diff --git a/TATA54/TENTOR/tenta-TATA54-20240822-losning.log b/TATA54/TENTOR/tenta-TATA54-20240822-losning.log index a8b5678cbff98852c6694d0ef62c9d30b24ba75d..e9be7f5ee43fd9a40629597210eda39e41fce46f 100644 --- a/TATA54/TENTOR/tenta-TATA54-20240822-losning.log +++ b/TATA54/TENTOR/tenta-TATA54-20240822-losning.log @@ -1,12 +1,9 @@ -This is pdfTeX, Version 3.141592653-2.6-1.40.25 (TeX Live 2023/Fedora 40) (preloaded format=pdflatex 2024.8.21) 22 AUG 2024 14:53 +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 entering extended mode restricted \write18 enabled. - file:line:error style messages enabled. %&-line parsing enabled. -**tenta-TATA54-20240822-losning.tex +**\nonstopmode\input 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 @@ -24,106 +21,7 @@ File: size10.clo 2022/07/02 v1.4n Standard LaTeX file (size option) \belowcaptionskip=\skip49 \bibindent=\dimen140 ) -(/usr/share/texlive/texmf-dist/tex/latex/psnfss/times.sty -Package: times 2020/03/25 PSNFSS-v9.3 (SPQR) -) -(/usr/share/texlive/texmf-dist/tex/latex/euler/euler.sty -Package: euler 1995/03/05 v2.5 - -Package: `euler' v2.5 <1995/03/05> (FJ and FMi) -LaTeX Font Info: Redeclaring symbol font `letters' on input line 35. -LaTeX Font Info: Encoding `OML' has changed to `U' for symbol font -(Font) `letters' in the math version `normal' on input line 35. -LaTeX Font Info: Overwriting symbol font `letters' in version `normal' -(Font) OML/cmm/m/it --> U/eur/m/n on input line 35. -LaTeX Font Info: Encoding `OML' has changed to `U' for symbol font -(Font) `letters' in the math version `bold' on input line 35. -LaTeX Font Info: Overwriting symbol font `letters' in version `bold' -(Font) OML/cmm/b/it --> U/eur/m/n on input line 35. -LaTeX Font Info: Overwriting symbol font `letters' in version `bold' -(Font) U/eur/m/n --> U/eur/b/n on input line 36. -LaTeX Font Info: Redeclaring math symbol \Gamma on input line 47. -LaTeX Font Info: Redeclaring math symbol \Delta on input line 48. -LaTeX Font Info: Redeclaring math symbol \Theta on input line 49. -LaTeX Font Info: Redeclaring math symbol \Lambda on input line 50. -LaTeX Font Info: Redeclaring math symbol \Xi on input line 51. -LaTeX Font Info: Redeclaring math symbol \Pi on input line 52. -LaTeX Font Info: Redeclaring math symbol \Sigma on input line 53. -LaTeX Font Info: Redeclaring math symbol \Upsilon on input line 54. -LaTeX Font Info: Redeclaring math symbol \Phi on input line 55. -LaTeX Font Info: Redeclaring math symbol \Psi on input line 56. -LaTeX Font Info: Redeclaring math symbol \Omega on input line 57. -\symEulerFraktur=\mathgroup4 -LaTeX Font Info: Overwriting symbol font `EulerFraktur' in version `bold' -(Font) U/euf/m/n --> U/euf/b/n on input line 63. -LaTeX Info: Redefining \oldstylenums on input line 85. -\symEulerScript=\mathgroup5 -LaTeX Font Info: Overwriting symbol font `EulerScript' in version `bold' -(Font) U/eus/m/n --> U/eus/b/n on input line 93. -LaTeX Font Info: Redeclaring math symbol \aleph on input line 97. -LaTeX Font Info: Redeclaring math symbol \Re on input line 98. -LaTeX Font Info: Redeclaring math symbol \Im on input line 99. -LaTeX Font Info: Redeclaring math delimiter \vert on input line 101. -LaTeX Font Info: Redeclaring math delimiter \backslash on input line 103. -LaTeX Font Info: Redeclaring math symbol \neg on input line 106. -LaTeX Font Info: Redeclaring math symbol \wedge on input line 108. -LaTeX Font Info: Redeclaring math symbol \vee on input line 110. -LaTeX Font Info: Redeclaring math symbol \setminus on input line 112. -LaTeX Font Info: Redeclaring math symbol \sim on input line 113. -LaTeX Font Info: Redeclaring math symbol \mid on input line 114. -LaTeX Font Info: Redeclaring math delimiter \arrowvert on input line 116. -LaTeX Font Info: Redeclaring math symbol \mathsection on input line 117. -\symEulerExtension=\mathgroup6 -LaTeX Font Info: Redeclaring math symbol \coprod on input line 125. -LaTeX Font Info: Redeclaring math symbol \prod on input line 125. -LaTeX Font Info: Redeclaring math symbol \sum on input line 125. -LaTeX Font Info: Redeclaring math symbol \intop on input line 130. -LaTeX Font Info: Redeclaring math symbol \ointop on input line 131. -LaTeX Font Info: Redeclaring math symbol \braceld on input line 132. -LaTeX Font Info: Redeclaring math symbol \bracerd on input line 133. -LaTeX Font Info: Redeclaring math symbol \bracelu on input line 134. -LaTeX Font Info: Redeclaring math symbol \braceru on input line 135. -LaTeX Font Info: Redeclaring math symbol \infty on input line 136. -LaTeX Font Info: Redeclaring math symbol \nearrow on input line 153. -LaTeX Font Info: Redeclaring math symbol \searrow on input line 154. -LaTeX Font Info: Redeclaring math symbol \nwarrow on input line 155. -LaTeX Font Info: Redeclaring math symbol \swarrow on input line 156. -LaTeX Font Info: Redeclaring math symbol \Leftrightarrow on input line 157. -LaTeX Font Info: Redeclaring math symbol \Leftarrow on input line 158. -LaTeX Font Info: Redeclaring math symbol \Rightarrow on input line 159. -LaTeX Font Info: Redeclaring math symbol \leftrightarrow on input line 160. -LaTeX Font Info: Redeclaring math symbol \leftarrow on input line 161. -LaTeX Font Info: Redeclaring math symbol \rightarrow on input line 163. -LaTeX Font Info: Redeclaring math delimiter \uparrow on input line 166. -LaTeX Font Info: Redeclaring math delimiter \downarrow on input line 168. -LaTeX Font Info: Redeclaring math delimiter \updownarrow on input line 170. -LaTeX Font Info: Redeclaring math delimiter \Uparrow on input line 172. -LaTeX Font Info: Redeclaring math delimiter \Downarrow on input line 174. -LaTeX Font Info: Redeclaring math delimiter \Updownarrow on input line 176. -LaTeX Font Info: Redeclaring math symbol \leftharpoonup on input line 177. -LaTeX Font Info: Redeclaring math symbol \leftharpoondown on input line 178. - -LaTeX Font Info: Redeclaring math symbol \rightharpoonup on input line 179. -LaTeX Font Info: Redeclaring math symbol \rightharpoondown on input line 180 -. -LaTeX Font Info: Redeclaring math delimiter \lbrace on input line 182. -LaTeX Font Info: Redeclaring math delimiter \rbrace on input line 184. -\symcmmigroup=\mathgroup7 -LaTeX Font Info: Overwriting symbol font `cmmigroup' in version `bold' -(Font) OML/cmm/m/it --> OML/cmm/b/it on input line 200. -LaTeX Font Info: Redeclaring math accent \vec on input line 201. -LaTeX Font Info: Redeclaring math symbol \triangleleft on input line 202. -LaTeX Font Info: Redeclaring math symbol \triangleright on input line 203. -LaTeX Font Info: Redeclaring math symbol \star on input line 204. -LaTeX Font Info: Redeclaring math symbol \lhook on input line 205. -LaTeX Font Info: Redeclaring math symbol \rhook on input line 206. -LaTeX Font Info: Redeclaring math symbol \flat on input line 207. -LaTeX Font Info: Redeclaring math symbol \natural on input line 208. -LaTeX Font Info: Redeclaring math symbol \sharp on input line 209. -LaTeX Font Info: Redeclaring math symbol \smile on input line 210. -LaTeX Font Info: Redeclaring math symbol \frown on input line 211. -LaTeX Font Info: Redeclaring math accent \hat on input line 254. -) (/usr/share/texlive/texmf-dist/tex/latex/a4wide/a4wide.sty +(/usr/share/texlive/texmf-dist/tex/latex/a4wide/a4wide.sty Package: a4wide 1994/08/30 (/usr/share/texlive/texmf-dist/tex/latex/ntgclass/a4.sty @@ -206,10 +104,11 @@ Package: amssymb 2013/01/14 v3.01 AMS font symbols (/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amsfonts.sty Package: amsfonts 2013/01/14 v3.01 Basic AMSFonts support -\symAMSa=\mathgroup8 -\symAMSb=\mathgroup9 +\symAMSa=\mathgroup4 +\symAMSb=\mathgroup5 LaTeX Font Info: Redeclaring math symbol \hbar on input line 98. -LaTeX Info: Redefining \frak on input line 111. +LaTeX Font Info: Overwriting math alphabet `\mathfrak' in version `bold' +(Font) U/euf/m/n --> U/euf/b/n on input line 106. )) (/usr/share/texlive/texmf-dist/tex/latex/amscls/amsthm.sty Package: amsthm 2020/05/29 v2.20.6 @@ -232,7 +131,7 @@ 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=\language85 +\l@unhyphenated=\language3 (/usr/share/texlive/texmf-dist/tex/generic/babel/txtbabel.def) \bbl@readstream=\read2 @@ -240,19 +139,21 @@ 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. -) -LaTeX Font Info: Trying to load font information for OT1+ptm on input line 1 -9. - -(/usr/share/texlive/texmf-dist/tex/latex/psnfss/ot1ptm.fd -File: ot1ptm.fd 2001/06/04 font definitions for OT1/ptm. -) -(/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 @@ -274,65 +175,6 @@ LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 19. LaTeX Font Info: ... okay on input line 19. LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 19. LaTeX Font Info: ... okay on input line 19. -LaTeX Font Info: Redeclaring symbol font `operators' on input line 19. -LaTeX Font Info: Overwriting symbol font `operators' in version `normal' -(Font) OT1/cmr/m/n --> OT1/ptm/m/up on input line 19. -LaTeX Font Info: Overwriting symbol font `operators' in version `bold' -(Font) OT1/cmr/bx/n --> OT1/ptm/m/up on input line 19. -LaTeX Font Info: Overwriting symbol font `operators' in version `bold' -(Font) OT1/ptm/m/up --> OT1/ptm/b/up on input line 19. -LaTeX Font Info: Redeclaring math alphabet \mathbf on input line 19. -LaTeX Font Info: Overwriting math alphabet `\mathbf' in version `normal' -(Font) OT1/cmr/bx/n --> OT1/ptm/b/up on input line 19. -LaTeX Font Info: Overwriting math alphabet `\mathbf' in version `bold' -(Font) OT1/cmr/bx/n --> OT1/ptm/b/up on input line 19. -LaTeX Font Info: Redeclaring math alphabet \mathsf on input line 19. -LaTeX Font Info: Overwriting math alphabet `\mathsf' in version `normal' -(Font) OT1/cmss/m/n --> OT1/phv/m/up on input line 19. -LaTeX Font Info: Overwriting math alphabet `\mathsf' in version `bold' -(Font) OT1/cmss/bx/n --> OT1/phv/m/up on input line 19. -LaTeX Font Info: Redeclaring math alphabet \mathit on input line 19. -LaTeX Font Info: Overwriting math alphabet `\mathit' in version `normal' -(Font) OT1/cmr/m/it --> OT1/ptm/m/it on input line 19. -LaTeX Font Info: Overwriting math alphabet `\mathit' in version `bold' -(Font) OT1/cmr/bx/it --> OT1/ptm/m/it on input line 19. -LaTeX Font Info: Redeclaring math alphabet \mathtt on input line 19. -LaTeX Font Info: Overwriting math alphabet `\mathtt' in version `normal' -(Font) OT1/cmtt/m/n --> OT1/pcr/m/up on input line 19. -LaTeX Font Info: Overwriting math alphabet `\mathtt' in version `bold' -(Font) OT1/cmtt/m/n --> OT1/pcr/m/up on input line 19. -LaTeX Font Info: Overwriting math alphabet `\mathsf' in version `bold' -(Font) OT1/phv/m/up --> OT1/phv/b/up on input line 19. -LaTeX Font Info: Overwriting math alphabet `\mathit' in version `bold' -(Font) OT1/ptm/m/it --> OT1/ptm/b/it on input line 19. - - -LaTeX Font Warning: Font shape `OT1/ptm/m/up' undefined -(Font) using `OT1/ptm/m/n' instead on input line 35. - -LaTeX Font Info: Trying to load font information for U+eur on input line 35. - -(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/ueur.fd -File: ueur.fd 2013/01/14 v3.01 Euler Roman -) -LaTeX Font Info: Trying to load font information for U+euf on input line 35. - - -(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/ueuf.fd -File: ueuf.fd 2013/01/14 v3.01 Euler Fraktur -) -LaTeX Font Info: Trying to load font information for U+eus on input line 35. - - -(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/ueus.fd -File: ueus.fd 2013/01/14 v3.01 Euler Script -) -LaTeX Font Info: Trying to load font information for U+euex on input line 35 -. - -(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/ueuex.fd -File: ueuex.fd 2013/01/14 v3.01 Euler extra symbols -) LaTeX Font Info: Trying to load font information for U+msa on input line 35. @@ -344,39 +186,43 @@ 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 -) [1 - -{/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map}{/usr/share/texlive/texmf-di -st/fonts/enc/dvips/base/8r.enc}] (./tenta-TATA54-20240822-losning.aux) +) +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 $0\OML/cmm/m/ +it/10 ; \OT1/cmr/m/n/10 1\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 58\OML/cmm/m/it/10 +=\OT1/cmr/m/n/10 59\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 117\OML/cmm/m/it/10 =\OT1 +/cmr/m/n/10 118$. + [] -LaTeX Font Warning: Some font shapes were not available, defaults substituted. +[1 - ) +{/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map}] +(./tenta-TATA54-20240822-losning.aux) ) Here is how much of TeX's memory you used: - 3118 strings out of 476041 - 50293 string characters out of 5793164 - 1859388 words of memory out of 6000000 - 23542 multiletter control sequences out of 15000+600000 - 520902 words of font info for 58 fonts, out of 8000000 for 9000 - 1137 hyphenation exceptions out of 8191 - 56i,5n,62p,252b,215s stack positions out of 10000i,1000n,20000p,200000b,200000s -</usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmex10.pfb></us -r/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy10.pfb></usr/shar -e/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy7.pfb></usr/share/texli -ve/texmf-dist/fonts/type1/public/amsfonts/euler/euex10.pfb></usr/share/texlive/ -texmf-dist/fonts/type1/public/amsfonts/euler/eufm10.pfb></usr/share/texlive/tex -mf-dist/fonts/type1/public/amsfonts/euler/eufm7.pfb></usr/share/texlive/texmf-d -ist/fonts/type1/public/amsfonts/euler/eurm10.pfb></usr/share/texlive/texmf-dist -/fonts/type1/public/amsfonts/euler/eurm5.pfb></usr/share/texlive/texmf-dist/fon -ts/type1/public/amsfonts/euler/eurm7.pfb></usr/share/texlive/texmf-dist/fonts/t -ype1/public/amsfonts/euler/eusm10.pfb></usr/share/texlive/texmf-dist/fonts/type -1/public/amsfonts/symbols/msbm10.pfb></usr/share/texlive/texmf-dist/fonts/type1 -/urw/times/utmb8a.pfb></usr/share/texlive/texmf-dist/fonts/type1/urw/times/utmr -8a.pfb> -Output written on tenta-TATA54-20240822-losning.pdf (1 page, 85679 bytes). + 2936 strings out of 478087 + 46908 string characters out of 5842640 + 1864388 words of memory out of 6000000 + 23044 multiletter control sequences out of 15000+600000 + 514294 words of font info for 41 fonts, out of 8000000 for 9000 + 14 hyphenation exceptions out of 8191 + 56i,9n,62p,271b,219s stack positions out of 10000i,1000n,20000p,200000b,200000s +</usr/share/texlive/texmf-dist/fonts/typ +e1/public/amsfonts/cm/cmbx10.pfb></usr/share/texlive/texmf-dist/fonts/type1/pub +lic/amsfonts/cm/cmex10.