter, Kinesiska restsatsen</a></li> +<li><a href="#org254ad94">KedjebrÃ¥k</a></li> </ul> </li> </ul> </li> -<li><a href="#org65b020a">Tidigare Ã¥r </a> +<li><a href="#orgcab2c84">Tidigare Ã¥r </a> <ul> -<li><a href="#org477262d">TATA54 Anteckningar frÃ¥n tidigare Ã¥r</a> +<li><a href="#org5db15ec">TATA54 Anteckningar frÃ¥n tidigare Ã¥r</a> <ul> -<li><a href="#org780ed90">2023</a></li> -<li><a href="#org780092f">2021</a></li> -<li><a href="#org2b03280">2020</a></li> -<li><a href="#org9b6101f">2019</a></li> -<li><a href="#orgba3d96f">2018</a></li> -<li><a href="#org45290d5">2017</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="#org22888c0">Index</a></li> +<li><a href="#org27e935f">Index</a></li> </ul> </div> </nav> -<section id="outline-container-orgb8be38a" class="outline-2"> -<h2 id="orgb8be38a">Kurshemsida för TATA54, Talteori <a id="orgf086129"></a></h2> -<div class="outline-text-2" id="text-orgb8be38a"> +<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-org46c8838" class="outline-3"> -<h3 id="org46c8838">ÄmnesomrÃ¥de</h3> -<div class="outline-text-3" id="text-org46c8838"> +<div id="outline-container-orgd386ff5" class="outline-3"> +<h3 id="orgd386ff5">ÄmnesomrÃ¥de</h3> +<div class="outline-text-3" id="text-orgd386ff5"> <p> Matematik </p> </div> </div> -<div id="outline-container-org0536e03" class="outline-3"> -<h3 id="org0536e03">Poäng</h3> -<div class="outline-text-3" id="text-org0536e03"> +<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-org483cd31" class="outline-3"> -<h3 id="org483cd31">Examinator</h3> -<div class="outline-text-3" id="text-org483cd31"> +<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-org79caf1d" class="outline-3"> -<h3 id="org79caf1d">Schema</h3> -<div class="outline-text-3" id="text-org79caf1d"> +<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/ri167XQQ538Z50Qm07065gZ6y2Y7306Q6Y43Y1.html">TimeEdit</a> </p> </div> </div> -<div id="outline-container-org3280174" class="outline-3"> -<h3 id="org3280174">Examination</h3> -<div class="outline-text-3" id="text-org3280174"> +<div id="outline-container-orgcbec67a" class="outline-3"> +<h3 id="orgcbec67a">Examination</h3> +<div class="outline-text-3" id="text-orgcbec67a"> <p> Skriftlig tentamen. </p> @@ -260,21 +260,21 @@ Skriftlig tentamen. </div> </div> </section> -<section id="outline-container-orge4d1d7b" class="outline-2"> -<h2 id="orge4d1d7b">Allra senaste nytt VT2024 <a id="org3ff915a"></a></h2> -<div class="outline-text-2" id="text-orge4d1d7b"> +<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"> </div> -<div id="outline-container-org79df182" class="outline-3"> -<h3 id="org79df182">2024-08-22</h3> -<div class="outline-text-3" id="text-org79df182"> +<div id="outline-container-org3caa1c9" class="outline-3"> +<h3 id="org3caa1c9">2024-08-22</h3> +<div class="outline-text-3" id="text-org3caa1c9"> <p> <a href="exams/2024/tenta-TATA54-20240822-losning.pdf">Lösningar</a> till <a href="exams/2024/tenta-TATA54-20240822.pdf">dagens tenta</a> finns nu att beskÃ¥da. </p> </div> </div> -<div id="outline-container-org4de2404" class="outline-3"> -<h3 id="org4de2404">2024-06-05</h3> -<div class="outline-text-3" id="text-org4de2404"> +<div id="outline-container-org5787ffb" class="outline-3"> +<h3 id="org5787ffb">2024-06-05</h3> +<div class="outline-text-3" id="text-org5787ffb"> <p> Jag har rättat era tentor; bra resultat, de flesta klarade sig! Resultaten kommer sannolikt att registreras idag, och tentorna kan hämtas p MAIs expedition f.o.m. @@ -282,18 +282,18 @@ nästa vecka. </p> </div> </div> -<div id="outline-container-org7866ed4" class="outline-3"> -<h3 id="org7866ed4">2024-06-01</h3> -<div class="outline-text-3" id="text-org7866ed4"> +<div id="outline-container-org820103f" class="outline-3"> +<h3 id="org820103f">2024-06-01</h3> +<div class="outline-text-3" id="text-org820103f"> <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-org896f14e" class="outline-3"> -<h3 id="org896f14e">2024-05-18</h3> -<div class="outline-text-3" id="text-org896f14e"> +<div id="outline-container-orgb795cef" class="outline-3"> +<h3 