https://wiki.cs.hse.ru/index.php?action=history&feed=atom&title=Algebra_DSBA_2025%2F2026 2026-09-20T20:50:50Z История изменений этой страницы в вики MediaWiki 1.43.9 https://wiki.cs.hse.ru/index.php?title=Algebra_DSBA_2025/2026&diff=96890&oldid=prev 2026-06-19T18:12:42Z

<p><span class="autocomment">Results</span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="ru"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Предыдущая версия</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Версия от 18:12, 19 июня 2026</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l99">Строка 99:</td> <td colspan="2" class="diff-lineno">Строка 99:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|}</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* Test</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* <ins style="font-weight: bold; text-decoration: none;">Written </ins>Test<ins style="font-weight: bold; text-decoration: none;">, Exam, Final Grade</ins></div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>! [ 251] !!  [ 252] !!  [ 253] !!  [ 254] !!  [ 255] !!  [ 256] !!  [ <del style="font-weight: bold; text-decoration: none;">257]</del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>! [<ins style="font-weight: bold; text-decoration: none;">https://docs.google.com/spreadsheets/d/1VdyBS-2at8ULg_Zu9JTWDDh1drQgTDm2oMQEC2hcMsQ/edit?gid=0#gid=0 </ins>251] !!  [<ins style="font-weight: bold; text-decoration: none;">https://docs.google.com/spreadsheets/d/1VdyBS-2at8ULg_Zu9JTWDDh1drQgTDm2oMQEC2hcMsQ/edit?gid=414893016#gid=414893016 </ins>252] !!  [<ins style="font-weight: bold; text-decoration: none;">https://docs.google.com/spreadsheets/d/1VdyBS-2at8ULg_Zu9JTWDDh1drQgTDm2oMQEC2hcMsQ/edit?gid=238120772#gid=238120772 </ins>253] !!  [<ins style="font-weight: bold; text-decoration: none;">https://docs.google.com/spreadsheets/d/1VdyBS-2at8ULg_Zu9JTWDDh1drQgTDm2oMQEC2hcMsQ/edit?gid=2026788883#gid=2026788883 </ins>254] !!  [<ins style="font-weight: bold; text-decoration: none;">https://docs.google.com/spreadsheets/d/1VdyBS-2at8ULg_Zu9JTWDDh1drQgTDm2oMQEC2hcMsQ/edit?gid=15906055#gid=15906055 </ins>255] !!  [<ins style="font-weight: bold; text-decoration: none;">https://docs.google.com/spreadsheets/d/1VdyBS-2at8ULg_Zu9JTWDDh1drQgTDm2oMQEC2hcMsQ/edit?gid=140868039#gid=140868039 </ins>256] !!  [<ins style="font-weight: bold; text-decoration: none;">https://docs.google.com/spreadsheets/d/1VdyBS-2at8ULg_Zu9JTWDDh1drQgTDm2oMQEC2hcMsQ/edit?gid</ins>=<ins style="font-weight: bold; text-decoration: none;">1523429419#gid</ins>=<ins style="font-weight: bold; text-decoration: none;">1523429419 </ins>257]</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">|}</del></div></td><td colspan="2" class="diff-side-added"></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2" class="diff-side-added"></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">* Summary Statement</del></div></td><td colspan="2" class="diff-side-added"></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2" class="diff-side-added"></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">{| class</del>=<del style="font-weight: bold; text-decoration: none;">"wikitable" style</del>=<del style="font-weight: bold; text-decoration: none;">"text-align:center"</del></div></td><td colspan="2" class="diff-side-added"></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">|-</del></div></td><td colspan="2" class="diff-side-added"></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">! [ 251] !!  [ 252] !!  [ 253] !!  [ 254] !!  [ 255] !!  [ 256] !!  [ </del>257] <del style="font-weight: bold; text-decoration: none;"> </del></div></td><td colspan="2" class="diff-side-added"></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|}</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <!-- diff cache key wiki_cs:diff:1.41:old-96782:rev-96890:php=table --> </table>

Mazhuga.A.M. https://wiki.cs.hse.ru/index.php?title=Algebra_DSBA_2025/2026&diff=96782&oldid=prev 2026-06-06T15:54:02Z