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/am +sfonts/cm/cmmi10.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts +/cm/cmmi7.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr +10.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr5.pfb>< +/usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr7.pfb></usr/sha +re/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy10.pfb></usr/share/tex +live/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy7.pfb></usr/share/texlive/te +xmf-dist/fonts/type1/public/amsfonts/symbols/msbm10.pfb></usr/share/texlive/tex +mf-dist/fonts/type1/public/amsfonts/symbols/msbm7.pfb> +Output written on tenta-TATA54-20240822-losning.pdf (1 page, 110723 bytes). PDF statistics: - 74 PDF objects out of 1000 (max. 8388607) - 44 compressed objects within 1 object stream + 63 PDF objects out of 1000 (max. 8388607) + 37 compressed objects within 1 object stream 0 named destinations out of 1000 (max. 500000) 1 words of extra memory for PDF output out of 10000 (max. 10000000) diff --git a/TATA54/TENTOR/tenta-TATA54-20240822-losning.pdf b/TATA54/TENTOR/tenta-TATA54-20240822-losning.pdf index 04a1c401d7ffbe6420aa5acb168628761eef8a87..34f831aaf168f2a7b0660a02384565b351b6565c 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 e0141a6216c829abdcd3adbed3f1d2f5c8cb8106..0c1a8b6a90798b77ca1b94f48d484fac3ba0e282 100644 --- a/TATA54/TENTOR/tenta-TATA54-20240822-losning.tex +++ b/TATA54/TENTOR/tenta-TATA54-20240822-losning.tex @@ -1,6 +1,6 @@ \documentclass[10pt,a4paper]{article} -\usepackage{times} -\usepackage{euler} +%\usepackage{times} +%\usepackage{euler} \usepackage{a4wide} \usepackage{enumerate} \usepackage{amsmath,amssymb,amsthm} @@ -65,15 +65,17 @@ BÃ¥da dessa avbildningar respekterar rationalitet, sÃ¥ de rationella punkterna p \(x^2 \equiv 187 \mod 23\)? \soln 23 är ett primtal, och -\(\legendre{187}{23} = \legendre{3}{23} = - \legendre{23}{3} = - \legendre{2}{3} -=1\). AlltsÃ¥ har 187 precis 2 kvadratrötter modulo 23. +\(\legendre{187}{23} = \legendre{3}{23} += - \legendre{23}{3} = - \legendre{2}{3}=1\). +AlltsÃ¥ har 187 precis 2 kvadratrötter modulo 23 (dessa är \(x \equiv \pm 7 \mod 23\)). \item Hur mÃ¥nga lösningar har kongruensen \(x^2 \equiv 23 \mod 187\)? \soln \(187=11*17\) och - \(\legendre{23}{17}=\legendre{6}{17} = \legendre{2}{17} \legendre{3}{17}\) + \(\legendre{23}{17}=\legendre{6}{17} = \legendre{2}{17} \legendre{3}{17} = -1\), + sÃ¥ lösningar saknas modulo 17. AlltsÃ¥ finns det inga lösningar modulo 187. \item LÃ¥t \(r=117/119\). Hitta positiva heltal \(a,b\) med \(b < 119\) @@ -84,6 +86,11 @@ BÃ¥da dessa avbildningar respekterar rationalitet, sÃ¥ de rationella punkterna p för alla positiva heltal \(c,d\) med \(d < 119\). + \soln KedjebrÃ¥ksutvecklingen är \(117/118 = [0; 1,58,2]\) + med konvergenter \(0,1,58/59, 117/118\). Enligt sats i boken kan ingen rationell approximation + till \(117/118\) slÃ¥ \(58/59\) utan att ha större nämnare. (Samma sak gäller i och för sig + ocksÃ¥ för den triviala + approximationen \(1/1\)). \item LÃ¥t \(\tau(n)\) beteckna antalet positiva delare till det positiva heltalet \(n\), @@ -95,7 +102,14 @@ BÃ¥da dessa avbildningar respekterar rationalitet, sÃ¥ de rationella punkterna p \] för alla positiva heltal \(n\)? Ge bevis eller motexempel. - %https://math.stackexchange.com/questions/1749204/sum-of-number-of-divisors-function-equals-sum-j-1n-lfloor-n-j-rfloor + + \soln + \begin{align*} + \sum_{k=1}^n \tau(k) &= \sum_{k=1}^n \sum_{1 \le d \le k, \,\divides{d}{k}} 1 \\ + & = \sum_{d=1}^n \sum_{1 \le k \le n,\, k \in d\Z} 1 \\ + & = \sum_{1 \le d \le n} \lfloor n/d \rfloor + \end{align*} + %https://math.stackexchange.com/questions/1749204/sum-of-number-of-divisors-function-equals-sum-j-1n-lfloor-n-j-rfloor \end{enumerate} diff --git a/TATA54/TENTOR/tenta-TATA54-20240822-skiss.org b/TATA54/TENTOR/tenta-TATA54-20240822-skiss.org index e2c2e47025de67e2ad892f99a79e231669c05c2d..922d77621f673301ce4834871afbf2d5031851ca 100644 --- a/TATA54/TENTOR/tenta-TATA54-20240822-skiss.org +++ b/TATA54/TENTOR/tenta-TATA54-20240822-skiss.org @@ -198,6 +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: @@ -206,6 +209,7 @@ f.roots(Integers(17),multiplicities=False) : [] : [10, 1] : [] +: [16, 7] ** U7 #+begin_src latex @@ -228,6 +232,7 @@ r=p/q cf = continued_fraction(r) cf best = cf.convergent(2) +best fel = abs(p/q - best) "kedjebrÃ¥kapprox fel", fel @@ -242,6 +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/homepage/exams/2024/tenta-TATA54-20240822-losning.pdf b/homepage/exams/2024/tenta-TATA54-20240822-losning.pdf new file mode 100644 index 0000000000000000000000000000000000000000..34f831aaf168f2a7b0660a02384565b351b6565c Binary files /dev/null and b/homepage/exams/2024/tenta-TATA54-20240822-losning.pdf differ diff --git a/homepage/exams/2024/tenta-TATA54-20240822.pdf b/homepage/exams/2024/tenta-TATA54-20240822.pdf new file mode 100644 index 0000000000000000000000000000000000000000..d839e73d319edc0de99e0682c720582432af21ae Binary files /dev/null and b/homepage/exams/2024/tenta-TATA54-20240822.pdf differ diff --git a/homepage/index.org b/homepage/index.org index 7b96fe3df032b9944f428db480ab90735ebc6666..983a2671c24151b7a05ca433b2ce203a4e23a2eb 100644 --- a/homepage/index.org +++ b/homepage/index.org @@ -413,6 +413,7 @@ De svenska versionerna är nyare. NÃ¥gra av föreläsningarna tar tvÃ¥ tillfäll | Datum | Examinator | Tentamen | Lösningar | |------------+-----------------+---------------------------+-----------------------------| +| 2024-08-22 | Jan Snellman | [[file:exams/2024/tenta-TATA54-20240822.pdf][TATA5420240822]] | [[file:exams/2024/tenta-TATA54-20240822-losning.pdf][TATA5420240822losn]] | | 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]] | diff --git a/homepage/sitemap.org b/homepage/sitemap.org index 6e844ccd2d633f1398c3404a71d30020fba6c1a3..89f01736841522bb59ce8f53b542657d9adff995 100644 --- a/homepage/sitemap.org +++ b/homepage/sitemap.org @@ -1,15 +1,15 @@ #+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:labs/lecture5.org][lecture5]] - [[file:labs/lecture4.org][lecture4]] - [[file:labs/lecture3.org][lecture3]] - [[file:labs/lecture2.org][lecture2]] - [[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]] -- [[file:lectures/Henselfaktorisering.org][Henselfaktorisering]] \ No newline at end of file +- [[file:newlectures/newlecture.org][Föreläsningar i Talteori]] +- [[file:newlectures/new-lect-0.org][Talteori översiktsföreläsning]] \ 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 new file mode 100644 index 0000000000000000000000000000000000000000..34f831aaf168f2a7b0660a02384565b351b6565c Binary files /dev/null and b/public/exams/2024/tenta-TATA54-20240822-losning.pdf differ diff --git a/public/exams/2024/tenta-TATA54-20240822.pdf b/public/exams/2024/tenta-TATA54-20240822.pdf new file mode 100644 index 0000000000000000000000000000000000000000..d839e73d319edc0de99e0682c720582432af21ae Binary files /dev/null and b/public/exams/2024/tenta-TATA54-20240822.pdf differ diff --git a/public/index.html b/public/index.html index 0d3ec795cd56a7b2163eb5ca468688068381f743..311d8f664186b7eb807f162298c2e9388573f49c 100644 --- a/public/index.html +++ b/public/index.html @@ -1,7 +1,7 @@ <!DOCTYPE html> <html lang="sv"> <head> -<!-- 2024-06-05 --> +<!-- 2024-08-22 --> <meta charset="utf-8" /> <meta name="viewport" content="width=device-width, initial-scale=1" /> <title>TATA54 Talteori</title> @@ -63,150 +63,150 @@ <h2>Innehåll</h2> <div id="text-table-of-contents" role="doc-toc"> <ul> -<li><a href="#org11cd8e4">Kurshemsida för TATA54, Talteori </a> +<li><a href="#orgb8be38a">Kurshemsida för TATA54, Talteori </a> <ul> -<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> +<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> </ul> </li> -<li><a href="#orgc6ffe16">Allra senaste nytt VT2024 </a> +<li><a href="#orge4d1d7b">Allra senaste nytt VT2024 </a> <ul> -<li><a href="#orgd106c4f">2024-06-05</a></li> -<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> +<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> <ul> -<li><a href="#org0f556e1">Uppgifter att räkna till nästa gÃ¥ng</a></li> -<li><a href="#orgbc6c0fd">Datorlaboration</a></li> +<li><a href="#org919c9e5">Uppgifter att räkna till nästa gÃ¥ng</a></li> +<li><a href="#orgef7eb4d">Datorlaboration</a></li> </ul> </li> -<li><a href="#org865cc31">2024-04-07</a> +<li><a href="#org4a80012">2024-04-07</a> <ul> -<li><a href="#orga5ff711">Uppgifter att räkna till nästa gÃ¥ng</a></li> -<li><a href="#org9f5a134">Beviset för kvadratisk reciprocitet</a></li> +<li><a href="#orgfb7845d">Uppgifter att räkna till nästa gÃ¥ng</a></li> +<li><a href="#orgd77ff3b">Beviset för kvadratisk reciprocitet</a></li> </ul> </li> -<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> +<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> <ul> -<li><a href="#org7ada8fb">Tvillingfria primtal</a></li> +<li><a href="#org53dcc9b">Tvillingfria primtal</a></li> </ul> </li> -<li><a href="#org5081bbc">2024-01-23</a></li> -<li><a href="#orgec17e4b">2024-01-16</a></li> +<li><a href="#orgd22b4e6">2024-01-23</a></li> +<li><a href="#org5900f63">2024-01-16</a></li> </ul> </li> -<li><a href="#org83cdbc2">Kurslitteratur </a> +<li><a href="#org4f543bd">Kurslitteratur </a> <ul> -<li><a href="#org969d2a9">Kursbok</a></li> -<li><a href="#orgfa4a7ab">Bredvidläsning</a> +<li><a href="#org09cac9a">Kursbok</a></li> +<li><a href="#orgdf2c024">Bredvidläsning</a> <ul> -<li><a href="#orge4da471">Fritt tillgängligt material</a></li> -<li><a href="#org2169300">Andra lämpliga böcker</a></li> +<li><a href="#org9934079">Fritt tillgängligt material</a></li> +<li><a href="#org486a906">Andra lämpliga böcker</a></li> </ul> </li> </ul> </li> -<li><a href="#orgc6c0ef4">KursinnehÃ¥ll </a> +<li><a href="#org83d546e">KursinnehÃ¥ll </a> <ul> -<li><a href="#org43c7b85">Avsnitt av kursboken</a> +<li><a href="#org34795a7">Avsnitt av kursboken</a> <ul> -<li><a href="#org0c49604">Rekommenderade uppgifter </a></li> +<li><a href="#org10138de">Rekommenderade uppgifter </a></li> </ul> </li> -<li><a href="#org33f6268">Kort beskrivning av kursinnehÃ¥llet</a></li> +<li><a href="#orgab0c2e2">Kort beskrivning av kursinnehÃ¥llet</a></li> </ul> </li> -<li><a href="#org0e51919">Föreläsningar </a></li> -<li><a href="#orgf5fd67d">Tentor </a></li> -<li><a href="#orgac41624">Datorlaborationer </a> +<li><a href="#org67ef94b">Föreläsningar </a></li> +<li><a href="#org9e66246">Tentor </a></li> +<li><a href="#orgf236219">Datorlaborationer </a> <ul> -<li><a href="#orgd0ccf06">SageMath</a></li> -<li><a href="#orgd3b0180">Kod frÃ¥n vissa föreläsningar</a></li> -<li><a href="#org85c34f4">Laborationer</a> +<li><a href="#org7a98c02">SageMath</a></li> +<li><a href="#org38724a4">Kod frÃ¥n vissa föreläsningar</a></li> +<li><a href="#org80ba8f8">Laborationer</a> <ul> -<li><a href="#orga1be7da">Hensellyft, Primitiva rötter, Kinesiska restsatsen</a></li> -<li><a href="#org2528f16">KedjebrÃ¥k</a></li> +<li><a href="#org4bb0ea2">Hensellyft, Primitiva rötter, Kinesiska restsatsen</a></li> +<li><a href="#org4f8b714">KedjebrÃ¥k</a></li> </ul> </li> </ul> </li> -<li><a href="#org27d49bb">Tidigare Ã¥r </a> +<li><a href="#org65b020a">Tidigare Ã¥r </a> <ul> -<li><a href="#orga1fa650">TATA54 Anteckningar frÃ¥n tidigare Ã¥r</a> +<li><a href="#org477262d">TATA54 Anteckningar frÃ¥n tidigare Ã¥r</a> <ul> -<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> +<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> </ul> </li> </ul> </li> -<li><a href="#orga44ea53">Index</a></li> +<li><a