id="orgb795cef">2024-05-18</h3> +<div class="outline-text-3" id="text-orgb795cef"> <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> @@ -304,13 +304,13 @@ 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="#orge3aa510">längre ned pÃ¥ denna sida</a>. +Rosen, finns <a href="#orgd3a32bb">längre ned pÃ¥ denna sida</a>. </p> </div> </div> -<div id="outline-container-org016a4e1" class="outline-3"> -<h3 id="org016a4e1">2024-05-16</h3> -<div class="outline-text-3" id="text-org016a4e1"> +<div id="outline-container-orgef16020" class="outline-3"> +<h3 id="orgef16020">2024-05-16</h3> +<div class="outline-text-3" id="text-orgef16020"> <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. @@ -321,35 +321,35 @@ Tentamen skall kunna bli av utan problem! </p> </div> </div> -<div id="outline-container-org4232b8e" class="outline-3"> -<h3 id="org4232b8e">2024-05-13</h3> -<div class="outline-text-3" id="text-org4232b8e"> +<div id="outline-container-orgd3edf39" class="outline-3"> +<h3 id="orgd3edf39">2024-05-13</h3> +<div class="outline-text-3" id="text-orgd3edf39"> <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-org95a2714" class="outline-3"> -<h3 id="org95a2714">2024-05-06</h3> -<div class="outline-text-3" id="text-org95a2714"> +<div id="outline-container-orgbb2c19c" class="outline-3"> +<h3 id="orgbb2c19c">2024-05-06</h3> +<div class="outline-text-3" id="text-orgbb2c19c"> <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-orgcae408e" class="outline-3"> -<h3 id="orgcae408e">2024-04-29</h3> -<div class="outline-text-3" id="text-orgcae408e"> +<div id="outline-container-org6916c72" class="outline-3"> +<h3 id="org6916c72">2024-04-29</h3> +<div class="outline-text-3" id="text-org6916c72"> <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-org9f9d6f3" class="outline-3"> -<h3 id="org9f9d6f3">2024-04-23</h3> -<div class="outline-text-3" id="text-org9f9d6f3"> +<div id="outline-container-org2fc933f" class="outline-3"> +<h3 id="org2fc933f">2024-04-23</h3> +<div class="outline-text-3" id="text-org2fc933f"> <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 @@ -362,9 +362,9 @@ beskrivningen kan visas med induktion. </p> </div> </div> -<div id="outline-container-orgb23df4f" class="outline-3"> -<h3 id="orgb23df4f">2024-04-22</h3> -<div class="outline-text-3" id="text-orgb23df4f"> +<div id="outline-container-org0e96bfa" class="outline-3"> +<h3 id="org0e96bfa">2024-04-22</h3> +<div class="outline-text-3" id="text-org0e96bfa"> <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). @@ -372,21 +372,21 @@ Till pÃ¥ fredag 12.4.5b, 12.4.6b </p> </div> </div> -<div id="outline-container-org6bf16cd" class="outline-3"> -<h3 id="org6bf16cd">2024-04-14</h3> -<div class="outline-text-3" id="text-org6bf16cd"> +<div id="outline-container-org796ce06" class="outline-3"> +<h3 id="org796ce06">2024-04-14</h3> +<div class="outline-text-3" id="text-org796ce06"> </div> -<div id="outline-container-orgfb7845d" class="outline-4"> -<h4 id="orgfb7845d">Uppgifter att räkna till nästa gÃ¥ng</h4> -<div class="outline-text-4" id="text-orgfb7845d"> +<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"> <p> 12.2.1bf, 12.2.2cd, 12.2.3c, 12.2.11 </p> </div> </div> -<div id="outline-container-orgef7eb4d" class="outline-4"> -<h4 id="orgef7eb4d">Datorlaboration</h4> -<div class="outline-text-4" id="text-orgef7eb4d"> +<div id="outline-container-org87e8642" class="outline-4"> +<h4 id="org87e8642">Datorlaboration</h4> +<div class="outline-text-4" id="text-org87e8642"> <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 @@ -395,21 +395,21 @@ gränsvärdet av a(k,m) dÃ¥ m gÃ¥r mot oändligheten? </div> </div> </div> -<div id="outline-container-org4a80012" class="outline-3"> -<h3 id="org4a80012">2024-04-07</h3> -<div class="outline-text-3" id="text-org4a80012"> +<div id="outline-container-orgff00c35" class="outline-3"> +<h3 id="orgff00c35">2024-04-07</h3> +<div class="outline-text-3" id="text-orgff00c35"> </div> -<div id="outline-container-org3f1c3a4" class="outline-4"> -<h4 id="org3f1c3a4">Uppgifter att räkna till nästa gÃ¥ng</h4> -<div class="outline-text-4" id="text-org3f1c3a4"> +<div