<p><span class="autocomment">Lecture abstracts</span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="ru"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Предыдущая версия</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Версия от 15:54, 6 июня 2026</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l44">Строка 44:</td> <td colspan="2" class="diff-lineno">Строка 44:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>= Lecture abstracts =</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>= Lecture abstracts =</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">'''Lecture&amp;nbsp;10''' (15.06.2026). The Diamond Lemma. A proof of the Buchberger criterion.</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">'''Lecture&amp;nbsp;9''' (06.06.2026).  S-polynomials and the Buchberger criterion. Ideals in a polynomial ring, the Buchberger algorithm to produce a Groebner basis of an ideal. A ring of remainders. Membership problem and variable elimination.</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&#039;&#039;&#039;Lecture&amp;nbsp;8&#039;&#039;&#039; (01.06.2026). Polynomials in several variables. Lexicographical orders, stabilization of strictly descending chains of monomials. An elementary reduction, a reduction with respect to a set of polynomials, remainders, Groebner basis. Stabilization of reduction.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&#039;&#039;&#039;Lecture&amp;nbsp;8&#039;&#039;&#039; (01.06.2026). Polynomials in several variables. Lexicographical orders, stabilization of strictly descending chains of monomials. An elementary reduction, a reduction with respect to a set of polynomials, remainders, Groebner basis. Stabilization of reduction.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> </table>

Mazhuga.A.M. https://wiki.cs.hse.ru/index.php?title=Algebra_DSBA_2025/2026&diff=96714&oldid=prev 2026-05-31T13:30:21Z

<p><span class="autocomment">Teachers and assistants</span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="ru"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Предыдущая версия</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Версия от 13:30, 31 мая 2026</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l6">Строка 6:</td> <td colspan="2" class="diff-lineno">Строка 6:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>! Группа !! 251 !! 252 !! 253 !! 254 !! 255 !! 256 !! 257</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>! Группа !! 251 !! 252 !! 253 !! 254 !! 255 !! 256 !! 257</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>|| Lecturer ||colspan="7"| <del style="font-weight: bold; text-decoration: none;"> </del>[https://www.hse.ru/org/persons/224875083 Andrew Mazhuga]</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>|| Lecturer ||colspan="7"| <ins style="font-weight: bold; text-decoration: none;">[https://www.hse.ru/org/persons/209508745 Дима Трушин], </ins>[https://www.hse.ru/org/persons/224875083 Andrew Mazhuga]</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-  </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-  </div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>|| Teacher || <del style="font-weight: bold; text-decoration: none;"> </del>[https://www.hse.ru/org/persons/225516943/ Ivan Beldiev] || [https://www.hse.ru/org/persons/224875083 Andrew Mazhuga] || [https://www.hse.ru/org/persons/305077523/ Andey Zhizhin] || [https://www.hse.ru/org/persons/697229842 Dmitry Gayfulin] || [https://www.hse.ru/en/org/persons/1083814039/ Subin Pulari] || [https://www.hse.ru/org/persons/697229842 Dmitry Gayfulin] || [https://www.hse.ru/en/org/persons/1087367159/ Ananya Pal]</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>|| Teacher || <ins style="font-weight: bold; text-decoration: none;">[https://www.hse.ru/org/persons/209508745 Дима Трушин], </ins>[https://www.hse.ru/org/persons/225516943/ Ivan Beldiev] || [https://www.hse.ru/org/persons/224875083 Andrew Mazhuga] || [https://www.hse.ru/org/persons/305077523/ Andey Zhizhin] || [https://www.hse.ru/org/persons/697229842 Dmitry Gayfulin] || [https://www.hse.ru/en/org/persons/1083814039/ Subin Pulari] || [https://www.hse.ru/org/persons/697229842 Dmitry Gayfulin] || [https://www.hse.ru/en/org/persons/1087367159/ Ananya Pal]</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|| Assistant ||  [https://t.me/svvika06 Viktoriya Sliva]  ||  [https://t.me/zilervarls Illarion Illarionov-Zervas]  ||  [https://t.me/marshmel_m Maria Sudarikova]  ||  [https://t.me/yachatoyer Vadim Andrianov]  ||  [https://t.me/Avgustine_iw Zakhar Zinkin]  ||  [https://t.me/zlata_vr Zlata Vronskaya]  ||  [https://t.me/Ignkos Ignat Kostyuchenko]  </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|| Assistant ||  [https://t.me/svvika06 Viktoriya Sliva]  ||  [https://t.me/zilervarls Illarion Illarionov-Zervas]  ||  [https://t.me/marshmel_m Maria Sudarikova]  ||  [https://t.me/yachatoyer Vadim Andrianov]  ||  [https://t.me/Avgustine_iw Zakhar Zinkin]  ||  [https://t.me/zlata_vr Zlata Vronskaya]  ||  [https://t.me/Ignkos Ignat Kostyuchenko]  </div></td></tr> </table>