href="#org22888c0">Index</a></li> </ul> </div> </nav> -<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"> +<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"> </div> -<div id="outline-container-orgbf145e8" class="outline-3"> -<h3 id="orgbf145e8">ÄmnesomrÃ¥de</h3> -<div class="outline-text-3" id="text-orgbf145e8"> +<div id="outline-container-org46c8838" class="outline-3"> +<h3 id="org46c8838">ÄmnesomrÃ¥de</h3> +<div class="outline-text-3" id="text-org46c8838"> <p> Matematik </p> </div> </div> -<div id="outline-container-orgbd10c80" class="outline-3"> -<h3 id="orgbd10c80">Poäng</h3> -<div class="outline-text-3" id="text-orgbd10c80"> +<div id="outline-container-org0536e03" class="outline-3"> +<h3 id="org0536e03">Poäng</h3> +<div class="outline-text-3" id="text-org0536e03"> <p> 6 hp </p> </div> </div> -<div id="outline-container-orgdf916de" class="outline-3"> -<h3 id="orgdf916de">Examinator</h3> -<div class="outline-text-3" id="text-orgdf916de"> +<div id="outline-container-org483cd31" class="outline-3"> +<h3 id="org483cd31">Examinator</h3> +<div class="outline-text-3" id="text-org483cd31"> <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-org0e97f91" class="outline-3"> -<h3 id="org0e97f91">Schema</h3> -<div class="outline-text-3" id="text-org0e97f91"> +<div id="outline-container-org79caf1d" class="outline-3"> +<h3 id="org79caf1d">Schema</h3> +<div class="outline-text-3" id="text-org79caf1d"> <p> Se <a href="https://cloud.timeedit.net/liu/web/schema/ri167XQQ538Z50Qm07065gZ6y2Y7306Q6Y43Y1.html">TimeEdit</a> </p> </div> </div> -<div id="outline-container-org978acab" class="outline-3"> -<h3 id="org978acab">Examination</h3> -<div class="outline-text-3" id="text-org978acab"> +<div id="outline-container-org3280174" class="outline-3"> +<h3 id="org3280174">Examination</h3> +<div class="outline-text-3" id="text-org3280174"> <p> Skriftlig tentamen. </p> @@ -259,13 +259,13 @@ Skriftlig tentamen. </div> </div> </section> -<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"> +<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"> </div> -<div id="outline-container-orgd106c4f" class="outline-3"> -<h3 id="orgd106c4f">2024-06-05</h3> -<div class="outline-text-3" id="text-orgd106c4f"> +<div id="outline-container-org4de2404" class="outline-3"> +<h3 id="org4de2404">2024-06-05</h3> +<div class="outline-text-3" id="text-org4de2404"> <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. @@ -273,18 +273,18 @@ nästa vecka. </p> </div> </div> -<div id="outline-container-orgba4c7fd" class="outline-3"> -<h3 id="orgba4c7fd">2024-06-01</h3> -<div class="outline-text-3" id="text-orgba4c7fd"> +<div id="outline-container-org7866ed4" class="outline-3"> +<h3 id="org7866ed4">2024-06-01</h3> +<div class="outline-text-3" id="text-org7866ed4"> <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"> +<div id="outline-container-org896f14e" class="outline-3"> +<h3 id="org896f14e">2024-05-18</h3> +<div class="outline-text-3" id="text-org896f14e"> <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> @@ -295,13 +295,13 @@ 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="#org06fee11">längre ned pÃ¥ denna sida</a>. +Rosen, finns <a href="#orge3aa510">längre ned pÃ¥ denna sida</a>. </p> </div> </div> -<div id="outline-container-org580c3f6" class="outline-3"> -<h3 id="org580c3f6">2024-05-16</h3> -<div class="outline-text-3" id="text-org580c3f6"> +<div id="outline-container-org016a4e1" class="outline-3"> +<h3 id="org016a4e1">2024-05-16</h3> +<div class="outline-text-3" id="text-org016a4e1"> <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. @@ -312,35 +312,35 @@ Tentamen skall kunna bli av utan problem! </p> </div> </div> -<div id="outline-container-orgfb06446" class="outline-3"> -<h3 id="orgfb06446">2024-05-13</h3> -<div class="outline-text-3" id="text-orgfb06446"> +<div id="outline-container-org4232b8e" class="outline-3"> +<h3 id="org4232b8e">2024-05-13</h3> +<div class="outline-text-3" id="text-org4232b8e"> <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-org36a5a6c" class="outline-3"> -<h3 id="org36a5a6c">2024-05-06</h3> -<div class="outline-text-3" id="text-org36a5a6c"> +<div id="outline-container-org95a2714" class="outline-3"> +<h3 id="org95a2714">2024-05-06</h3> +<div class="outline-text-3" id="text-org95a2714"> <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-orge2800f4" class="outline-3"> -<h3 id="orge2800f4">2024-04-29</h3> -<div class="outline-text-3" id="text-orge2800f4"> +<div id="outline-container-orgcae408e" class="outline-3"> +<h3 id="orgcae408e">2024-04-29</h3> +<div class="outline-text-3" id="text-orgcae408e"> <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-org8296c85" class="outline-3"> -<h3 id="org8296c85">2024-04-23</h3> -<div class="outline-text-3" id="text-org8296c85"> +<div id="outline-container-org9f9d6f3" class="outline-3"> +<h3 id="org9f9d6f3">2024-04-23</h3> +<div class="outline-text-3" id="text-org9f9d6f3"> <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 @@ -353,9 +353,9 @@ beskrivningen kan visas med induktion. </p> </div> </div> -<div id="outline-container-orgc936b6f" class="outline-3"> -<h3 id="orgc936b6f">2024-04-22</h3> -<div class="outline-text-3" id="text-orgc936b6f"> +<div id="outline-container-orgb23df4f" class="outline-3"> +<h3 id="orgb23df4f">2024-04-22</h3> +<div class="outline-text-3" id="text-orgb23df4f"> <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). @@ -363,21 +363,21 @@ Till pÃ¥ fredag 12.4.5b, 12.4.6b </p> </div> </div> -<div id="outline-container-org4dc177a" class="outline-3"> -<h3 id="org4dc177a">2024-04-14</h3> -<div class="outline-text-3" id="text-org4dc177a"> +<div id="outline-container-org6bf16cd" class="outline-3"> +<h3 id="org6bf16cd">2024-04-14</h3> +<div class="outline-text-3" id="text-org6bf16cd"> </div> -<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"> +<div id="outline-container-org919c9e5" class="outline-4"> +<h4 id="org919c9e5">Uppgifter att räkna till nästa gÃ¥ng</h4> +<div class="outline-text-4" id="text-org919c9e5"> <p> 12.2.1bf, 12.2.2cd, 12.2.3c, 12.2.11 </p> </div> </div> -<div id="outline-container-orgbc6c0fd" class="outline-4"> -<h4 id="orgbc6c0fd">Datorlaboration</h4> -<div class="outline-text-4" id="text-orgbc6c0fd"> +<div id="outline-container-orgef7eb4d" class="outline-4"> +<h4 id="orgef7eb4d">Datorlaboration</h4> +<div class="outline-text-4" id="text-orgef7eb4d"> <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 @@ -386,21 +386,21 @@ gränsvärdet av a(k,m) dÃ¥ m gÃ¥r mot oändligheten? </div> </div> </div> -<div id="outline-container-org865cc31" class="outline-3"> -<h3 id="org865cc31">2024-04-07</h3> -<div class="outline-text-3" id="text-org865cc31"> +<div id="outline-container-org4a80012" class="outline-3"> +<h3 id="org4a80012">2024-04-07</h3> +<div class="outline-text-3" id="text-org4a80012"> </div> -<div id="outline-container-orga5ff711" class="outline-4"> -<h4 id="orga5ff711">Uppgifter att räkna till nästa gÃ¥ng</h4> -<div class="outline-text-4" id="text-orga5ff711"> +<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"> <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-org9f5a134" class="outline-4"> -<h4 id="org9f5a134">Beviset för kvadratisk reciprocitet</h4> -<div class="outline-text-4" id="text-org9f5a134"> +<div id="outline-container-orgd77ff3b" class="outline-4"> +<h4 id="orgd77ff3b">Beviset för kvadratisk reciprocitet</h4> +<div class="outline-text-4" id="text-orgd77ff3b"> <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. @@ -409,17 +409,17 @@ 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-org429e5d4" class="outline-3"> -<h3 id="org429e5d4">2024-04-02</h3> -<div class="outline-text-3" id="text-org429e5d4"> +<div id="outline-container-orgb250740" class="outline-3"> +<h3 id="orgb250740">2024-04-02</h3> +<div class="outline-text-3" id="text-orgb250740"> <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-orgfa53138" class="outline-3"> -<h3 id="orgfa53138">2024-03-11</h3> -<div class="outline-text-3" id="text-orgfa53138"> +<div id="outline-container-orged4ff0b" class="outline-3"> +<h3 id="orged4ff0b">2024-03-11</h3> +<div class="outline-text-3" id="text-orged4ff0b"> <p> Jag har nu bokat om föreläsningarna till Fredagar kl 13-15 (fortfarande i kompakta rummet) samt mÃ¥ndag 25 mars kl 13-15, @@ -428,9 +428,9 @@ Det blir 10 tillfällen totalt, vilket bör räcka. </p> </div> </div> -<div id="outline-container-org54eab67" class="outline-3"> -<h3 id="org54eab67">2024-03-06</h3> -<div class="outline-text-3" id="text-org54eab67"> +<div id="outline-container-org0de71ab" class="outline-3"> +<h3 id="org0de71ab">2024-03-06</h3> +<div class="outline-text-3" id="text-org0de71ab"> <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. @@ -439,9 +439,9 @@ 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-org73f95a7" class="outline-3"> -<h3 id="org73f95a7">2024-03-05</h3> -<div class="outline-text-3" id="text-org73f95a7"> +<div id="outline-container-org84eda8d" class="outline-3"> +<h3 id="org84eda8d">2024-03-05</h3> +<div class="outline-text-3" id="text-org84eda8d"> <p> Det har framförts önskemÃ¥l om att byta tid för lektionerna i period 4 för att undvika kollision med kursen i optimeringslära. @@ -462,9 +462,9 @@ Det rör sig om 11 tillfällen totalt. </p> </div> </div> -<div id="outline-container-orgf0c9193" class="outline-3"> -<h3 id="orgf0c9193">2024-02-29</h3> -<div class="outline-text-3" id="text-orgf0c9193"> +<div id="outline-container-orgea6ed65" class="outline-3"> +<h3 id="orgea6ed65">2024-02-29</h3> +<div class="outline-text-3" id="text-orgea6ed65"> <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. @@ -478,9 +478,9 @@ Till lektionen efter det (27 mars) sÃ¥ räknar ni </div> </div> -<div id="outline-container-org7f7d557" class="outline-3"> -<h3 id="org7f7d557">2024-02-20</h3> -<div class="outline-text-3" id="text-org7f7d557"> +<div id="outline-container-org823f5e2" class="outline-3"> +<h3 id="org823f5e2">2024-02-20</h3> +<div class="outline-text-3" id="text-org823f5e2"> <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. @@ -491,7 +491,7 @@ grad 5 eller 6. </p> <div class="org-src-container"> -<pre class="src src-sage" id="org4d90c6b">def H_L_tree(f, p: int, r: int): +<pre class="src src-sage" id="orgce6ce24">def H_L_tree(f, p: int, r: int): vert = [(0,0)] for j in range(1,r+1): @@ -520,25 +520,25 @@ H_L_tree(f,p,r).plot(layout='tree') </div> -<figure id="orgd0b857d"> +<figure id="orgcf88db9"> <img src="img/Henseluppgift.png" alt="Henseluppgift.png"> </figure> </div> </div> -<div id="outline-container-org6fc379e" class="outline-3"> -<h3 id="org6fc379e">2024-02-12</h3> -<div class="outline-text-3" id="text-org6fc379e"> +<div id="outline-container-org1c24ff1" class="outline-3"> +<h3 id="org1c24ff1">2024-02-12</h3> +<div class="outline-text-3" id="text-org1c24ff1"> <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-org7b22a27" class="outline-3"> -<h3 id="org7b22a27">2024-02-07</h3> -<div class="outline-text-3" id="text-org7b22a27"> +<div id="outline-container-org499023d" class="outline-3"> +<h3 id="org499023d">2024-02-07</h3> +<div class="outline-text-3" id="text-org499023d"> <p> Till nästa lektion (12 feb) sÃ¥ tittar ni pÃ¥ uppgifterna 4.1.5, 4.1.9b, 4.2.8c,4.3.3. @@ -548,9 +548,9 @@ att vara i Kompakta rummet. </div> </div> -<div id="outline-container-orgbc98f91" class="outline-3"> -<h3 id="orgbc98f91">2024-01-30</h3> -<div class="outline-text-3" id="text-orgbc98f91"> +<div id="outline-container-orgf683b42" class="outline-3"> +<h3 id="orgf683b42">2024-01-30</h3> +<div class="outline-text-3" id="text-orgf683b42"> <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> @@ -559,9 +559,9 @@ att vara i Kompakta rummet. </ul> </div> -<div id="outline-container-org7ada8fb" class="outline-4"> -<h4 id="org7ada8fb">Tvillingfria primtal</h4> -<div class="outline-text-4" id="text-org7ada8fb"> +<div id="outline-container-org53dcc9b" class="outline-4"> +<h4 id="org53dcc9b">Tvillingfria primtal</h4> +<div class="outline-text-4" id="text-org53dcc9b"> <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 @@ -569,7 +569,7 @@ garanterar oändligt mÃ¥nga primtal i nZ + k. </p> <div class="org-src-container"> -<pre class="src src-sage" id="org1e013cf">def repr(n): +<pre class="src src-sage" id="org400f273">def repr(n): return [k for k in range(n) if gcd(k,n)==1] def isolated(n): @@ -600,17 +600,17 @@ Körning visar att n=15, k=7 är minsta exemplet. </div> </div> -<div id="outline-container-org5081bbc" class="outline-3"> -<h3 id="org5081bbc">2024-01-23</h3> -<div class="outline-text-3" id="text-org5081bbc"> +<div id="outline-container-orgd22b4e6" class="outline-3"> +<h3 id="orgd22b4e6">2024-01-23</h3> +<div class="outline-text-3" id="text-orgd22b4e6"> <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-orgec17e4b" class="outline-3"> -<h3 id="orgec17e4b">2024-01-16</h3> -<div class="outline-text-3" id="text-orgec17e4b"> +<div id="outline-container-org5900f63" class="outline-3"> +<h3 id="org5900f63">2024-01-16</h3> +<div class="outline-text-3" id="text-org5900f63"> <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> @@ -618,7 +618,7 @@ 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="#orgd99cfc5">rekommenderade uppgifter</a>) +(hämtade frÃ¥n listan med <a href="#org7db4ce4">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. @@ -632,19 +632,19 @@ till, nu med fokus pÃ¥ att förstÃ¥ bevisen.