id="outline-container-org10c6215" class="outline-4"> +<h4 id="org10c6215">Uppgifter att räkna till nästa gÃ¥ng</h4> +<div class="outline-text-4" id="text-org10c6215"> <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-orgd77ff3b" class="outline-4"> -<h4 id="orgd77ff3b">Beviset för kvadratisk reciprocitet</h4> -<div class="outline-text-4" id="text-orgd77ff3b"> +<div id="outline-container-orgcb6d72a" class="outline-4"> +<h4 id="orgcb6d72a">Beviset för kvadratisk reciprocitet</h4> +<div class="outline-text-4" id="text-orgcb6d72a"> <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. @@ -418,17 +418,17 @@ 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-orgb250740" class="outline-3"> -<h3 id="orgb250740">2024-04-02</h3> -<div class="outline-text-3" id="text-orgb250740"> +<div id="outline-container-org84ac4df" class="outline-3"> +<h3 id="org84ac4df">2024-04-02</h3> +<div class="outline-text-3" id="text-org84ac4df"> <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-orged4ff0b" class="outline-3"> -<h3 id="orged4ff0b">2024-03-11</h3> -<div class="outline-text-3" id="text-orged4ff0b"> +<div id="outline-container-orgecb5391" class="outline-3"> +<h3 id="orgecb5391">2024-03-11</h3> +<div class="outline-text-3" id="text-orgecb5391"> <p> Jag har nu bokat om föreläsningarna till Fredagar kl 13-15 (fortfarande i kompakta rummet) samt mÃ¥ndag 25 mars kl 13-15, @@ -437,9 +437,9 @@ Det blir 10 tillfällen totalt, vilket bör räcka. </p> </div> </div> -<div id="outline-container-org0de71ab" class="outline-3"> -<h3 id="org0de71ab">2024-03-06</h3> -<div class="outline-text-3" id="text-org0de71ab"> +<div id="outline-container-orged53d50" class="outline-3"> +<h3 id="orged53d50">2024-03-06</h3> +<div class="outline-text-3" id="text-orged53d50"> <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. @@ -448,9 +448,9 @@ 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-org84eda8d" class="outline-3"> -<h3 id="org84eda8d">2024-03-05</h3> -<div class="outline-text-3" id="text-org84eda8d"> +<div id="outline-container-org69c699e" class="outline-3"> +<h3 id="org69c699e">2024-03-05</h3> +<div class="outline-text-3" id="text-org69c699e"> <p> Det har framförts önskemÃ¥l om att byta tid för lektionerna i period 4 för att undvika kollision med kursen i optimeringslära. @@ -471,9 +471,9 @@ Det rör sig om 11 tillfällen totalt. </p> </div> </div> -<div id="outline-container-orgea6ed65" class="outline-3"> -<h3 id="orgea6ed65">2024-02-29</h3> -<div class="outline-text-3" id="text-orgea6ed65"> +<div id="outline-container-org8b45b59" class="outline-3"> +<h3 id="org8b45b59">2024-02-29</h3> +<div class="outline-text-3" id="text-org8b45b59"> <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. @@ -487,9 +487,9 @@ Till lektionen efter det (27 mars) sÃ¥ räknar ni </div> </div> -<div id="outline-container-org823f5e2" class="outline-3"> -<h3 id="org823f5e2">2024-02-20</h3> -<div class="outline-text-3" id="text-org823f5e2"> +<div id="outline-container-org6ee578d" class="outline-3"> +<h3 id="org6ee578d">2024-02-20</h3> +<div class="outline-text-3" id="text-org6ee578d"> <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. @@ -500,7 +500,7 @@ grad 5 eller 6. </p> <div class="org-src-container"> -<pre class="src src-sage" id="orgce6ce24">def H_L_tree(f, p: int, r: int): +<pre class="src src-sage" id="org2172c13">def H_L_tree(f, p: int, r: int): vert = [(0,0)] for j in range(1,r+1): @@ -529,25 +529,25 @@ H_L_tree(f,p,r).plot(layout='tree') </div> -<figure id="org4ce6b2f"> +<figure id="org81e109e"> <img src="img/Henseluppgift.png" alt="Henseluppgift.png"> </figure> </div> </div> -<div id="outline-container-org1c24ff1" class="outline-3"> -<h3 id="org1c24ff1">2024-02-12</h3> -<div class="outline-text-3" id="text-org1c24ff1"> +<div id="outline-container-org15914f2" class="outline-3"> +<h3 id="org15914f2">2024-02-12</h3> +<div class="outline-text-3" id="text-org15914f2"> <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-org499023d" class="outline-3"> -<h3 id="org499023d">2024-02-07</h3> -<div class="outline-text-3" id="text-org499023d"> +<div