Mazhuga.A.M. https://wiki.cs.hse.ru/index.php?title=Algebra_DSBA_2025/2026&diff=96710&oldid=prev 2026-05-31T12:39:38Z

<p><span class="autocomment">Lecture abstracts</span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="ru"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Предыдущая версия</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Версия от 12:39, 31 мая 2026</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l44">Строка 44:</td> <td colspan="2" class="diff-lineno">Строка 44:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>= Lecture abstracts =</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>= Lecture abstracts =</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">'''Lecture&amp;nbsp;8''' (01.06.2026). Polynomials in several variables. Lexicographical orders, stabilization of strictly descending chains of monomials. An elementary reduction, a reduction with respect to a set of polynomials, remainders, Groebner basis. Stabilization of reduction.</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&#039;&#039;&#039;Lecture&amp;nbsp;7&#039;&#039;&#039; (25.05.2026). Characteristic of a field. Field extensions, an extension by a root. Finite fields: number of elements in a finite field, multiplicative group of a finite field is cyclic, classification of finite fields (without proof). How to produce finite fields. Galois random generator. Stream cipher.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&#039;&#039;&#039;Lecture&amp;nbsp;7&#039;&#039;&#039; (25.05.2026). Characteristic of a field. Field extensions, an extension by a root. Finite fields: number of elements in a finite field, multiplicative group of a finite field is cyclic, classification of finite fields (without proof). How to produce finite fields. Galois random generator. Stream cipher.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> </table>

Mazhuga.A.M. https://wiki.cs.hse.ru/index.php?title=Algebra_DSBA_2025/2026&diff=96653&oldid=prev 2026-05-25T15:56:44Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="ru"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Предыдущая версия</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Версия от 15:56, 25 мая 2026</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l6">Строка 6:</td> <td colspan="2" class="diff-lineno">Строка 6:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>! Группа !! 251 !! 252 !! 253 !! 254 !! 255 !! 256 !! 257</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>! Группа !! 251 !! 252 !! 253 !! 254 !! 255 !! 256 !! 257</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>|| Lecturer ||colspan="7"| <del style="font-weight: bold; text-decoration: none;">[https://www.hse.ru/org/persons/224875083 Andrew Mazhuga], </del>[https://www.hse.ru/org/persons/224875083 Andrew Mazhuga]</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>|| Lecturer ||colspan="7"| <ins style="font-weight: bold; text-decoration: none;"> </ins>[https://www.hse.ru/org/persons/224875083 Andrew Mazhuga]</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-  </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-  </div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>|| Teacher || <del style="font-weight: bold; text-decoration: none;">[https://www.hse.ru/org/persons/209508745 Дима Трушин], </del>[https://www.hse.ru/org/persons/225516943/ Ivan Beldiev] || [https://www.hse.ru/org/persons/224875083 Andrew Mazhuga] || [https://www.hse.ru/org/persons/305077523/ Andey Zhizhin] || [https://www.hse.ru/org/persons/697229842 Dmitry Gayfulin] || [https://www.hse.ru/en/org/persons/1083814039/ Subin Pulari] || [https://www.hse.ru/org/persons/697229842 Dmitry Gayfulin] || [https://www.hse.ru/en/org/persons/1087367159/ Ananya Pal]</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>|| Teacher || <ins style="font-weight: bold; text-decoration: none;"> </ins>[https://www.hse.ru/org/persons/225516943/ Ivan Beldiev] || [https://www.hse.ru/org/persons/224875083 Andrew Mazhuga] || [https://www.hse.ru/org/persons/305077523/ Andey Zhizhin] || [https://www.hse.ru/org/persons/697229842 Dmitry Gayfulin] || [https://www.hse.ru/en/org/persons/1083814039/ Subin Pulari] || [https://www.hse.ru/org/persons/697229842 Dmitry Gayfulin] || [https://www.hse.ru/en/org/persons/1087367159/ Ananya Pal]</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|| Assistant ||  [https://t.me/svvika06 Viktoriya Sliva]  ||  [https://t.me/zilervarls Illarion Illarionov-Zervas]  ||  [https://t.me/marshmel_m Maria Sudarikova]  ||  [https://t.me/yachatoyer Vadim Andrianov]  ||  [https://t.me/Avgustine_iw Zakhar Zinkin]  ||  [https://t.me/zlata_vr Zlata Vronskaya]  ||  [https://t.me/Ignkos Ignat Kostyuchenko]  </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|| Assistant ||  [https://t.me/svvika06 Viktoriya Sliva]  ||  [https://t.me/zilervarls Illarion Illarionov-Zervas]  ||  [https://t.me/marshmel_m Maria Sudarikova]  ||  [https://t.me/yachatoyer Vadim Andrianov]  ||  [https://t.me/Avgustine_iw Zakhar Zinkin]  ||  [https://t.me/zlata_vr Zlata Vronskaya]  ||  [https://t.me/Ignkos Ignat Kostyuchenko]  </div></td></tr> </table>