</li> </div> </section> -<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"> +<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"> </div> -<div id="outline-container-org969d2a9" class="outline-3"> -<h3 id="org969d2a9">Kursbok</h3> -<div class="outline-text-3" id="text-org969d2a9"> +<div id="outline-container-org09cac9a" class="outline-3"> +<h3 id="org09cac9a">Kursbok</h3> +<div class="outline-text-3" id="text-org09cac9a"> <p> Kursbok är <a href="https://www.prisjakt.nu/produkt.php?p=8083662">Elementary Number Theory</a> av Kenneth Rosen. </p> -<figure id="orgc8a4fed"> +<figure id="org09cfcfd"> <img src="img/Rosen6ed.png" alt="Rosen6ed.png" width="40%"> <figcaption><span class="figure-number">Illustration 1 </span>Elementary Number Theory, Kenneth Rosen</figcaption> @@ -656,13 +656,13 @@ vilket inte pÃ¥verkar innehÃ¥llet. </p> </div> </div> -<div id="outline-container-orgfa4a7ab" class="outline-3"> -<h3 id="orgfa4a7ab">Bredvidläsning</h3> -<div class="outline-text-3" id="text-orgfa4a7ab"> +<div id="outline-container-orgdf2c024" class="outline-3"> +<h3 id="orgdf2c024">Bredvidläsning</h3> +<div class="outline-text-3" id="text-orgdf2c024"> </div> -<div id="outline-container-orge4da471" class="outline-4"> -<h4 id="orge4da471">Fritt tillgängligt material</h4> -<div class="outline-text-4" id="text-orge4da471"> +<div id="outline-container-org9934079" class="outline-4"> +<h4 id="org9934079">Fritt tillgängligt material</h4> +<div class="outline-text-4" id="text-org9934079"> <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 @@ -680,9 +680,9 @@ Jolly för en metod att hitta primitiva rötter.</li> </ul> </div> </div> -<div id="outline-container-org2169300" class="outline-4"> -<h4 id="org2169300">Andra lämpliga böcker</h4> -<div class="outline-text-4" id="text-org2169300"> +<div id="outline-container-org486a906" class="outline-4"> +<h4 id="org486a906">Andra lämpliga böcker</h4> +<div class="outline-text-4" id="text-org486a906"> <ul class="org-ul"> <li>BAKER. A concise introduction to the theory of numbers.</li> <li>DAVENPORT. The higher arithmetic.</li> @@ -702,13 +702,13 @@ fortbildning efter denna kurs.</li> -<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"> +<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"> </div> -<div id="outline-container-org43c7b85" class="outline-3"> -<h3 id="org43c7b85">Avsnitt av kursboken</h3> -<div class="outline-text-3" id="text-org43c7b85"> +<div id="outline-container-org34795a7" class="outline-3"> +<h3 id="org34795a7">Avsnitt av kursboken</h3> +<div class="outline-text-3" id="text-org34795a7"> <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 @@ -718,15 +718,15 @@ frÃ¥n just dessa avsnitt. </p> </div> -<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 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> <ul class="org-ul"> -<li><a id="org1cc7e3a"></a>Kap 1<br> +<li><a id="org15b8e33"></a>Kap 1<br> <ul class="org-ul"> -<li><a id="org978ec51"></a>1.5<br> -<div class="outline-text-6" id="text-org978ec51"> +<li><a id="orgb33f2f0"></a>1.5<br> +<div class="outline-text-6" id="text-orgb33f2f0"> <p> 8a,9b,18,36,37 </p> @@ -734,46 +734,46 @@ frÃ¥n just dessa avsnitt. </li> </ul> </li> -<li><a id="org0585282"></a>Kap 3<br> +<li><a id="org681038a"></a>Kap 3<br> <ul class="org-ul"> -<li><a id="orgba991bb"></a>3.1<br> -<div class="outline-text-6" id="text-orgba991bb"> +<li><a id="org0f22bbf"></a>3.1<br> +<div class="outline-text-6" id="text-org0f22bbf"> <p> 1ab, 2f,6. </p> </div> </li> -<li><a id="org1d83cec"></a>3.2<br> -<div class="outline-text-6" id="text-org1d83cec"> +<li><a id="orga37167f"></a>3.2<br> +<div class="outline-text-6" id="text-orga37167f"> <ol class="org-ol"> <li></li> </ol> </div> </li> -<li><a id="org1f58297"></a>3.3<br> -<div class="outline-text-6" id="text-org1f58297"> +<li><a id="orgb03bced"></a>3.3<br> +<div class="outline-text-6" id="text-orgb03bced"> <p> 1df,2ef,10,24,30,31 </p> </div> </li> -<li><a id="org658bec3"></a>3.4<br> -<div class="outline-text-6" id="text-org658bec3"> +<li><a id="orgec1beae"></a>3.4<br> +<div class="outline-text-6" id="text-orgec1beae"> <p> 1bc, 19*, 20*. </p> </div> </li> -<li><a id="orgb0fdc9e"></a>3.5<br> -<div class="outline-text-6" id="text-orgb0fdc9e"> +<li><a id="orgcb8a7bd"></a>3.5<br> +<div class="outline-text-6" id="text-orgcb8a7bd"> <p> 1il, 2, 4c, 29cd, 32*, 34, 58ac. </p> </div> </li> -<li><a id="org45b4d99"></a>3.7<br> -<div class="outline-text-6" id="text-org45b4d99"> +<li><a id="orga2dfbe1"></a>3.7<br> +<div class="outline-text-6" id="text-orga2dfbe1"> <p> 1cd </p> @@ -781,31 +781,31 @@ frÃ¥n just dessa avsnitt. </li> </ul> </li> -<li><a id="orgbb7b14d"></a>Kap 4<br> +<li><a id="org37c2a66"></a>Kap 4<br> <ul class="org-ul"> -<li><a id="org06c1fef"></a>4.1<br> -<div class="outline-text-6" id="text-org06c1fef"> +<li><a id="org6253340"></a>4.1<br> +<div class="outline-text-6" id="text-org6253340"> <p> 4,5,7ab,9bc. </p> </div> </li> -<li><a id="org53f1544"></a>4.2<br> -<div class="outline-text-6" id="text-org53f1544"> +<li><a id="org54fbae8"></a>4.2<br> +<div class="outline-text-6" id="text-org54fbae8"> <p> 1df, 8c, 9d. </p> </div> </li> -<li><a id="org490796e"></a>4.3<br> -<div class="outline-text-6" id="text-org490796e"> +<li><a id="org5ae1ea7"></a>4.3<br> +<div class="outline-text-6" id="text-org5ae1ea7"> <p> 3,4. </p> </div> </li> -<li><a id="orgb4590fd"></a>4.4<br> -<div class="outline-text-6" id="text-orgb4590fd"> +<li><a id="org7fb6f3a"></a>4.4<br> +<div class="outline-text-6" id="text-org7fb6f3a"> <p> 2ab. </p> @@ -813,10 +813,10 @@ frÃ¥n just dessa avsnitt. </li> </ul> </li> -<li><a id="org8aea6f0"></a>Kap 5<br> +<li><a id="org67c0b01"></a>Kap 5<br> <ul class="org-ul"> -<li><a id="org34987f8"></a>5.1<br> -<div class="outline-text-6" id="text-org34987f8"> +<li><a id="org72b5624"></a>5.1<br> +<div class="outline-text-6" id="text-org72b5624"> <p> 4ab. </p> @@ -824,26 +824,26 @@ frÃ¥n just dessa avsnitt. </li> </ul> </li> -<li><a id="org44c4796"></a>Kap 6<br> +<li><a id="org3e672b9"></a>Kap 6<br> <ul class="org-ul"> -<li><a id="org5467c3d"></a>6.1<br> -<div class="outline-text-6" id="text-org5467c3d"> +<li><a id="org1f56359"></a>6.1<br> +<div class="outline-text-6" id="text-org1f56359"> <p> 4,5,6,9,10,14,18,19,22,24,24,28,36,38*,41,48*,52. </p> </div> </li> -<li><a id="orgcb44edd"></a>6.2<br> -<div class="outline-text-6" id="text-orgcb44edd"> +<li><a id="org6facf0b"></a>6.2<br> +<div class="outline-text-6" id="text-org6facf0b"> <p> 2,8,12,16ab. </p> </div> </li> -<li><a id="orga80d292"></a>6.3<br> -<div class="outline-text-6" id="text-orga80d292"> +<li><a id="org3eb9c1b"></a>6.3<br> +<div class="outline-text-6" id="text-org3eb9c1b"> <p> 1d,6,7,22* </p> @@ -852,31 +852,31 @@ frÃ¥n just dessa avsnitt. </ul> </li> -<li><a id="orgdcdc40f"></a>Kap 7<br> +<li><a id="orgdc43d50"></a>Kap 7<br> <ul class="org-ul"> -<li><a id="org90dcdab"></a>7.1<br> -<div class="outline-text-6" id="text-org90dcdab"> +<li><a id="org70452c6"></a>7.1<br> +<div class="outline-text-6" id="text-org70452c6"> <p> 2bc,5,8. </p> </div> </li> -<li><a id="org39c711c"></a>7.2<br> -<div class="outline-text-6" id="text-org39c711c"> +<li><a id="org613722d"></a>7.2<br> +<div class="outline-text-6" id="text-org613722d"> <p> 1bd,2cd,8,34*,35,38*. </p> </div> </li> -<li><a id="org2d9e7af"></a>7.3<br> -<div class="outline-text-6" id="text-org2d9e7af"> +<li><a id="orgf2f87e9"></a>7.3<br> +<div class="outline-text-6" id="text-orgf2f87e9"> <p> 3b,4,7,8,10,18,22**,28*,29cd. </p> </div> </li> -<li><a id="org01dd2e1"></a>7.4<br> -<div class="outline-text-6" id="text-org01dd2e1"> +<li><a id="org540c16c"></a>7.4<br> +<div class="outline-text-6" id="text-org540c16c"> <p> 1bd,2be,14,22,23,24,30,31. </p> @@ -885,47 +885,47 @@ frÃ¥n just dessa avsnitt. </ul> </li> -<li><a id="org22e6c42"></a>Kap 9<br> +<li><a id="orgd525786"></a>Kap 9<br> <ul class="org-ul"> -<li><a id="org3171b1b"></a>9.1<br> -<div class="outline-text-6" id="text-org3171b1b"> +<li><a id="org8894071"></a>9.1<br> +<div class="outline-text-6" id="text-org8894071"> <p> 1ad, 2cd, 5b, 6df, 8, 10, 20*, 22*. </p> </div> </li> -<li><a id="org9d9f07a"></a>9.2<br> -<div class="outline-text-6" id="text-org9d9f07a"> +<li><a id="org68316e6"></a>9.2<br> +<div class="outline-text-6" id="text-org68316e6"> <p> 1d, 2d, 3e, 6. </p> </div> </li> -<li><a id="orgf0b7847"></a>9.3<br> -<div class="outline-text-6" id="text-orgf0b7847"> +<li><a id="orgabc73c3"></a>9.3<br> +<div class="outline-text-6" id="text-orgabc73c3"> <p> 2,3c, 5c,6c, 8b, 10. </p> </div> </li> -<li><a id="org9f8fe1f"></a>9.4<br> -<div class="outline-text-6" id="text-org9f8fe1f"> +<li><a id="org63ae623"></a>9.4<br> +<div class="outline-text-6" id="text-org63ae623"> <p> 1, 2b, 3a, 4, 9, 10, 19, 20*. </p> </div> </li> -<li><a id="org99d1763"></a>9.5<br> -<div class="outline-text-6" id="text-org99d1763"> +<li><a id="org9c13bc0"></a>9.5<br> +<div class="outline-text-6" id="text-org9c13bc0"> <p> 2,3,10. </p> </div> </li> -<li><a id="orgfa55cb8"></a>9.6<br> -<div class="outline-text-6" id="text-orgfa55cb8"> +<li><a id="org5015ce5"></a>9.6<br> +<div class="outline-text-6" id="text-org5015ce5"> <p> 1bcg, 4def, 13*, 14*. </p> @@ -934,31 +934,31 @@ frÃ¥n just dessa avsnitt. </ul> </li> -<li><a id="org94cf781"></a>Kap 11<br> +<li><a id="org82f34bf"></a>Kap 11<br> <ul class="org-ul"> -<li><a id="org7d092f2"></a>11.1<br> -<div class="outline-text-6" id="text-org7d092f2"> +<li><a id="org3d2f276"></a>11.1<br> +<div class="outline-text-6" id="text-org3d2f276"> <p> 1d, 4, 25. </p> </div> </li> -<li><a id="org88bf99e"></a>11.2<br> -<div class="outline-text-6" id="text-org88bf99e"> +<li><a id="orgc0c01e2"></a>11.2<br> +<div class="outline-text-6" id="text-orgc0c01e2"> <p> 1cd, 2, 4, 5. </p> </div> </li> -<li><a id="org01d2881"></a>11.3<br> -<div class="outline-text-6" id="text-org01d2881"> +<li><a id="org1af5d6e"></a>11.3<br> +<div class="outline-text-6" id="text-org1af5d6e"> <p> 1ef, 5, 6. </p> </div> </li> -<li><a id="orgad3a1ae"></a>11.4<br> -<div class="outline-text-6" id="text-orgad3a1ae"> +<li><a id="orgfe1e34d"></a>11.4<br> +<div class="outline-text-6" id="text-orgfe1e34d"> <p> 1, 2, 5, 6. </p> @@ -967,32 +967,32 @@ frÃ¥n just dessa avsnitt. </ul> </li> -<li><a id="org44aa093"></a>Kap 12<br> +<li><a id="org2cc3178"></a>Kap 12<br> <ul class="org-ul"> -<li><a id="org936a20d"></a>12.2<br> -<div class="outline-text-6" id="text-org936a20d"> +<li><a id="org7cac01e"></a>12.2<br> +<div class="outline-text-6" id="text-org7cac01e"> <p> 1bf, 2cd, 3c, 4c. </p> </div> </li> -<li><a id="org30d8efe"></a>12.3<br> -<div class="outline-text-6" id="text-org30d8efe"> +<li><a id="orgb90f3a1"></a>12.3<br> +<div class="outline-text-6" id="text-orgb90f3a1"> <p> 1c, 2a, 6*, 7. </p> </div> </li> -<li><a id="orgc28fd4b"></a>12.4<br> -<div class="outline-text-6" id="text-orgc28fd4b"> +<li><a id="orgca93be0"></a>12.4<br> +<div class="outline-text-6" id="text-orgca93be0"> <p> 1c, 2c, 3b, 4a, 5b, 6b, 7b, 8, 10, 17. </p> </div> </li> -<li><a id="org6fe52f2"></a>12.5<br> -<div class="outline-text-6" id="text-org6fe52f2"> +<li><a id="org677f1bb"></a>12.5<br> +<div class="outline-text-6" id="text-org677f1bb"> <ol class="org-ol"> <li></li> </ol> @@ -1001,32 +1001,32 @@ frÃ¥n just dessa avsnitt. </ul> </li> -<li><a id="org3f74cbe"></a>Kap 13<br> +<li><a id="orgedd8e06"></a>Kap 13<br> <ul class="org-ul"> -<li><a id="orgd9fc89a"></a>13.1<br> -<div class="outline-text-6" id="text-orgd9fc89a"> +<li><a id="orgbcdde20"></a>13.1<br> +<div class="outline-text-6" id="text-orgbcdde20"> <p> 1, 2, 3, 8, 16. </p> </div> </li> -<li><a id="org80effe7"></a>13.2<br> -<div class="outline-text-6" id="text-org80effe7"> +<li><a id="org8e3a488"></a>13.2<br> +<div class="outline-text-6" id="text-org8e3a488"> <p> 3, 4, 6*, 8, 10, 11*, 20. </p> </div> </li> -<li><a id="orgc699f00"></a>13.3<br> -<div class="outline-text-6" id="text-orgc699f00"> +<li><a id="org528308d"></a>13.3<br> +<div class="outline-text-6" id="text-org528308d"> <p> 1b, 2gh,3cd, 6, 7, 9c, 10ef. </p> </div> </li> -<li><a id="orgb9e9b7b"></a>13.4<br> -<div class="outline-text-6" id="text-orgb9e9b7b"> +<li><a id="orgf68bc5b"></a>13.4<br> +<div class="outline-text-6" id="text-orgf68bc5b"> <p> 1c, 2a, 3def, 4ab, 6de, 8*. @@ -1036,25 +1036,25 @@ frÃ¥n just dessa avsnitt. </ul> </li> -<li><a id="org1a1cc94"></a>Kap 14<br> +<li><a id="orgdcc1ad3"></a>Kap 14<br> <ul class="org-ul"> -<li><a id="org8bd881e"></a>14.1<br> -<div class="outline-text-6" id="text-org8bd881e"> +<li><a id="org59fea14"></a>14.1<br> +<div class="outline-text-6" id="text-org59fea14"> <p> 1ac, 12, 13, 17a. </p> </div> </li> -<li><a id="org659103e"></a>14.2<br> -<div class="outline-text-6" id="text-org659103e"> +<li><a id="orgb5250d8"></a>14.2<br> +<div