id="outline-container-org445fa32" class="outline-3"> +<h3 id="org445fa32">2024-02-07</h3> +<div class="outline-text-3" id="text-org445fa32"> <p> Till nästa lektion (12 feb) sÃ¥ tittar ni pÃ¥ uppgifterna 4.1.5, 4.1.9b, 4.2.8c,4.3.3. @@ -557,9 +557,9 @@ att vara i Kompakta rummet. </div> </div> -<div id="outline-container-orgf683b42" class="outline-3"> -<h3 id="orgf683b42">2024-01-30</h3> -<div class="outline-text-3" id="text-orgf683b42"> +<div id="outline-container-org887cf9c" class="outline-3"> +<h3 id="org887cf9c">2024-01-30</h3> +<div class="outline-text-3" id="text-org887cf9c"> <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> @@ -568,9 +568,9 @@ att vara i Kompakta rummet. </ul> </div> -<div id="outline-container-org53dcc9b" class="outline-4"> -<h4 id="org53dcc9b">Tvillingfria primtal</h4> -<div class="outline-text-4" id="text-org53dcc9b"> +<div id="outline-container-orge760dad" class="outline-4"> +<h4 id="orge760dad">Tvillingfria primtal</h4> +<div class="outline-text-4" id="text-orge760dad"> <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 @@ -578,7 +578,7 @@ garanterar oändligt mÃ¥nga primtal i nZ + k. </p> <div class="org-src-container"> -<pre class="src src-sage" id="org400f273">def repr(n): +<pre class="src src-sage" id="org173cf70">def repr(n): return [k for k in range(n) if gcd(k,n)==1] def isolated(n): @@ -609,17 +609,17 @@ Körning visar att n=15, k=7 är minsta exemplet. </div> </div> -<div id="outline-container-orgd22b4e6" class="outline-3"> -<h3 id="orgd22b4e6">2024-01-23</h3> -<div class="outline-text-3" id="text-orgd22b4e6"> +<div id="outline-container-org488e68b" class="outline-3"> +<h3 id="org488e68b">2024-01-23</h3> +<div class="outline-text-3" id="text-org488e68b"> <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-org5900f63" class="outline-3"> -<h3 id="org5900f63">2024-01-16</h3> -<div class="outline-text-3" id="text-org5900f63"> +<div id="outline-container-org96d1546" class="outline-3"> +<h3 id="org96d1546">2024-01-16</h3> +<div class="outline-text-3" id="text-org96d1546"> <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> @@ -627,7 +627,7 @@ 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="#org7db4ce4">rekommenderade uppgifter</a>) +(hämtade frÃ¥n listan med <a href="#org9bd3039">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. @@ -641,19 +641,19 @@ till, nu med fokus pÃ¥ att förstÃ¥ bevisen.</li> </div> </section> -<section id="outline-container-org4f543bd" class="outline-2"> -<h2 id="org4f543bd">Kurslitteratur <a id="org98e7bee"></a></h2> -<div class="outline-text-2" id="text-org4f543bd"> +<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-org09cac9a" class="outline-3"> -<h3 id="org09cac9a">Kursbok</h3> -<div class="outline-text-3" id="text-org09cac9a"> +<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="org09cfcfd"> +<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> @@ -665,13 +665,13 @@ vilket inte pÃ¥verkar innehÃ¥llet. </p> </div> </div> -<div id="outline-container-orgdf2c024" class="outline-3"> -<h3 id="orgdf2c024">Bredvidläsning</h3> -<div class="outline-text-3" id="text-orgdf2c024"> +<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-org9934079" class="outline-4"> -<h4 id="org9934079">Fritt tillgängligt material</h4> -<div class="outline-text-4" id="text-org9934079"> +<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 pÃ¥ nätet. Kursboken är väldigt grundlig och täcker kursinnehÃ¥llet, men det kan ändÃ¥ vara bra att se olika @@ -689,9 +689,9 @@ Jolly för en metod att hitta primitiva rötter.</li> </ul> </div> </div> -<div id="outline-container-org486a906" class="outline-4"> -<h4 id="org486a906">Andra lämpliga böcker</h4> -<div class="outline-text-4" id="text-org486a906"> +<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> @@ -711,13 +711,13 @@ fortbildning efter denna kurs.