Tvozn https://wiki.cs.hse.ru/index.php?title=Algebra_DSBA_2025/2026&diff=96652&oldid=prev 2026-05-25T15:56:03Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="ru"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Предыдущая версия</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Версия от 15:56, 25 мая 2026</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l6">Строка 6:</td> <td colspan="2" class="diff-lineno">Строка 6:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>! Группа !! 251 !! 252 !! 253 !! 254 !! 255 !! 256 !! 257</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>! Группа !! 251 !! 252 !! 253 !! 254 !! 255 !! 256 !! 257</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>|| Lecturer ||colspan="7"| [https://www.hse.ru/org/persons/<del style="font-weight: bold; text-decoration: none;">209508745 Дима Трушин</del>], [https://www.hse.ru/org/persons/224875083 Andrew Mazhuga]</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>|| Lecturer ||colspan="7"| [https://www.hse.ru/org/persons/<ins style="font-weight: bold; text-decoration: none;">224875083 Andrew Mazhuga</ins>], [https://www.hse.ru/org/persons/224875083 Andrew Mazhuga]</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-  </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-  </div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|| Teacher || [https://www.hse.ru/org/persons/209508745 Дима Трушин], [https://www.hse.ru/org/persons/225516943/ Ivan Beldiev] || [https://www.hse.ru/org/persons/224875083 Andrew Mazhuga] || [https://www.hse.ru/org/persons/305077523/ Andey Zhizhin] || [https://www.hse.ru/org/persons/697229842 Dmitry Gayfulin] || [https://www.hse.ru/en/org/persons/1083814039/ Subin Pulari] || [https://www.hse.ru/org/persons/697229842 Dmitry Gayfulin] || [https://www.hse.ru/en/org/persons/1087367159/ Ananya Pal]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|| Teacher || [https://www.hse.ru/org/persons/209508745 Дима Трушин], [https://www.hse.ru/org/persons/225516943/ Ivan Beldiev] || [https://www.hse.ru/org/persons/224875083 Andrew Mazhuga] || [https://www.hse.ru/org/persons/305077523/ Andey Zhizhin] || [https://www.hse.ru/org/persons/697229842 Dmitry Gayfulin] || [https://www.hse.ru/en/org/persons/1083814039/ Subin Pulari] || [https://www.hse.ru/org/persons/697229842 Dmitry Gayfulin] || [https://www.hse.ru/en/org/persons/1087367159/ Ananya Pal]</div></td></tr> </table>

Tvozn https://wiki.cs.hse.ru/index.php?title=Algebra_DSBA_2025/2026&diff=96643&oldid=prev 2026-05-24T12:33:04Z