class="outline-text-6" id="text-orgb5250d8"> <p> 16ab, 17bc. </p> </div> </li> -<li><a id="org20cf5b1"></a>14.3<br> -<div class="outline-text-6" id="text-org20cf5b1"> +<li><a id="org3675a33"></a>14.3<br> +<div class="outline-text-6" id="text-org3675a33"> <p> 1bc, 2c </p> @@ -1066,15 +1066,15 @@ frÃ¥n just dessa avsnitt. </div> </div> -<div id="outline-container-org33f6268" class="outline-3"> -<h3 id="org33f6268">Kort beskrivning av kursinnehÃ¥llet</h3> +<div id="outline-container-orgab0c2e2" class="outline-3"> +<h3 id="orgab0c2e2">Kort beskrivning av kursinnehÃ¥llet</h3> </div> </section> -<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"> +<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"> <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. @@ -1253,9 +1253,9 @@ De svenska versionerna är nyare. NÃ¥gra av föreläsningarna tar tvÃ¥ tillfäll </section> -<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"> +<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"> <table> @@ -1277,6 +1277,13 @@ De svenska versionerna är nyare. NÃ¥gra av föreläsningarna tar tvÃ¥ tillfäll </tr> </thead> <tbody> +<tr> +<td class="org-right">2024-08-22</td> +<td class="org-left">Jan Snellman</td> +<td class="org-left"><a href="exams/2024/tenta-TATA54-20240822.pdf">TATA5420240822</a></td> +<td class="org-left"><a href="exams/2024/tenta-TATA54-20240822-losning.pdf">TATA5420240822losn</a></td> +</tr> + <tr> <td class="org-right">2024-06-01</td> <td class="org-left">Jan Snellman</td> @@ -1464,13 +1471,13 @@ De svenska versionerna är nyare. NÃ¥gra av föreläsningarna tar tvÃ¥ tillfäll </section> -<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"> +<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"> </div> -<div id="outline-container-orgd0ccf06" class="outline-3"> -<h3 id="orgd0ccf06">SageMath</h3> -<div class="outline-text-3" id="text-orgd0ccf06"> +<div id="outline-container-org7a98c02" class="outline-3"> +<h3 id="org7a98c02">SageMath</h3> +<div class="outline-text-3" id="text-org7a98c02"> <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>, @@ -1486,9 +1493,9 @@ Ett tredje alternativ, enkelt och flärdfritt, är att mata in sin kod till <a h </p> </div> </div> -<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"> +<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"> <ul class="org-ul"> <li><a href="labs/lecture0.html">Föreläsning 0</a></li> <li><a href="labs/lecture1.html">Föreläsning 1</a></li> @@ -1499,21 +1506,21 @@ Ett tredje alternativ, enkelt och flärdfritt, är att mata in sin kod till <a h </ul> </div> </div> -<div id="outline-container-org85c34f4" class="outline-3"> -<h3 id="org85c34f4">Laborationer</h3> -<div class="outline-text-3" id="text-org85c34f4"> +<div id="outline-container-org80ba8f8" class="outline-3"> +<h3 id="org80ba8f8">Laborationer</h3> +<div class="outline-text-3" id="text-org80ba8f8"> </div> -<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"> +<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"> <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-org2528f16" class="outline-4"> -<h4 id="org2528f16">KedjebrÃ¥k</h4> -<div class="outline-text-4" id="text-org2528f16"> +<div id="outline-container-org4f8b714" class="outline-4"> +<h4 id="org4f8b714">KedjebrÃ¥k</h4> +<div class="outline-text-4" id="text-org4f8b714"> <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> @@ -1524,20 +1531,20 @@ Finns att <a href="labs/kedjebraklab.html">läsa direkt</a> eller som <a href="l -<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"> +<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"> </div> -<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 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> -<div id="outline-container-orgd4aaf8a" class="outline-4"> -<h4 id="orgd4aaf8a">2023</h4> -<div class="outline-text-4" id="text-orgd4aaf8a"> +<div id="outline-container-org780ed90" class="outline-4"> +<h4 id="org780ed90">2023</h4> +<div class="outline-text-4" id="text-org780ed90"> <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 @@ -1591,9 +1598,9 @@ tryckfel (skall vara w(d)). 7.2.38 är komplicerad och kan skippas.</li> </div> -<div id="outline-container-orgc39991d" class="outline-4"> -<h4 id="orgc39991d">2021</h4> -<div class="outline-text-4" id="text-orgc39991d"> +<div id="outline-container-org780092f" class="outline-4"> +<h4 id="org780092f">2021</h4> +<div class="outline-text-4" id="text-org780092f"> <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 @@ -1641,9 +1648,9 @@ nÃ¥gon inbjudan, sÃ¥ mejla mig.</li> </div> </div> -<div id="outline-container-org6bff760" class="outline-4"> -<h4 id="org6bff760">2020</h4> -<div class="outline-text-4" id="text-org6bff760"> +<div id="outline-container-org2b03280" class="outline-4"> +<h4 id="org2b03280">2020</h4> +<div class="outline-text-4" id="text-org2b03280"> <ul class="org-ul"> <li><p> 2020-12-12: Kursen kommer att ges VT2021, med start den 19e januari. @@ -1696,9 +1703,9 @@ someone else (perhaps </div> </div> -<div id="outline-container-org85cd779" class="outline-4"> -<h4 id="org85cd779">2019</h4> -<div class="outline-text-4" id="text-org85cd779"> +<div id="outline-container-org9b6101f" class="outline-4"> +<h4 id="org9b6101f">2019</h4> +<div class="outline-text-4" id="text-org9b6101f"> <ul class="org-ul"> <li>2019-11-01: The course will not be given spring 2020.</li> @@ -1713,9 +1720,9 @@ available.</li> </div> </div> -<div id="outline-container-org21f5089" class="outline-4"> -<h4 id="org21f5089">2018</h4> -<div class="outline-text-4" id="text-org21f5089"> +<div id="outline-container-orgba3d96f" class="outline-4"> +<h4 id="orgba3d96f">2018</h4> +<div class="outline-text-4" id="text-orgba3d96f"> <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 @@ -1728,9 +1735,9 @@ available.</li> </div> </div> -<div id="outline-container-org7ce4987" class="outline-4"> -<h4 id="org7ce4987">2017</h4> -<div class="outline-text-4" id="text-org7ce4987"> +<div id="outline-container-org45290d5" class="outline-4"> +<h4 id="org45290d5">2017</h4> +<div class="outline-text-4" id="text-org45290d5"> <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 @@ -1753,7 +1760,7 @@ Another text is <a href="https://wstein.org/ent/">Elementary Number Theory</a> a </ul> -<figure id="org2bc4bd6"> +<figure id="org73a3f81"> <img src="img/sieveE.jpg" alt="sieveE.jpg"> </figure> @@ -1763,9 +1770,9 @@ Another text is <a href="https://wstein.org/ent/">Elementary Number Theory</a> a </section> -<section id="outline-container-orga44ea53" class="outline-2"> -<h2 id="orga44ea53">Index</h2> -<div class="outline-text-2" id="text-orga44ea53"> +<section id="outline-container-org22888c0" class="outline-2"> +<h2 id="org22888c0">Index</h2> +<div class="outline-text-2" id="text-org22888c0"> <p> <a href="sitemap.html">Samtliga nÃ¥bara filer</a> </p> @@ -1774,7 +1781,7 @@ 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: 2024-06-05</p> +<p class="date">Created: 2024-08-22</p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> </footer> </body> diff --git a/public/labs/HenselLyftLabHT2023.html b/public/labs/HenselLyftLabHT2023.html index 4031be2aaad04e833493413665d219255f7877cb..d4fffeff6afdf9d33de3b960af6acd5658170983 100644 --- a/public/labs/HenselLyftLabHT2023.html +++ b/public/labs/HenselLyftLabHT2023.html @@ -1,7 +1,7 @@ <!DOCTYPE html> <html lang="en"> <head> -<!-- 2024-04-05 --> +<!-- 2024-08-22 --> <meta charset="utf-8" /> <meta name="viewport" content="width=device-width, initial-scale=1" /> <title>SageMath-övningar pÃ¥ Hensellyft, primitiva rötter, och KRS</title> @@ -50,11 +50,11 @@ <body> <header id="top" class="status"> <div id="navbar" style ="text-align: center;"> - <a href='https://liu.se'>LiU</a> - - <a href='https://liu.se/organisation/liu/mai'>MAI</a> - - <a href='https://liu.se/organisation/liu/mai'>Grundutbildning</a> - - <a href='https://courses.mai.liu.se/Lists/html/'>Kurser</a> - - <a href='index.html'>TATA54</a></div> + <a href='https://liu.se'>LiU</a> - + <a href='https://liu.se/organisation/liu/mai'>MAI</a> - + <a href='https://liu.se/organisation/liu/mai'>Grundutbildning</a> - + <a href='https://courses.mai.liu.se/Lists/html/'>Kurser</a> - + <a href='index.html'>TATA54</a></div> </header> <main id="content" class="content"> <header> @@ -65,22 +65,22 @@ <ul> <li><a href="#unika-hensellyft">Ej unika hensellyft</a> <ul> -<li><a href="#orgb923ff8">Exempel 1, unika lyft</a> +<li><a href="#orgd387462">Exempel 1, unika lyft</a> <ul> -<li><a href="#org6be1fa2">Övning 1</a></li> -<li><a href="#orgc35d91f">Större p, fortfarande unika lyft</a></li> -<li><a href="#orgd3c72b3">Övning 2</a></li> +<li><a href="#org553e3fc">Övning 1</a></li> +<li><a href="#orgf02802e">Större p, fortfarande unika lyft</a></li> +<li><a href="#org6242051">Övning 2</a></li> </ul> </li> </ul> </li> -<li><a href="#org659b2ca">Unika lyft</a> +<li><a href="#org104f746">Unika lyft</a> <ul> <li><a href="#exempel-4.21">Exempel 4.21</a></li> -<li><a href="#org632696a">övning 3</a></li> +<li><a href="#org1868400">övning 3</a></li> <li><a href="#ex-4.23">Ex 4.23</a> <ul> -<li><a href="#org59ffa70">Övning 4</a></li> +<li><a href="#orgb19d4b7">Övning 4</a></li> </ul> </li> </ul> @@ -89,11 +89,11 @@ <ul> <li><a href="#ex-4.22">Ex 4.22</a> <ul> -<li><a href="#orgd02384a">Övning 5</a></li> -<li><a href="#org7f5a24e">Övning 6</a></li> +<li><a href="#org9fa80b2">Övning 5</a></li> +<li><a href="#org9dff539">Övning 6</a></li> </ul> </li> -<li><a href="#org1b1b5b2">Allt lyfter inte</a></li> +<li><a href="#orgde4c67d">Allt lyfter inte</a></li> </ul> </li> <li><a href="#kvadratrötter-mm">Kvadratrötter mm</a> @@ -113,7 +113,7 @@ </div> </nav> <div class="org-src-container"> -<pre class="src src-sage" id="org8903563">def H_L_tree(f, p: int, r: int): +<pre class="src src-sage" id="org750e867">def H_L_tree(f, p: int, r: int): vert = [(0,0)] for j in range(1,r+1): @@ -136,9 +136,9 @@ <div class="outline-text-2" id="text-unika-hensellyft"> </div> -<div id="outline-container-orgb923ff8" class="outline-3"> -<h3 id="orgb923ff8">Exempel 1, unika lyft</h3> -<div class="outline-text-3" id="text-orgb923ff8"> +<div id="outline-container-orgd387462" class="outline-3"> +<h3 id="orgd387462">Exempel 1, unika lyft</h3> +<div class="outline-text-3" id="text-orgd387462"> <p> \(x^{^{p-1}} -1 \mod p^r\) </p> @@ -160,7 +160,7 @@ H_L_tree(f,p,r).plot(layout='tree') </div> -<figure id="org6aac4a1"> +<figure id="orgab9b3e3"> <img src="../img/HenselLyftLabHT2023_fig1.png" alt="HenselLyftLabHT2023_fig1.png"> </figure> @@ -180,7 +180,7 @@ H_L_tree(f,p,r).plot(layout='tree') </div> -<figure id="org97d4a85"> +<figure id="orgf3bbcb5"> <img src="../img/HenselLyftLabHT2023_fig1.png" alt="HenselLyftLabHT2023_fig1.png"> </figure> @@ -197,7 +197,7 @@ H_L_tree(f,p,r).plot(layout='tree') </div> -<figure id="orgadb1bc0"> +<figure id="org747f18f"> <img src="../img/HenselLyftLabHT2023_fig1.png" alt="HenselLyftLabHT2023_fig1.png"> </figure> @@ -213,7 +213,7 @@ H_L_tree(f,p,r).plot(layout='tree') </div> -<figure id="orgee6db14"> +<figure id="org02252c4"> <img src="../img/HenselLyftLabHT2023_fig1.png" alt="HenselLyftLabHT2023_fig1.png"> </figure> @@ -287,9 +287,9 @@ y </div> </div> -<div id="outline-container-org6be1fa2" class="outline-4"> -<h4 id="org6be1fa2">Övning 1</h4> -<div class="outline-text-4" id="text-org6be1fa2"> +<div id="outline-container-org553e3fc" class="outline-4"> +<h4 id="org553e3fc">Övning 1</h4> +<div class="outline-text-4" id="text-org553e3fc"> <p> Välj en tredje rot och lyft den </p> @@ -298,9 +298,9 @@ Välj en tredje rot och lyft den -<div id="outline-container-orgc35d91f" class="outline-4"> -<h4 id="orgc35d91f">Större p, fortfarande unika lyft</h4> -<div class="outline-text-4" id="text-orgc35d91f"> +<div id="outline-container-orgf02802e" class="outline-4"> +<h4 id="orgf02802e">Större p, fortfarande unika lyft</h4> +<div class="outline-text-4" id="text-orgf02802e"> <p> Hitta nollställena mod p<sup>n</sup> till följande: </p> @@ -316,7 +316,7 @@ H_L_tree(f,p,r).plot(layout='tree') </div> -<figure id="orgfe5b92a"> +<figure id="org86d33c9"> <img src="../img/HenselLyftLabHT2023_fig2.png" alt="HenselLyftLabHT2023_fig2.png"> </figure> @@ -325,9 +325,9 @@ H_L_tree(f,p,r).plot(layout='tree') -<div id="outline-container-orgd3c72b3" class="outline-4"> -<h4 id="orgd3c72b3">Övning 2</h4> -<div class="outline-text-4" id="text-orgd3c72b3"> +<div id="outline-container-org6242051" class="outline-4"> +<h4 id="org6242051">Övning 2</h4> +<div class="outline-text-4" id="text-org6242051"> <p> Har f nÃ¥gra rationella rötter? (Ignorera bilden, gör en egen utredning). Välj nÃ¥gon rot mod p och lyft den. @@ -338,9 +338,9 @@ Välj nÃ¥gon rot mod p och lyft den. </section> -<section id="outline-container-org659b2ca" class="outline-2"> -<h2 id="org659b2ca">Unika lyft</h2> -<div class="outline-text-2" id="text-org659b2ca"> +<section id="outline-container-org104f746" class="outline-2"> +<h2 id="org104f746">Unika lyft</h2> +<div class="outline-text-2" id="text-org104f746"> </div> <div