</li> -<section id="outline-container-org83d546e" class="outline-2"> -<h2 id="org83d546e">KursinnehÃ¥ll <a id="orge3aa510"></a></h2> -<div class="outline-text-2" id="text-org83d546e"> +<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"> </div> -<div id="outline-container-org34795a7" class="outline-3"> -<h3 id="org34795a7">Avsnitt av kursboken</h3> -<div class="outline-text-3" id="text-org34795a7"> +<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 @@ -727,15 +727,15 @@ frÃ¥n just dessa avsnitt. </p> </div> -<div id="outline-container-org10138de" class="outline-4"> -<h4 id="org10138de">Rekommenderade uppgifter <a id="org7db4ce4"></a></h4> -<div class="outline-text-4" id="text-org10138de"> +<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> <ul class="org-ul"> -<li><a id="org15b8e33"></a>Kap 1<br> +<li><a id="org180341a"></a>Kap 1<br> <ul class="org-ul"> -<li><a id="orgb33f2f0"></a>1.5<br> -<div class="outline-text-6" id="text-orgb33f2f0"> +<li><a id="org7ad84d9"></a>1.5<br> +<div class="outline-text-6" id="text-org7ad84d9"> <p> 8a,9b,18,36,37 </p> @@ -743,46 +743,46 @@ frÃ¥n just dessa avsnitt. </li> </ul> </li> -<li><a id="org681038a"></a>Kap 3<br> +<li><a id="org87a9a00"></a>Kap 3<br> <ul class="org-ul"> -<li><a id="org0f22bbf"></a>3.1<br> -<div class="outline-text-6" id="text-org0f22bbf"> +<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="orga37167f"></a>3.2<br> -<div class="outline-text-6" id="text-orga37167f"> +<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="orgb03bced"></a>3.3<br> -<div class="outline-text-6" id="text-orgb03bced"> +<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="orgec1beae"></a>3.4<br> -<div class="outline-text-6" id="text-orgec1beae"> +<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="orgcb8a7bd"></a>3.5<br> -<div class="outline-text-6" id="text-orgcb8a7bd"> +<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="orga2dfbe1"></a>3.7<br> -<div class="outline-text-6" id="text-orga2dfbe1"> +<li><a id="orge8d3c38"></a>3.7<br> +<div class="outline-text-6" id="text-orge8d3c38"> <p> 1cd </p> @@ -790,31 +790,31 @@ frÃ¥n just dessa avsnitt. </li> </ul> </li> -<li><a id="org37c2a66"></a>Kap 4<br> +<li><a id="org3c52ecc"></a>Kap 4<br> <ul class="org-ul"> -<li><a id="org6253340"></a>4.1<br> -<div class="outline-text-6" id="text-org6253340"> +<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="org54fbae8"></a>4.2<br> -<div class="outline-text-6" id="text-org54fbae8"> +<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="org5ae1ea7"></a>4.3<br> -<div class="outline-text-6" id="text-org5ae1ea7"> +<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="org7fb6f3a"></a>4.4<br> -<div class="outline-text-6" id="text-org7fb6f3a"> +<li><a id="orgce85497"></a>4.4<br> +<div class="outline-text-6" id="text-orgce85497"> <p> 2ab. </p> @@ -822,10 +822,10 @@ frÃ¥n just dessa avsnitt. </li> </ul> </li> -<li><a id="org67c0b01"></a>Kap 5<br> +<li><a id="orgce38e81"></a>Kap 5<br> <ul class="org-ul"> -<li><a id="org72b5624"></a>5.1<br> -<div class="outline-text-6" id="text-org72b5624"> +<li><a id="org290a8f0"></a>5.1<br> +<div class="outline-text-6" id="text-org290a8f0"> <p> 4ab. </p> @@ -833,26 +833,26 @@ frÃ¥n just dessa avsnitt. </li> </ul> </li> -<li><a id="org3e672b9"></a>Kap 6<br> +<li><a id="org079c6dc"></a>Kap 6<br> <ul class="org-ul"> -<li><a id="org1f56359"></a>6.1<br> -<div class="outline-text-6" id="text-org1f56359"> +<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="org6facf0b"></a>6.2<br> -<div class="outline-text-6" id="text-org6facf0b"> +<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="org3eb9c1b"></a>6.3<br> -<div class="outline-text-6" id="text-org3eb9c1b"> +<li><a id="orgffebf1d"></a>6.3<br> +<div class="outline-text-6" id="text-orgffebf1d"> <p> 1d,6,7,22* </p> @@ -861,31 +861,31 @@ frÃ¥n just dessa avsnitt. </ul> </li> -<li><a id="orgdc43d50"></a>Kap 7<br> +<li><a id="orgcfc4d04"></a>Kap 7<br> <ul class="org-ul"> -<li><a id="org70452c6"></a>7.1<br> -<div class="outline-text-6" id="text-org70452c6"> +<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="org613722d"></a>7.2<br> -<div class="outline-text-6" id="text-org613722d"> +<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="orgf2f87e9"></a>7.3<br> -<div