<p><span class="autocomment">Lecture abstracts</span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="ru"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Предыдущая версия</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Версия от 12:33, 24 мая 2026</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l44">Строка 44:</td> <td colspan="2" class="diff-lineno">Строка 44:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>= Lecture abstracts =</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>= Lecture abstracts =</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">'''Lecture&amp;nbsp;7''' (25.05.2026). Characteristic of a field. Field extensions, an extension by a root. Finite fields: number of elements in a finite field, multiplicative group of a finite field is cyclic, classification of finite fields (without proof). How to produce finite fields. Galois random generator. Stream cipher.</ins></div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&#039;&#039;&#039;Lecture&amp;nbsp;6&#039;&#039;&#039; (18.05.2026). Polynomials in one variable. Euclidean algorithm, greatest common divisor, ideals of F[x]. Irreducible polynomials and unique factorization of polynomials in F[x]. Ring of remainders, the Chinese Remainder Theorem for polynomials.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&#039;&#039;&#039;Lecture&amp;nbsp;6&#039;&#039;&#039; (18.05.2026). Polynomials in one variable. Euclidean algorithm, greatest common divisor, ideals of F[x]. Irreducible polynomials and unique factorization of polynomials in F[x]. Ring of remainders, the Chinese Remainder Theorem for polynomials.</div></td></tr> </table>

Mazhuga.A.M. https://wiki.cs.hse.ru/index.php?title=Algebra_DSBA_2025/2026&diff=96577&oldid=prev 2026-05-17T10:51:43Z

<p><span class="autocomment">Lecture abstracts</span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="ru"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Предыдущая версия</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Версия от 10:51, 17 мая 2026</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l44">Строка 44:</td> <td colspan="2" class="diff-lineno">Строка 44:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>= Lecture abstracts =</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>= Lecture abstracts =</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">'''Lecture&amp;nbsp;6''' (18.05.2026). Polynomials in one variable. Euclidean algorithm, greatest common divisor, ideals of F[x]. Irreducible polynomials and unique factorization of polynomials in F[x]. Ring of remainders, the Chinese Remainder Theorem for polynomials.</ins></div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&#039;&#039;&#039;Lecture&amp;nbsp;5&#039;&#039;&#039; (11.05.2026). Rings, commutative rings, fields, subrings. Invertible elements, zero divisors, nilpotent and idempotent elements. Ideals. Description of ideals in Z and Z_n. Homomorphisms and isomorphisms of rings. The Chinese remainder theorem for rings. The kernel and the image of a homomorphism, their properties.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&#039;&#039;&#039;Lecture&amp;nbsp;5&#039;&#039;&#039; (11.05.2026). Rings, commutative rings, fields, subrings. Invertible elements, zero divisors, nilpotent and idempotent elements. Ideals. Description of ideals in Z and Z_n. Homomorphisms and isomorphisms of rings. The Chinese remainder theorem for rings. The kernel and the image of a homomorphism, their properties.</div></td></tr> <!-- diff cache key wiki_cs:diff:1.41:old-96576:rev-96577:php=table --> </table>

Mazhuga.A.M. https://wiki.cs.hse.ru/index.php?title=Algebra_DSBA_2025/2026&diff=96576&oldid=prev 2026-05-17T10:50:35Z