id="outline-container-exempel-4.21" class="outline-3"> <h3 id="exempel-4.21">Exempel 4.21</h3> @@ -359,7 +359,7 @@ f = R(x^3 + x^2 + 29) </div> -<figure id="org7058de8"> +<figure id="org37c700b"> <img src="../img/HenselLyftLabHT2023_fig3.png" alt="HenselLyftLabHT2023_fig3.png"> </figure> @@ -424,9 +424,9 @@ fq, fq.hensel_lift(p,3) </div> -<div id="outline-container-org632696a" class="outline-3"> -<h3 id="org632696a">övning 3</h3> -<div class="outline-text-3" id="text-org632696a"> +<div id="outline-container-org1868400" class="outline-3"> +<h3 id="org1868400">övning 3</h3> +<div class="outline-text-3" id="text-org1868400"> <p> Lyft ännu högre, jämför bÃ¥da metoderna </p> @@ -450,15 +450,15 @@ f = x^3 + x^2 +2*x + 26 </div> -<figure id="org1cc7864"> +<figure id="orgf426430"> <img src="../img/HenselLyftLabHT2023_fig4.png" alt="HenselLyftLabHT2023_fig4.png"> </figure> </div> -<div id="outline-container-org59ffa70" class="outline-4"> -<h4 id="org59ffa70">Övning 4</h4> -<div class="outline-text-4" id="text-org59ffa70"> +<div id="outline-container-orgb19d4b7" class="outline-4"> +<h4 id="orgb19d4b7">Övning 4</h4> +<div class="outline-text-4" id="text-orgb19d4b7"> <p> Gör de unika lyften via Hensel! </p> @@ -487,15 +487,15 @@ f = x^2 + x + 7 </div> -<figure id="orge5ad7dd"> +<figure id="org8dd820b"> <img src="../img/HenselLyftLabHT2023_fig5.png" alt="HenselLyftLabHT2023_fig5.png"> </figure> </div> -<div id="outline-container-orgd02384a" class="outline-4"> -<h4 id="orgd02384a">Övning 5</h4> -<div class="outline-text-4" id="text-orgd02384a"> +<div id="outline-container-org9fa80b2" class="outline-4"> +<h4 id="org9fa80b2">Övning 5</h4> +<div class="outline-text-4" id="text-org9fa80b2"> <p> SÃ¥ finns lösningar upp till mod \(p^3\) men ej mod \(p^4\), varför? Red ut detta, ledning nedan @@ -540,9 +540,9 @@ För vart och ett av dessa sÃ¥ är antingen alla eller inga av dess lyft nollst </div> -<div id="outline-container-org7f5a24e" class="outline-4"> -<h4 id="org7f5a24e">Övning 6</h4> -<div class="outline-text-4" id="text-org7f5a24e"> +<div id="outline-container-org9dff539" class="outline-4"> +<h4 id="org9dff539">Övning 6</h4> +<div class="outline-text-4" id="text-org9dff539"> <p> Finns det polynom med icke-unika lyft som trots allt har nollställen mod \(p^n\) alla n, som inte kommer frÃ¥n rationella nollställen? @@ -553,9 +553,9 @@ inte kommer frÃ¥n rationella nollställen? -<div id="outline-container-org1b1b5b2" class="outline-3"> -<h3 id="org1b1b5b2">Allt lyfter inte</h3> -<div class="outline-text-3" id="text-org1b1b5b2"> +<div id="outline-container-orgde4c67d" class="outline-3"> +<h3 id="orgde4c67d">Allt lyfter inte</h3> +<div class="outline-text-3" id="text-orgde4c67d"> <p> Ex: den rationella roten -1 är den enda som lyfter mot oändligheten </p> @@ -571,7 +571,7 @@ H_L_tree(f,p,r).plot(layout='tree') </div> -<figure id="org64a6106"> +<figure id="org0fc508c"> <img src="../img/HenselLyftLabHT2023_fig6.png" alt="HenselLyftLabHT2023_fig6.png"> </figure> @@ -592,8 +592,8 @@ som lyfter icke-unikt mot evigheten? <ul class="org-ul"> -<li><a id="orgf69f4c9"></a>Ledning nedan om du kör fast<br> -<div class="outline-text-5" id="text-orgf69f4c9"> +<li><a id="orga4baaa3"></a>Ledning nedan om du kör fast<br> +<div class="outline-text-5" id="text-orga4baaa3"> <p> försök med \(p=2\) och @@ -715,7 +715,7 @@ f = x^2 -3 </div> -<figure id="orgd7e68e1"> +<figure id="orge682744"> <img src="../img/HenselLyftLabHT2023_fig21.png" alt="HenselLyftLabHT2023_fig21.png"> </figure> @@ -1092,7 +1092,7 @@ f = R(x^3 + x^2 + 29) </div> -<figure id="orgac5479f"> +<figure id="org46df024"> <img src="../img/HenselLyftLabHT2023_fig31.png" alt="HenselLyftLabHT2023_fig31.png"> </figure> @@ -1103,7 +1103,7 @@ f = R(x^3 + x^2 + 29) </div> -<figure id="orgf54282b"> +<figure id="orgfe1eb75"> <img src="../img/HenselLyftLabHT2023_fig33.png" alt="HenselLyftLabHT2023_fig33.png"> </figure> @@ -1114,7 +1114,7 @@ f = R(x^3 + x^2 + 29) </div> -<figure id="orgefb2d91"> +<figure id="orga92116c"> <img src="../img/HenselLyftLabHT2023_fig35.png" alt="HenselLyftLabHT2023_fig35.png"> </figure> @@ -1142,7 +1142,7 @@ f = R(x^3 + x^2 + 29) </main> <footer id="postamble" class="status"> <p class="author">Author: Jan Snellman</p> -<p class="date">Created: 2024-04-05</p> +<p class="date">Created: 2024-08-22</p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> </footer> </body> diff --git a/public/labs/kedjebraklab.html b/public/labs/kedjebraklab.html index c20ccf340a367290bff5e6ba2813c9ab3f507dee..c78d888c3b003b0da087cfcc9e9b4ba5757a79af 100644 --- a/public/labs/kedjebraklab.html +++ b/public/labs/kedjebraklab.html @@ -1,7 +1,7 @@ <!DOCTYPE html> <html lang="en"> <head> -<!-- 2024-01-12 --> +<!-- 2024-08-22 --> <meta charset="utf-8" /> <meta name="viewport" content="width=device-width, initial-scale=1" /> <title>Sagemath-övningar pÃ¥ kedjebrÃ¥k</title> @@ -196,11 +196,11 @@ <body> <header id="top" class="status"> <div id="navbar" style ="text-align: center;"> - <a href='https://liu.se'>LiU</a> - - <a href='https://liu.se/organisation/liu/mai'>MAI</a> - - <a href='https://liu.se/organisation/liu/mai'>Grundutbildning</a> - - <a href='https://courses.mai.liu.se/Lists/html/'>Kurser</a> - - <a href='index.html'>TATA54</a></div> + <a href='https://liu.se'>LiU</a> - + <a href='https://liu.se/organisation/liu/mai'>MAI</a> - + <a href='https://liu.se/organisation/liu/mai'>Grundutbildning</a> - + <a href='https://courses.mai.liu.se/Lists/html/'>Kurser</a> - + <a href='index.html'>TATA54</a></div> </header> <main id="content" class="content"> <header> @@ -259,7 +259,7 @@ kb1 </div> -<figure id="org370e5f5"> +<figure id="org52de908"> <img src="img/kedjebraklab_fig_1.png" alt="kedjebraklab_fig_1.png"> </figure> @@ -396,8 +396,8 @@ ut </main> <footer id="postamble" class="status"> <p class="author">Author: Jan Snellman</p> -<p class="date">Created: 2024-01-12</p> +<p class="date">Created: 2024-08-22</p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> </footer> </body> -</html> \ No newline at end of file +</html> diff --git a/public/labs/lecture0.html b/public/labs/lecture0.html index 09ae0d686fda4a3ebbb802893ca69f4cd0cd6e16..271658af0f2b154685a54e5b4f9463b68b534680 100644 --- a/public/labs/lecture0.html +++ b/public/labs/lecture0.html @@ -1,7 +1,7 @@ <!DOCTYPE html> <html lang="en"> <head> -<!-- 2024-01-12 --> +<!-- 2024-08-22 --> <meta charset="utf-8" /> <meta name="viewport" content="width=device-width, initial-scale=1" /> <title>‎</title> @@ -196,11 +196,11 @@ <body> <header id="top" class="status"> <div id="navbar" style ="text-align: center;"> - <a href='https://liu.se'>LiU</a> - - <a href='https://liu.se/organisation/liu/mai'>MAI</a> - - <a href='https://liu.se/organisation/liu/mai'>Grundutbildning</a> - - <a href='https://courses.mai.liu.se/Lists/html/'>Kurser</a> - - <a href='index.html'>TATA54</a></div> + <a href='https://liu.se'>LiU</a> - + <a href='https://liu.se/organisation/liu/mai'>MAI</a> - + <a href='https://liu.se/organisation/liu/mai'>Grundutbildning</a> - + <a href='https://courses.mai.liu.se/Lists/html/'>Kurser</a> - + <a href='index.html'>TATA54</a></div> </header> <main id="content" class="content"> <div class="org-src-container"> @@ -212,7 +212,7 @@ plot([prime_pi(x),x/ln(x)],(1,100)) </div> -<figure id="org9dde164"> +<figure id="orgfedf573"> <img src="file:///tmp/tmpob0hnw37/tmp_zm_txld0.png" alt="tmp_zm_txld0.png"> </figure> @@ -227,7 +227,7 @@ plot([prime_pi(x)/x]+FL,(100,1000)) </div> -<figure id="org666e17f"> +<figure id="org8e7e000"> <img src="file:///tmp/tmpob0hnw37/tmp_a0i_rmcl.png" alt="tmp_a0i_rmcl.png"> </figure> @@ -254,7 +254,7 @@ for L in P5: </pre> </div> -<pre class="example" id="org840d8c5"> +<pre class="example" id="org4624854"> [5] ***** [4, 1] @@ -290,15 +290,15 @@ for L in P5: </div> -<figure id="org28cf4cd"> +<figure id="org8c50c08"> <img src="file:///tmp/tmpob0hnw37/tmp_40jucrn2.png" alt="tmp_40jucrn2.png"> </figure> </main> <footer id="postamble" class="status"> <p class="author">Author: Jan Snellman</p> -<p class="date">Created: 2024-01-12</p> +<p class="date">Created: 2024-08-22</p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> </footer> </body> -</html> \ No newline at end of file +</html> diff --git a/public/labs/lecture1.html b/public/labs/lecture1.html index 2a407cbdbd194cee28122153733737ec07c11900..7b758efb08a1619d9fb06031f797b0bace1bc18d 100644 --- a/public/labs/lecture1.html +++ b/public/labs/lecture1.html @@ -1,7 +1,7 @@ <!DOCTYPE html> <html lang="en"> <head> -<!-- 2024-01-12 --> +<!-- 2024-08-22 --> <meta charset="utf-8" /> <meta name="viewport" content="width=device-width, initial-scale=1" /> <title>‎</title> @@ -196,11 +196,11 @@ <body> <header id="top" class="status"> <div id="navbar" style ="text-align: center;"> - <a href='https://liu.se'>LiU</a> - - <a href='https://liu.se/organisation/liu/mai'>MAI</a> - - <a href='https://liu.se/organisation/liu/mai'>Grundutbildning</a> - - <a href='https://courses.mai.liu.se/Lists/html/'>Kurser</a> - - <a href='index.html'>TATA54</a></div> + <a href='https://liu.se'>LiU</a> - + <a href='https://liu.se/organisation/liu/mai'>MAI</a> - + <a href='https://liu.se/organisation/liu/mai'>Grundutbildning</a> - + <a href='https://courses.mai.liu.se/Lists/html/'>Kurser</a> - + <a href='index.html'>TATA54</a></div> </header> <main id="content" class="content"> <div class="org-src-container"> @@ -210,7 +210,7 @@ Q.plot() </div> -<figure id="org14e4735"> +<figure id="org0cb5663"> <img src="9ac1a989740cf989527eb8832af86aed4687c15c.png" alt="9ac1a989740cf989527eb8832af86aed4687c15c.png"> </figure> @@ -222,7 +222,7 @@ W.plot() </div> -<figure id="orga853ba9"> +<figure id="org19bc0a2"> <img src="fefcb50303c1aece74eb2f07e81f7dcba64c9305.png" alt="fefcb50303c1aece74eb2f07e81f7dcba64c9305.png"> </figure> @@ -244,7 +244,7 @@ W.plot() </pre> </div> -<pre class="example" id="org21704c4"> +<pre class="example" id="org893ac51"> --------------------------------------------------------------------------- TypeError Traceback (most recent call last) <ipython-input-8-58a5f6bfd37d> in <module>() @@ -262,7 +262,7 @@ TypeError: gcd() takes at most 2 arguments (3 given) </pre> </div> -<pre class="example" id="org610cede"> +<pre class="example" id="org3296028"> Object `diophantine` not found. </pre> @@ -281,7 +281,7 @@ Object `diophantine` not found. </div> -<figure id="org777c8dd"> +<figure id="org2407621"> <img src="326e354523c67057c4312517686106179ab4db51.png" alt="326e354523c67057c4312517686106179ab4db51.png"> </figure> @@ -293,8 +293,8 @@ Object `diophantine` not found. </main> <footer id="postamble" class="status"> <p class="author">Author: Jan Snellman</p> -<p class="date">Created: 2024-01-12</p> +<p class="date">Created: 2024-08-22</p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> </footer> </body> -</html> \ No newline at end of file +</html> diff --git a/public/labs/lecture2.html b/public/labs/lecture2.html index 31c825e179737d21168a187f1a838560ef32f7a0..eab766bdc1cba17bdf5d7a80f75e9b405daac1dc 100644 --- a/public/labs/lecture2.html +++ b/public/labs/lecture2.html @@ -1,7 +1,7 @@ <!DOCTYPE html> <html lang="en"> <head> -<!-- 2024-01-12 --> +<!-- 2024-08-22 --> <meta charset="utf-8" /> <meta name="viewport" content="width=device-width, initial-scale=1" /> <title>‎</title> @@ -196,11 +196,11 @@ <body> <header id="top" class="status"> <div id="navbar" style ="text-align: center;"> - <a href='https://liu.se'>LiU</a> - - <a href='https://liu.se/organisation/liu/mai'>MAI</a> - - <a href='https://liu.se/organisation/liu/mai'>Grundutbildning</a> - - <a href='https://courses.mai.liu.se/Lists/html/'>Kurser</a> - - <a href='index.html'>TATA54</a></div> + <a href='https://liu.se'>LiU</a> - + <a href='https://liu.se/organisation/liu/mai'>MAI</a> - + <a href='https://liu.se/organisation/liu/mai'>Grundutbildning</a> - + <a href='https://courses.mai.liu.se/Lists/html/'>Kurser</a> - + <a href='index.html'>TATA54</a></div> </header> <main id="content" class="content"> <div class="org-src-container"> @@ -217,7 +217,7 @@ P8 = point([(6+3*cos(2*pi*4/15),3*sin(2*pi*4/15))], color='green',size=30) </div> -<figure id="orge57e015"> +<figure id="org51df67d"> <img src="c67ffb39f62f2392dfa28b6784c3c3d3bcd05ee8.png" alt="c67ffb39f62f2392dfa28b6784c3c3d3bcd05ee8.png"> </figure> @@ -283,7 +283,7 @@ Cyclic4 </div> -<figure id="org2291500"> +<figure id="org4ef1e24"> <img src="baac293abd935204538782ac3c46dafecc9de285.png" alt="baac293abd935204538782ac3c46dafecc9de285.png"> </figure> @@ -294,7 +294,7 @@ Cyclic4 </div> -<figure id="org1d4e4cd"> +<figure id="org4c7626a"> <img src="c0e9ecb85854981cf29210e7cd25e81d382aa9b3.png" alt="c0e9ecb85854981cf29210e7cd25e81d382aa9b3.png"> </figure> @@ -314,7 +314,7 @@ Cyclic4 </pre> </div> -<pre class="example" id="org721ef33"> +<pre class="example" id="org3eeb40e"> 1 2 2 @@ -331,7 +331,7 @@ Cyclic4 </div> -<figure id="org1178560"> +<figure id="org3a1f8ae"> <img src="79b2d76d2217581bc5e8ff8caf581a6d3bfcc9ad.png" alt="79b2d76d2217581bc5e8ff8caf581a6d3bfcc9ad.png"> </figure> @@ -343,8 +343,8 @@ Cyclic4 </main> <footer id="postamble" class="status"> <p class="author">Author: Jan Snellman</p> -<p class="date">Created: 2024-01-12</p> +<p class="date">Created: 2024-08-22</p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> </footer> </body> -</html> \ No newline at end of file +</html> diff --git a/public/labs/lecture3.html b/public/labs/lecture3.html index 26327ea63b2294df175c8ed8d6d9b4a5c532b247..f7a31dfa79531e38bfba24eb271617cf698addf4 100644 --- a/public/labs/lecture3.html +++ b/public/labs/lecture3.html @@ -1,7 +1,7 @@ <!DOCTYPE html> <html lang="en"> <head> -<!