class="outline-text-6" id="text-orgf2f87e9"> +<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="org540c16c"></a>7.4<br> -<div class="outline-text-6" id="text-org540c16c"> +<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> @@ -894,47 +894,47 @@ frÃ¥n just dessa avsnitt. </ul> </li> -<li><a id="orgd525786"></a>Kap 9<br> +<li><a id="orgd9614bf"></a>Kap 9<br> <ul class="org-ul"> -<li><a id="org8894071"></a>9.1<br> -<div class="outline-text-6" id="text-org8894071"> +<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="org68316e6"></a>9.2<br> -<div class="outline-text-6" id="text-org68316e6"> +<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="orgabc73c3"></a>9.3<br> -<div class="outline-text-6" id="text-orgabc73c3"> +<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="org63ae623"></a>9.4<br> -<div class="outline-text-6" id="text-org63ae623"> +<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="org9c13bc0"></a>9.5<br> -<div class="outline-text-6" id="text-org9c13bc0"> +<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="org5015ce5"></a>9.6<br> -<div class="outline-text-6" id="text-org5015ce5"> +<li><a id="orgf9dc898"></a>9.6<br> +<div class="outline-text-6" id="text-orgf9dc898"> <p> 1bcg, 4def, 13*, 14*. </p> @@ -943,31 +943,31 @@ frÃ¥n just dessa avsnitt. </ul> </li> -<li><a id="org82f34bf"></a>Kap 11<br> +<li><a id="org2d75d4e"></a>Kap 11<br> <ul class="org-ul"> -<li><a id="org3d2f276"></a>11.1<br> -<div class="outline-text-6" id="text-org3d2f276"> +<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="orgc0c01e2"></a>11.2<br> -<div class="outline-text-6" id="text-orgc0c01e2"> +<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="org1af5d6e"></a>11.3<br> -<div class="outline-text-6" id="text-org1af5d6e"> +<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="orgfe1e34d"></a>11.4<br> -<div class="outline-text-6" id="text-orgfe1e34d"> +<li><a id="org53fd7ee"></a>11.4<br> +<div class="outline-text-6" id="text-org53fd7ee"> <p> 1, 2, 5, 6. </p> @@ -976,32 +976,32 @@ frÃ¥n just dessa avsnitt. </ul> </li> -<li><a id="org2cc3178"></a>Kap 12<br> +<li><a id="org4de3188"></a>Kap 12<br> <ul class="org-ul"> -<li><a id="org7cac01e"></a>12.2<br> -<div class="outline-text-6" id="text-org7cac01e"> +<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="orgb90f3a1"></a>12.3<br> -<div class="outline-text-6" id="text-orgb90f3a1"> +<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="orgca93be0"></a>12.4<br> -<div class="outline-text-6" id="text-orgca93be0"> +<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="org677f1bb"></a>12.5<br> -<div class="outline-text-6" id="text-org677f1bb"> +<li><a id="org1a8a715"></a>12.5<br> +<div class="outline-text-6" id="text-org1a8a715"> <ol class="org-ol"> <li></li> </ol> @@ -1010,32 +1010,32 @@ frÃ¥n just dessa avsnitt. </ul> </li> -<li><a id="orgedd8e06"></a>Kap 13<br> +<li><a id="org919ec71"></a>Kap 13<br> <ul class="org-ul"> -<li><a id="orgbcdde20"></a>13.1<br> -<div class="outline-text-6" id="text-orgbcdde20"> +<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="org8e3a488"></a>13.2<br> -<div class="outline-text-6" id="text-org8e3a488"> +<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="org528308d"></a>13.3<br> -<div class="outline-text-6" id="text-org528308d"> +<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="orgf68bc5b"></a>13.4<br> -<div class="outline-text-6" id="text-orgf68bc5b"> +<li><a id="org3183550"></a>13.4<br> +<div class="outline-text-6" id="text-org3183550"> <p> 1c, 2a, 3def, 4ab, 6de, 8*. @@ -1045,25 +1045,25 @@ frÃ¥n just dessa avsnitt. </ul> </li> -<li><a id="orgdcc1ad3"></a>Kap 14<br> +<li><a id="org63d399d"></a>Kap 14<br> <ul class="org-ul"> -<li><a id="org59fea14"></a>14.1<br> -<div class="outline-text-6" id="text-org59fea14"> +<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="orgb5250d8"></a>14.2<br> -<div class="outline-text-6" id="text-orgb5250d8"> +<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="org3675a33"></a>14.3<br> -<div class="outline-text-6" id="text-org3675a33"> +<li><a id="orgff2bf56"></a>14.3<br> +<div class="outline-text-6" id="text-orgff2bf56"> <p> 