-- 2024-01-12 --> +<!-- 2024-08-22 --> <meta charset="utf-8" /> <meta name="viewport" content="width=device-width, initial-scale=1" /> <title>‎</title> @@ -196,11 +196,11 @@ <body> <header id="top" class="status"> <div id="navbar" style ="text-align: center;"> - <a href='https://liu.se'>LiU</a> - - <a href='https://liu.se/organisation/liu/mai'>MAI</a> - - <a href='https://liu.se/organisation/liu/mai'>Grundutbildning</a> - - <a href='https://courses.mai.liu.se/Lists/html/'>Kurser</a> - - <a href='index.html'>TATA54</a></div> + <a href='https://liu.se'>LiU</a> - + <a href='https://liu.se/organisation/liu/mai'>MAI</a> - + <a href='https://liu.se/organisation/liu/mai'>Grundutbildning</a> - + <a href='https://courses.mai.liu.se/Lists/html/'>Kurser</a> - + <a href='index.html'>TATA54</a></div> </header> <main id="content" class="content"> <div class="org-src-container"> @@ -209,7 +209,7 @@ </div> -<figure id="orge200e74"> +<figure id="org140733c"> <img src="eec132b7c338bf28fddfea6ec0238fd154197cd1.png" alt="eec132b7c338bf28fddfea6ec0238fd154197cd1.png"> </figure> @@ -222,7 +222,7 @@ DN.show() </div> -<figure id="org3ee5e13"> +<figure id="org909ae18"> <img src="f23f2c41ea39457fc3c9bf916511610731f1daf2.png" alt="f23f2c41ea39457fc3c9bf916511610731f1daf2.png"> </figure> @@ -259,7 +259,7 @@ L.plot(vertex_colors=H,pos=mypos) </div> -<figure id="orgf75fa7b"> +<figure id="org6572d27"> <img src="3de4085389dcddfbf10a5a83509b5920afc0c3ce.png" alt="3de4085389dcddfbf10a5a83509b5920afc0c3ce.png"> </figure> @@ -273,7 +273,7 @@ eul+ep </div> -<figure id="org7112945"> +<figure id="org8b45232"> <img src="1118cc771effff59b550fa536c0cfb54e17ab5d2.png" alt="1118cc771effff59b550fa536c0cfb54e17ab5d2.png"> </figure> @@ -285,8 +285,8 @@ eul+ep </main> <footer id="postamble" class="status"> <p class="author">Author: Jan Snellman</p> -<p class="date">Created: 2024-01-12</p> +<p class="date">Created: 2024-08-22</p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> </footer> </body> -</html> \ No newline at end of file +</html> diff --git a/public/labs/lecture4.html b/public/labs/lecture4.html index 4c806c809f1745eef5e6c6fdfff686cdee07f250..d61f0df62ef74a33f2004c2058cfa85730c65972 100644 --- a/public/labs/lecture4.html +++ b/public/labs/lecture4.html @@ -1,7 +1,7 @@ <!DOCTYPE html> <html lang="en"> <head> -<!-- 2024-01-12 --> +<!-- 2024-08-22 --> <meta charset="utf-8" /> <meta name="viewport" content="width=device-width, initial-scale=1" /> <title>‎</title> @@ -196,11 +196,11 @@ <body> <header id="top" class="status"> <div id="navbar" style ="text-align: center;"> - <a href='https://liu.se'>LiU</a> - - <a href='https://liu.se/organisation/liu/mai'>MAI</a> - - <a href='https://liu.se/organisation/liu/mai'>Grundutbildning</a> - - <a href='https://courses.mai.liu.se/Lists/html/'>Kurser</a> - - <a href='index.html'>TATA54</a></div> + <a href='https://liu.se'>LiU</a> - + <a href='https://liu.se/organisation/liu/mai'>MAI</a> - + <a href='https://liu.se/organisation/liu/mai'>Grundutbildning</a> - + <a href='https://courses.mai.liu.se/Lists/html/'>Kurser</a> - + <a href='index.html'>TATA54</a></div> </header> <main id="content" class="content"> <div class="org-src-container"> @@ -286,8 +286,8 @@ ff </main> <footer id="postamble" class="status"> <p class="author">Author: Jan Snellman</p> -<p class="date">Created: 2024-01-12</p> +<p class="date">Created: 2024-08-22</p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> </footer> </body> -</html> \ No newline at end of file +</html> diff --git a/public/labs/lecture5.html b/public/labs/lecture5.html index f275e964e4bc84d7e052781b8693ef78a3ee7d31..cca5d282af73f604a54b321db2f8d45738de7f5f 100644 --- a/public/labs/lecture5.html +++ b/public/labs/lecture5.html @@ -1,7 +1,7 @@ <!DOCTYPE html> <html lang="en"> <head> -<!-- 2024-01-12 --> +<!-- 2024-08-22 --> <meta charset="utf-8" /> <meta name="viewport" content="width=device-width, initial-scale=1" /> <title>‎</title> @@ -196,11 +196,11 @@ <body> <header id="top" class="status"> <div id="navbar" style ="text-align: center;"> - <a href='https://liu.se'>LiU</a> - - <a href='https://liu.se/organisation/liu/mai'>MAI</a> - - <a href='https://liu.se/organisation/liu/mai'>Grundutbildning</a> - - <a href='https://courses.mai.liu.se/Lists/html/'>Kurser</a> - - <a href='index.html'>TATA54</a></div> + <a href='https://liu.se'>LiU</a> - + <a href='https://liu.se/organisation/liu/mai'>MAI</a> - + <a href='https://liu.se/organisation/liu/mai'>Grundutbildning</a> - + <a href='https://courses.mai.liu.se/Lists/html/'>Kurser</a> - + <a href='index.html'>TATA54</a></div> </header> <main id="content" class="content"> <div class="org-src-container"> @@ -209,7 +209,7 @@ print p </pre> </div> -<pre class="example" id="orge2fd40e"> +<pre class="example" id="orgf8a44a9"> 2441 </pre> @@ -219,7 +219,7 @@ print(myfact) </pre> </div> -<pre class="example" id="orgbde3826"> +<pre class="example" id="org0f9e188"> 2^3 * 5 * 61 </pre> @@ -242,7 +242,7 @@ for fact in myfact: </pre> </div> -<pre class="example" id="org01dd320"> +<pre class="example" id="orgf2f4ac7"> x^4 + 2440 x^8 + 2440 {672, 1, 1122, 1319, 2440, 1769, 2156, 285} {2440, 1769, 672, 1} 1122 x + 2440 x^5 + 2440 {1, 583, 1478, 590, 2230} {1} 1478 x + 2440 x^61 + 2440 {1280, 1024, 1283, 1029, 1, 1547, 268, 1421, 1166, 1679, 1040, 1002, 2067, 1300, 534, 26, 261, 32, 676, 2086, 1832, 1195, 684, 2290, 50, 40, 2104, 697, 59, 956, 189, 446, 2214, 832, 1035, 331, 2380, 845, 2157, 2127, 2000, 1600, 855, 1625, 335, 2360, 1888, 739, 1253, 103, 828, 1642, 1387, 237, 1904, 753, 1778, 489, 509, 1534, 2344} {1} 1280 @@ -254,7 +254,7 @@ print multiplicative_order(c) </pre> </div> -<pre class="example" id="org27f5926"> +<pre class="example" id="org5645c51"> {1280, 1122, 1478} 2141 2440 </pre> @@ -283,8 +283,8 @@ thelifts </main> <footer id="postamble" class="status"> <p class="author">Author: Jan Snellman</p> -<p class="date">Created: 2024-01-12</p> +<p class="date">Created: 2024-08-22</p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> </footer> </body> -</html> \ No newline at end of file +</html> diff --git a/public/lectures/Henselfaktorisering.html b/public/lectures/Henselfaktorisering.html index 0d2f47a3df095b7c99f43fa08f8debcc050ddd1c..52ff66746252f6f7af317c2d7f85a4b89ccb57a8 100644 --- a/public/lectures/Henselfaktorisering.html +++ b/public/lectures/Henselfaktorisering.html @@ -1,7 +1,7 @@ <!DOCTYPE html> <html lang="en"> <head> -<!-- 2024-01-12 --> +<!-- 2024-08-22 --> <meta charset="utf-8" /> <meta name="viewport" content="width=device-width, initial-scale=1" /> <title>Henselfaktorisering</title> @@ -196,19 +196,19 @@ <body> <header id="top" class="status"> <div id="navbar" style ="text-align: center;"> - <a href='https://liu.se'>LiU</a> - - <a href='https://liu.se/organisation/liu/mai'>MAI</a> - - <a href='https://liu.se/organisation/liu/mai'>Grundutbildning</a> - - <a href='https://courses.mai.liu.se/Lists/html/'>Kurser</a> - - <a href='index.html'>TATA54</a></div> + <a href='https://liu.se'>LiU</a> - + <a href='https://liu.se/organisation/liu/mai'>MAI</a> - + <a href='https://liu.se/organisation/liu/mai'>Grundutbildning</a> - + <a href='https://courses.mai.liu.se/Lists/html/'>Kurser</a> - + <a href='index.html'>TATA54</a></div> </header> <main id="content" class="content"> <header> <h1 class="title">Henselfaktorisering</h1> </header> -<section id="outline-container-orgdb8e25d" class="outline-2"> -<h2 id="orgdb8e25d">Faktorisering via Hensel</h2> -<div class="outline-text-2" id="text-orgdb8e25d"> +<section id="outline-container-orge485e39" class="outline-2"> +<h2 id="orge485e39">Faktorisering via Hensel</h2> +<div class="outline-text-2" id="text-orge485e39"> <p> <img src="../img/faktorhensel-1.png" alt="faktorhensel-1.png"> <img src="../img/faktorhensel-2.png" alt="faktorhensel-2.png"> @@ -221,8 +221,8 @@ </main> <footer id="postamble" class="status"> <p class="author">Author: Jan Snellman</p> -<p class="date">Created: 2024-01-12</p> +<p class="date">Created: 2024-08-22</p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> </footer> </body> -</html> \ No newline at end of file +</html> diff --git a/public/newlectures/new-lect-0.html b/public/newlectures/new-lect-0.html index feebd46ed01ade411aec2768801655a11a8e8809..46acbc60458254cda40a8874f8176e14df3709b8 100644 --- a/public/newlectures/new-lect-0.html +++ b/public/newlectures/new-lect-0.html @@ -1,7 +1,7 @@ <!DOCTYPE html> <html lang="sv"> <head> -<!-- 2024-02-06 --> +<!-- 2024-08-22 --> <meta charset="utf-8" /> <meta name="viewport" content="width=device-width, initial-scale=1" /> <title>Talteori översiktsföreläsning</title> @@ -240,11 +240,11 @@ margin: 10px; <body> <header id="top" class="status"> <div id="navbar" style ="text-align: center;"> - <a href='https://liu.se'>LiU</a> - - <a href='https://liu.se/organisation/liu/mai'>MAI</a> - - <a href='https://liu.se/organisation/liu/mai'>Grundutbildning</a> - - <a href='https://courses.mai.liu.se/Lists/html/'>Kurser</a> - - <a href='index.html'>TATA54</a></div> + <a href='https://liu.se'>LiU</a> - + <a href='https://liu.se/organisation/liu/mai'>MAI</a> - + <a href='https://liu.se/organisation/liu/mai'>Grundutbildning</a> - + <a href='https://courses.mai.liu.se/Lists/html/'>Kurser</a> - + <a href='index.html'>TATA54</a></div> </header> <main id="content" class="content"> <header> @@ -276,10 +276,10 @@ margin: 10px; <div class="outline-text-3" id="text-primtalsräkning"> </div> -<div id="outline-container-org2af6cb7" class="outline-4"> -<h4 id="org2af6cb7"><span class="section-number-4">1.1.1.</span> Primtalsräknarfunktionen</h4> +<div id="outline-container-org45447a0" class="outline-4"> +<h4 id="org45447a0"><span class="section-number-4">1.1.1.</span> Primtalsräknarfunktionen</h4> <div class="outline-text-4" id="text-1-1-1"> -<div class="definition" id="org9039127"> +<div class="definition" id="orgeb70eab"> <p> \(\pi(x) = \sum_{k \le x} \mathrm{IsPrime}(k)\) </p> @@ -287,7 +287,7 @@ margin: 10px; </div> -<div class="theorem" id="orgc80f0b9"> +<div class="theorem" id="org17daf5c"> <p> \(\pi(x) \sim \frac{x}{\log x}\) dÃ¥ \(x \to \infty\). </p> @@ -297,11 +297,11 @@ margin: 10px; </div> -<div id="outline-container-orga3f0554" class="outline-4"> -<h4 id="orga3f0554"><span class="section-number-4">1.1.2.</span> Hadamard</h4> +<div id="outline-container-orgd34e969" class="outline-4"> +<h4 id="orgd34e969"><span class="section-number-4">1.1.2.</span> Hadamard</h4> <div class="outline-text-4" id="text-1-1-2"> -<figure id="orgced749d"> +<figure id="orge3c1c3c"> <img src="../img/wikiHadamard.jpg" alt="wikiHadamard.jpg"> <figcaption><span class="figure-number">Illustration 1 </span>Hadamard</figcaption> @@ -309,24 +309,24 @@ margin: 10px; </div> </div> -<div id="outline-container-org8682363" class="outline-4"> -<h4 id="org8682363"><span class="section-number-4">1.1.3.</span> Primtalens täthet</h4> +<div id="outline-container-org632b497" class="outline-4"> +<h4 id="org632b497"><span class="section-number-4">1.1.3.</span> Primtalens täthet</h4> <div class="outline-text-4" id="text-1-1-3"> -<div class="definition" id="org6a0f093"> +<div class="definition" id="org5ff0715"> <p> Primtalstäthetsfunktion \(\pi(x)/x\). </p> </div> -<div class="theorem" id="org466aa4e"> +<div class="theorem" id="org50be3a0"> <p> \(\pi(x)/x \sim 1/\log(x)\). </p> </div> -<div class="proof" id="orgf0bf128"> +<div class="proof" id="orgb72f116"> <p> Följer av primtalssatsen. </p> @@ -349,10 +349,10 @@ primtal \(\le 1000\). </div> </div> -<div id="outline-container-orgad7f8ad" class="outline-4"> -<h4 id="orgad7f8ad"><span class="section-number-4">1.1.4.</span> Approximation av primtalstäthet</h4> +<div id="outline-container-orge130570" class="outline-4"> +<h4 id="orge130570"><span class="section-number-4">1.1.4.</span> Approximation av primtalstäthet</h4> <div class="outline-text-4" id="text-1-1-4"> -<div class="theorem" id="orgff1fc81"> +<div class="theorem" id="org97f6cf0"> <p> \(p(x)/x = \sum_{k=1}^{n-1} \frac{(k-1)!}{\log(x)^k} + \mathcal{O}\left( \frac{(n-1)!}{(log(x)^n)} \right)\) as @@ -362,7 +362,7 @@ primtal \(\le 1000\). </div> -<figure id="org9113ffd"> +<figure id="orga3fb710"> <img src="prim-funk-approx.png" alt="prim-funk-approx.png"> <figcaption><span class="figure-number">Illustration 2 </span>Första tre approximationerna till primtalstäthetsfunktionen</figcaption> @@ -472,7 +472,7 @@ innehÃ¥ller \(D\) gitterpunkt skild frÃ¥n origo. </p> -<figure id="org810adab"> +<figure id="org25e12e6"> <img src="wikikowski.png" alt="wikikowski.png"> </figure> @@ -701,7 +701,7 @@ komplicerad kombinatorik</li> <footer id="postamble" class="status"> <p class="date">Datum: 2024-01-13</p> <p class="author">Författare: Jan Snellman</p> -<p class="date">Created: 2024-02-06</p> +<p class="date">Created: 2024-08-22</p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> </footer> </body> diff --git a/public/newlectures/newlecture.html b/public/newlectures/newlecture.html index 6779d359563d4be83ab70eb91b311d81646375f5..a707d249d97131e4a16fe8512d8d55c4d9d132dd 100644 --- a/public/newlectures/newlecture.html +++ b/public/newlectures/newlecture.html @@ -1,7 +1,7 @@ <!DOCTYPE html> <html lang="sv"> <head> -<!-- 2024-02-06 --> +<!-- 2024-08-22 --> <meta charset="utf-8" /> <meta name="viewport" content="width=device-width, initial-scale=1" /> <title>Föreläsningar i Talteori</title> @@ -230,11 +230,11 @@ <body> <header id="top" class="status"> <div id="navbar" style ="text-align: center;"> - <a href='https://liu.se'>LiU</a> - - <a href='https://liu.se/organisation/liu/mai'>MAI</a> - - <a href='https://liu.se/organisation/liu/mai'>Grundutbildning</a> - - <a href='https://courses.mai.liu.se/Lists/html/'>Kurser</a> - - <a href='index.html'>TATA54</a></div> + <a href='https://liu.se'>LiU</a> - + <a href='https://liu.se/organisation/liu/mai'>MAI</a> - + <a href='https://liu.se/organisation/liu/mai'>Grundutbildning</a> - + <a href='https://courses.mai.liu.se/Lists/html/'>Kurser</a> - + <a href='index.html'>TATA54</a></div> </header> <main id="content" class="content"> <header> @@ -243,8 +243,8 @@ <h2>Innehåll</h2> <div id="text-table-of-contents" role="doc-toc"> <ul> -<li><a href="#orgbf7615a">1. Introduktion</a></li> -<li><a href="#org6fea25c">2. Kongruensräkning</a> +<li><a href="#orgd9f10a0">1. Introduktion</a></li> +<li><a href="#org328cad5">2. Kongruensräkning</a> <ul> <li><a href="#delbarhet">2.1. Delbarhet</a> <ul> @@ -260,25 +260,25 @@ </li> </ul> </li> -<li><a href="#org6a9dc81">3. Aritmetiska funktioner</a></li> -<li><a href="#orged85f3a">4. Hensel-lyft</a></li> -<li><a href="#orga4ca7ab">5. Primitiva rötter</a></li> -<li><a href="#orge5a8741">6. Kvadratiska residyer</a></li> -<li><a href="#org2e926bc">7. Kvadratisk reciprocitet</a></li> -<li><a href="#orgedcfbaa">8. KedjebrÃ¥k</a></li> -<li><a href="#org557cc8f">9. Icke-linjära diofantiska ekvationer</a></li> -<li><a href="#org1c08b0a">10. Gaussiska heltal</a></li> -<li><a href="#orgdc134b1">11. Övrigt</a></li> +<li><a href="#org6907ef0">3. Aritmetiska funktioner</a></li> +<li><a href="#org91936fe">4. Hensel-lyft</a></li> +<li><a href="#org60aa502">5. Primitiva rötter</a></li> +<li><a href="#org43aac80">6. Kvadratiska residyer</a></li> +<li><a href="#org14febe8">7. Kvadratisk reciprocitet</a></li> +<li><a href="#org104725a">8. KedjebrÃ¥k</a></li> +<li><a href="#org1e6ef78">9. Icke-linjära diofantiska ekvationer</a></li> +<li><a href="#orgc9e8006">10. Gaussiska heltal</a></li> +<li><a href="#orged8c772">11. Övrigt</a></li> </ul> </div> </nav> -<section id="outline-container-orgbf7615a" class="outline-2"> -<h2 id="orgbf7615a"><span class="section-number-2">1.</span> Introduktion</h2> +<section id="outline-container-orgd9f10a0" class="outline-2"> +<h2 id="orgd9f10a0"><span class="section-number-2">1.</span> Introduktion</h2> </section> -<section id="outline-container-org6fea25c" class="outline-2"> -<h2 id="org6fea25c"><span class="section-number-2">2.</span> Kongruensräkning</h2> +<section id="outline-container-org328cad5" class="outline-2"> +<h2 id="org328cad5"><span class="section-number-2">2.</span> Kongruensräkning</h2> <div class="outline-text-2" id="text-2"> </div> <div id="outline-container-delbarhet" class="outline-3"> @@ -345,7 +345,7 @@ Om inte annat sägs sÃ¥ \(a,b,c,x,y,r,s \in {\mathbb{Z}}\), men <h4 id="partial-order"><span class="section-number-4">2.1.3.</span> Partial order</h4> <div class="outline-text-4" id="text-partial-order"> -<figure id="orge252b57"> +<figure id="org7c82efd"> <img src="divisorlattice7.png" alt="divisorlattice7.png"> <figcaption><span class="figure-number">Illustration 1 </span>Heltalen under delbarhet</figcaption> @@ -833,7 +833,7 @@ Algorithm <div class="org-center"> -<figure id="orgbdb8fe6"> +<figure id="org806be6c"> <img src="sieveE.jpg" alt="sieveE.jpg"> </figure> @@ -885,7 +885,7 @@ villkoret nödvändigt. </div> </li> -<li><a id="org03cfdf4"></a>Dirichlet<br> +<li><a id="orgd4329fe"></a>Dirichlet<br> <div class="outline-text-6" id="text-2-1-8-2-2"> </div> </li> @@ -896,38 +896,38 @@ villkoret nödvändigt. </div> </section> -<section id="outline-container-org6a9dc81" class="outline-2"> -<h2 id="org6a9dc81"><span class="section-number-2">3.</span> Aritmetiska funktioner</h2> +<section id="outline-container-org6907ef0" class="outline-2"> +<h2 id="org6907ef0"><span class="section-number-2">3.</span> Aritmetiska funktioner</h2> </section> -<section id="outline-container-orged85f3a" class="outline-2"> -<h2 id="orged85f3a"><span class="section-number-2">4.</span> Hensel-lyft</h2> +<section id="outline-container-org91936fe" class="outline-2"> +<h2 id="org91936fe"><span class="section-number-2">4.</span> Hensel-lyft</h2> </section> -<section id="outline-container-orga4ca7ab" class="outline-2"> -<h2 id="orga4ca7ab"><span class="section-number-2">5.</span> Primitiva rötter</h2> +<section id="outline-container-org60aa502" class="outline-2"> +<h2 id="org60aa502"><span class="section-number-2">5.</span> Primitiva rötter</h2> </section> -<section id="outline-container-orge5a8741" class="outline-2"> -<h2 id="orge5a8741"><span class="section-number-2">6.</span> Kvadratiska residyer</h2> +<section id="outline-container-org43aac80" class="outline-2"> +<h2 id="org43aac80"><span class="section-number-2">6.</span> Kvadratiska residyer</h2> </section> -<section id="outline-container-org2e926bc" class="outline-2"> -<h2 id="org2e926bc"><span class="section-number-2">7.</span> Kvadratisk reciprocitet</h2> +<section id="outline-container-org14febe8" class="outline-2"> +<h2 id="org14febe8"><span class="section-number-2">7.</span> Kvadratisk reciprocitet</h2> </section> -<section id="outline-container-orgedcfbaa" class="outline-2"> -<h2 id="orgedcfbaa"><span class="section-number-2">8.</span> KedjebrÃ¥k</h2> +<section id="outline-container-org104725a" class="outline-2"> +<h2 id="org104725a"><span class="section-number-2">8.</span> KedjebrÃ¥k</h2> </section> -<section id="outline-container-org557cc8f" class="outline-2"> -<h2 id="org557cc8f"><span class="section-number-2">9.</span> Icke-linjära diofantiska ekvationer</h2> +<section id="outline-container-org1e6ef78" class="outline-2"> +<h2 id="org1e6ef78"><span class="section-number-2">9.</span> Icke-linjära diofantiska ekvationer</h2> </section> -<section id="outline-container-org1c08b0a" class="outline-2"> -<h2 id="org1c08b0a"><span class="section-number-2">10.</span> Gaussiska heltal</h2> +<section id="outline-container-orgc9e8006" class="outline-2"> +<h2 id="orgc9e8006"><span class="section-number-2">10.</span> Gaussiska heltal</h2> </section> -<section id="outline-container-orgdc134b1" class="outline-2"> -<h2 id="orgdc134b1"><span class="section-number-2">11.</span> Övrigt</h2> +<section id="outline-container-orged8c772" class="outline-2"> +<h2 id="orged8c772"><span class="section-number-2">11.</span> Övrigt</h2> </section> </main> <footer id="postamble" class="status"> <p class="date">Datum: 2024-01-13</p> <p class="author">Författare: Jan Snellman</p> -<p class="date">Created: 2024-02-06</p> +<p class="date">Created: 2024-08-22</p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> </footer> </body> diff --git a/public/senaste-nytt.html b/public/senaste-nytt.html index 1ad694954ce236d8245a5862683ae45d07955889..c488eb5f729908ab10ff32645c05c41a2954a5f5 100644 --- a/public/senaste-nytt.html +++ b/public/senaste-nytt.html @@ -1,7 +1,7 @@ <!DOCTYPE html> <html lang="en"> <head> -<!-- 2024-02-06 --> +<!-- 2024-08-22 --> <meta charset="utf-8" /> <meta name="viewport" content="width=device-width, initial-scale=1" /> <title>‎</title> @@ -196,23 +196,23 @@ <body> <header id="top" class="status"> <div id="navbar" style ="text-align: center;"> - <a href='https://liu.se'>LiU</a> - - <a href='https://liu.se/organisation/liu/mai'>MAI</a> - - <a href='https://liu.se/organisation/liu/mai'>Grundutbildning</a> - - <a href='https://courses.mai.liu.se/Lists/html/'>Kurser</a> - - <a href='index.html'>TATA54</a></div> + <a href='https://liu.se'>LiU</a> - + <a href='https://liu.se/organisation/liu/mai'>MAI</a> - + <a href='https://liu.se/organisation/liu/mai'>Grundutbildning</a> - + <a href='https://courses.mai.liu.se/Lists/html/'>Kurser</a> - + <a href='index.html'>TATA54</a></div> </header> <main id="content" class="content"> -<section id="outline-container-org83ece8d" class="outline-2"> -<h2 id="org83ece8d">TATA54 Anteckningar frÃ¥n tidigare Ã¥r</h2> -<div class="outline-text-2" id="text-org83ece8d"> +<section id="outline-container-orgacdba95" class="outline-2"> +<h2 id="orgacdba95">TATA54 Anteckningar frÃ¥n tidigare Ã¥r</h2> +<div class="outline-text-2" id="text-orgacdba95"> </div> -<div id="outline-container-orgb8552ba" class="outline-3"> -<h3 id="orgb8552ba">2023</h3> -<div class="outline-text-3" id="text-orgb8552ba"> +<div id="outline-container-orgd75a871" class="outline-3"> +<h3 id="orgd75a871">2023</h3> +<div class="outline-text-3" id="text-orgd75a871"> <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 @@ -266,9 +266,9 @@ tryckfel (skall vara w(d)). 7.2.38 är komplicerad och kan skippas.</li> </div> -<div id="outline-container-orgc048d37" class="outline-3"> -<h3 id="orgc048d37">2021</h3> -<div class="outline-text-3" id="text-orgc048d37"> +<div id="outline-container-orgf4540a0" class="outline-3"> +<h3 id="orgf4540a0">2021</h3> +<div class="outline-text-3" id="text-orgf4540a0"> <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 @@ -316,9 +316,9 @@ nÃ¥gon inbjudan, sÃ¥ mejla mig.</li> </div> </div> -<div id="outline-container-orgcebf283" class="outline-3"> -<h3 id="orgcebf283">2020</h3> -<div class="outline-text-3" id="text-orgcebf283"> +<div id="outline-container-orgd33d225" class="outline-3"> +<h3 id="orgd33d225">2020</h3> +<div class="outline-text-3" id="text-orgd33d225"> <ul class="org-ul"> <li><p> 2020-12-12: Kursen kommer att ges VT2021, med start den 19e januari. @@ -371,9 +371,9 @@ someone else (perhaps </div> </div> -<div id="outline-container-orgc11f03a" class="outline-3"> -<h3 id="orgc11f03a">2019</h3> -<div class="outline-text-3" id="text-orgc11f03a"> +<div id="outline-container-org01726fb" class="outline-3"> +<h3 id="org01726fb">2019</h3> +<div class="outline-text-3" id="text-org01726fb"> <ul class="org-ul"> <li>2019-11-01: The course will not be given spring 2020.</li> @@ -388,9 +388,9 @@ available.</li> </div> </div> -<div id="outline-container-org39bfc1f" class="outline-3"> -<h3 id="org39bfc1f">2018</h3> -<div class="outline-text-3" id="text-org39bfc1f"> +<div id="outline-container-org2020805" class="outline-3"> +<h3 id="org2020805">2018</h3> +<div class="outline-text-3" id="text-org2020805"> <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 @@ -403,9 +403,9 @@ available.</li> </div> </div> -<div id="outline-container-org3f27bad" class="outline-3"> -<h3 id="org3f27bad">2017</h3> -<div class="outline-text-3" id="text-org3f27bad"> +<div id="outline-container-orga47b531" class="outline-3"> +<h3 id="orga47b531">2017</h3> +<div class="outline-text-3" id="text-orga47b531"> <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 @@ -428,7 +428,7 @@ Another text is <a href="https://wstein.org/ent/">Elementary Number Theory</a> a </ul> -<figure id="org4f39495"> +<figure id="org643f358"> <img src="img/sieveE.jpg" alt="sieveE.jpg"> </figure> @@ -438,7 +438,7 @@ Another text is <a href="https://wstein.org/ent/">Elementary Number Theory</a> a </main> <footer id="postamble" class="status"> <p class="author">Author: Jan Snellman</p> -<p class="date">Created: 2024-02-06</p> +<p class="date">Created: 2024-08-22</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 d3b306c3849d95927b6ce9a106c73dec29ddfc20..64e5f08f906c91dba039c6075c55ff819e0b35e8 100644 --- a/public/sitemap.html +++ b/public/sitemap.html @@ -1,7 +1,7 @@ <!DOCTYPE html> <html lang="en"> <head> -<!-- 2024-06-05 --> +<!-- 2024-08-22 --> <meta charset="utf-8" /> <meta name="viewport" content="width=device-width, initial-scale=1" /> <title>Kurshemsida</title> @@ -206,24 +206,24 @@ <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="labs/lecture5.html">lecture5</a></li> <li><a href="labs/lecture4.html">lecture4</a></li> <li><a href="labs/lecture3.html">lecture3</a></li> <li><a href="labs/lecture2.html">lecture2</a></li> <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> +<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: 2024-06-05</p> +<p class="date">Created: 2024-08-22</p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> </footer> </body>