1bc, 2c </p> @@ -1075,15 +1075,15 @@ frÃ¥n just dessa avsnitt. </div> </div> -<div id="outline-container-orgab0c2e2" class="outline-3"> -<h3 id="orgab0c2e2">Kort beskrivning av kursinnehÃ¥llet</h3> +<div id="outline-container-orgf97dd5f" class="outline-3"> +<h3 id="orgf97dd5f">Kort beskrivning av kursinnehÃ¥llet</h3> </div> </section> -<section id="outline-container-org67ef94b" class="outline-2"> -<h2 id="org67ef94b">Föreläsningar <a id="orgb94c813"></a></h2> -<div class="outline-text-2" id="text-org67ef94b"> +<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. NÃ¥gra av föreläsningarna tar tvÃ¥ tillfällen för att gÃ¥ igenom. @@ -1262,9 +1262,9 @@ De svenska versionerna är nyare. NÃ¥gra av föreläsningarna tar tvÃ¥ tillfäll </section> -<section id="outline-container-org9e66246" class="outline-2"> -<h2 id="org9e66246">Tentor <a id="orgcbd53f3"></a></h2> -<div class="outline-text-2" id="text-org9e66246"> +<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> @@ -1480,13 +1480,13 @@ De svenska versionerna är nyare. NÃ¥gra av föreläsningarna tar tvÃ¥ tillfäll </section> -<section id="outline-container-orgf236219" class="outline-2"> -<h2 id="orgf236219">Datorlaborationer <a id="org965b1f7"></a></h2> -<div class="outline-text-2" id="text-orgf236219"> +<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-org7a98c02" class="outline-3"> -<h3 id="org7a98c02">SageMath</h3> -<div class="outline-text-3" id="text-org7a98c02"> +<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 pÃ¥ egen hand kan ni enkelt <a href="https://doc.sagemath.org/html/en/installation/index.html">installera programmet pÃ¥ er dator</a>, @@ -1502,9 +1502,9 @@ Ett tredje alternativ, enkelt och flärdfritt, är att mata in sin kod till <a h </p> </div> </div> -<div id="outline-container-org38724a4" class="outline-3"> -<h3 id="org38724a4">Kod frÃ¥n vissa föreläsningar</h3> -<div class="outline-text-3" id="text-org38724a4"> +<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"> <ul class="org-ul"> <li><a href="labs/lecture0.html">Föreläsning 0</a></li> <li><a href="labs/lecture1.html">Föreläsning 1</a></li> @@ -1515,21 +1515,21 @@ Ett tredje alternativ, enkelt och flärdfritt, är att mata in sin kod till <a h </ul> </div> </div> -<div id="outline-container-org80ba8f8" class="outline-3"> -<h3 id="org80ba8f8">Laborationer</h3> -<div class="outline-text-3" id="text-org80ba8f8"> +<div id="outline-container-org771ae33" class="outline-3"> +<h3 id="org771ae33">Laborationer</h3> +<div class="outline-text-3" id="text-org771ae33"> </div> -<div id="outline-container-org4bb0ea2" class="outline-4"> -<h4 id="org4bb0ea2">Hensellyft, Primitiva rötter, Kinesiska restsatsen</h4> -<div class="outline-text-4" id="text-org4bb0ea2"> +<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"> <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-org4f8b714" class="outline-4"> -<h4 id="org4f8b714">KedjebrÃ¥k</h4> -<div class="outline-text-4" id="text-org4f8b714"> +<div id="outline-container-org254ad94" class="outline-4"> +<h4 id="org254ad94">KedjebrÃ¥k</h4> +<div class="outline-text-4" id="text-org254ad94"> <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> @@ -1540,20 +1540,20 @@ Finns att <a href="labs/kedjebraklab.html">läsa direkt</a> eller som <a href="l -<section id="outline-container-org65b020a" class="outline-2"> -<h2 id="org65b020a">Tidigare Ã¥r <a id="orgca3cfe8"></a></h2> -<div class="outline-text-2" id="text-org65b020a"> +<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"> </div> -<div id="outline-container-org477262d" class="outline-3"> -<h3 id="org477262d">TATA54 Anteckningar frÃ¥n tidigare Ã¥r</h3> -<div class="outline-text-3" id="text-org477262d"> +<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> -<div id="outline-container-org780ed90" class="outline-4"> -<h4 id="org780ed90">2023</h4> -<div class="outline-text-4" id="text-org780ed90"> +<div id="outline-container-org2e74361" class="outline-4"> +<h4 id="org2e74361">2023</h4> +<div class="outline-text-4" id="text-org2e74361"> <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 @@ -1607,9 +1607,9 @@ tryckfel (skall vara w(d)). 7.2.38 är komplicerad och kan skippas.</li> </div> -<div id="outline-container-org780092f" class="outline-4"> -<h4 id="org780092f">2021</h4> -<div class="outline-text-4" id="text-org780092f"> +<div id="outline-container-org39f254e" class="outline-4"> +<h4 id="org39f254e">2021</h4> +<div class="outline-text-4" id="text-org39f254e"> <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 @@ -1657,9 +1657,9 @@ nÃ¥gon inbjudan, sÃ¥ mejla mig.</li> </div> </div> -<div id="outline-container-org2b03280" class="outline-4"> -<h4 id="org2b03280">2020</h4> -<div class="outline-text-4" id="text-org2b03280"> +<div id="outline-container-orgab915cd" class="outline-4"> +<h4 id="orgab915cd">2020</h4> +<div class="outline-text-4" id="text-orgab915cd"> <ul class="org-ul"> <li><p> 2020-12-12: Kursen kommer att ges VT2021, med start den 19e januari. @@ -1712,9 +1712,9 @@ someone else (perhaps </div> </div> -<div id="outline-container-org9b6101f" class="outline-4"> -<h4 id="org9b6101f">2019</h4> -<div class="outline-text-4" id="text-org9b6101f"> +<div id="outline-container-org51934a3" class="outline-4"> +<h4 id="org51934a3">2019</h4> +<div class="outline-text-4" id="text-org51934a3"> <ul class="org-ul"> <li>2019-11-01: The course will not be given spring 2020.</li> @@ -1729,9 +1729,9 @@ available.</li> </div> </div> -<div id="outline-container-orgba3d96f" class="outline-4"> -<h4 id="orgba3d96f">2018</h4> -<div class="outline-text-4" id="text-orgba3d96f"> +<div id="outline-container-org51909e4" class="outline-4"> +<h4 id="org51909e4">2018</h4> +<div class="outline-text-4" id="text-org51909e4"> <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 @@ -1744,9 +1744,9 @@ available.</li> </div> </div> -<div id="outline-container-org45290d5" class="outline-4"> -<h4 id="org45290d5">2017</h4> -<div class="outline-text-4" id="text-org45290d5"> +<div id="outline-container-org50057cb" class="outline-4"> +<h4 id="org50057cb">2017</h4> +<div class="outline-text-4" id="text-org50057cb"> <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 @@ -1769,7 +1769,7 @@ Another text is <a href="https://wstein.org/ent/">Elementary Number Theory</a> a </ul> -<figure id="org09a4929"> +<figure id="orgc676d9d"> <img src="img/sieveE.jpg" alt="sieveE.jpg"> </figure> @@ -1779,9 +1779,9 @@ Another text is <a href="https://wstein.org/ent/">Elementary Number Theory</a> a </section> -<section id="outline-container-org22888c0" class="outline-2"> -<h2 id="org22888c0">Index</h2> -<div class="outline-text-2" id="text-org22888c0"> +<section id="outline-container-org27e935f" class="outline-2"> +<h2 id="org27e935f">Index</h2> +<div class="outline-text-2" id="text-org27e935f"> <p> <a href="sitemap.html">Samtliga nÃ¥bara filer</a> </p> @@ -1790,7 +1790,7 @@ 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: 2024-08-22</p> +<p class="date">Created: 2024-08-23</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 64e5f08f906c91dba039c6075c55ff819e0b35e8..774907dcb88d77fdc0aa54a8e61857197e640d8f 100644 --- a/public/sitemap.html +++ b/public/sitemap.html @@ -1,7 +1,7 @@ <!DOCTYPE html> <html lang="en"> <head> -<!-- 2024-08-22 --> +<!-- 2024-08-23 --> <meta charset="utf-8" /> <meta name="viewport" content="width=device-width, initial-scale=1" /> <title>Kurshemsida</title> @@ -206,9 +206,11 @@ <header> <h1 class="title">Kurshemsida</h1> </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="index.html">TATA54 Talteori</a></li> -<li><a href="senaste-nytt.html">senaste-nytt</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 +219,11 @@ <li><a href="labs/lecture0.html">lecture0</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="newlectures/newlecture.html">Föreläsningar i Talteori</a></li> -<li><a href="newlectures/new-lect-0.html">Talteori översiktsföreläsning</a></li> </ul> </main> <footer id="postamble" class="status"> <p class="author">Author: Jan Snellman</p> -<p class="date">Created: 2024-08-22</p> +<p class="date">Created: 2024-08-23</p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> </footer> </body>