<p><span class="autocomment">Teachers and assistants</span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="ru"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Предыдущая версия</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Версия от 10:50, 17 мая 2026</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l6">Строка 6:</td> <td colspan="2" class="diff-lineno">Строка 6:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>! Группа !! 251 !! 252 !! 253 !! 254 !! 255 !! 256 !! 257</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>! Группа !! 251 !! 252 !! 253 !! 254 !! 255 !! 256 !! 257</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>|| Lecturer ||colspan="7"| [https://www.hse.ru/org/persons/224875083 Andrew Mazhuga]</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>|| Lecturer ||colspan="7"| <ins style="font-weight: bold; text-decoration: none;">[https://www.hse.ru/org/persons/209508745 Дима Трушин], </ins>[https://www.hse.ru/org/persons/224875083 Andrew Mazhuga]</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-  </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-  </div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>|| Teacher || [https://www.hse.ru/org/persons/225516943/ Ivan Beldiev] || [https://www.hse.ru/org/persons/224875083 Andrew Mazhuga] || [https://www.hse.ru/org/persons/305077523/ Andey Zhizhin] || [https://www.hse.ru/org/persons/697229842 Dmitry Gayfulin] || [https://www.hse.ru/en/org/persons/1083814039/ Subin Pulari] || [https://www.hse.ru/org/persons/697229842 Dmitry Gayfulin] || [https://www.hse.ru/en/org/persons/1087367159/ Ananya Pal]</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>|| Teacher || <ins style="font-weight: bold; text-decoration: none;">[https://www.hse.ru/org/persons/209508745 Дима Трушин], </ins>[https://www.hse.ru/org/persons/225516943/ Ivan Beldiev] || [https://www.hse.ru/org/persons/224875083 Andrew Mazhuga] || [https://www.hse.ru/org/persons/305077523/ Andey Zhizhin] || [https://www.hse.ru/org/persons/697229842 Dmitry Gayfulin] || [https://www.hse.ru/en/org/persons/1083814039/ Subin Pulari] || [https://www.hse.ru/org/persons/697229842 Dmitry Gayfulin] || [https://www.hse.ru/en/org/persons/1087367159/ Ananya Pal]</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|| Assistant ||  [https://t.me/svvika06 Viktoriya Sliva]  ||  [https://t.me/zilervarls Illarion Illarionov-Zervas]  ||  [https://t.me/marshmel_m Maria Sudarikova]  ||  [https://t.me/yachatoyer Vadim Andrianov]  ||  [https://t.me/Avgustine_iw Zakhar Zinkin]  ||  [https://t.me/zlata_vr Zlata Vronskaya]  ||  [https://t.me/Ignkos Ignat Kostyuchenko]  </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|| Assistant ||  [https://t.me/svvika06 Viktoriya Sliva]  ||  [https://t.me/zilervarls Illarion Illarionov-Zervas]  ||  [https://t.me/marshmel_m Maria Sudarikova]  ||  [https://t.me/yachatoyer Vadim Andrianov]  ||  [https://t.me/Avgustine_iw Zakhar Zinkin]  ||  [https://t.me/zlata_vr Zlata Vronskaya]  ||  [https://t.me/Ignkos Ignat Kostyuchenko]  </div></td></tr> </table>

Mazhuga.A.M. https://wiki.cs.hse.ru/index.php?title=Algebra_DSBA_2025/2026&diff=96493&oldid=prev 2026-05-10T20:43:11Z

<p><span class="autocomment">Lecture abstracts</span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="ru"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Предыдущая версия</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Версия от 20:43, 10 мая 2026</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l45">Строка 45:</td> <td colspan="2" class="diff-lineno">Строка 45:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>= Lecture abstracts =</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>= Lecture abstracts =</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>'''Lecture&amp;nbsp;<del style="font-weight: bold; text-decoration: none;">1</del>''' (<del style="font-weight: bold; text-decoration: none;">06</del>.<del style="font-weight: bold; text-decoration: none;">04</del>.2026). <del style="font-weight: bold; text-decoration: none;">Binary operations</del>. <del style="font-weight: bold; text-decoration: none;">Associativity</del>, <del style="font-weight: bold; text-decoration: none;">neutral element</del>, <del style="font-weight: bold; text-decoration: none;">inverse element, commutativity</del>. <del style="font-weight: bold; text-decoration: none;">Definition </del>of <del style="font-weight: bold; text-decoration: none;">a group</del>. <del style="font-weight: bold; text-decoration: none;">Additive </del>and <del style="font-weight: bold; text-decoration: none;">multiplicative notations</del>. <del style="font-weight: bold; text-decoration: none;">Subgroups and cyclic subgroups</del>. The <del style="font-weight: bold; text-decoration: none;">order of an element </del>of a <del style="font-weight: bold; text-decoration: none;">group</del>.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>'''Lecture&amp;nbsp;<ins style="font-weight: bold; text-decoration: none;">5</ins>''' (<ins style="font-weight: bold; text-decoration: none;">11</ins>.<ins style="font-weight: bold; text-decoration: none;">05</ins>.2026). <ins style="font-weight: bold; text-decoration: none;">Rings, commutative rings, fields, subrings</ins>. <ins style="font-weight: bold; text-decoration: none;">Invertible elements</ins>, <ins style="font-weight: bold; text-decoration: none;">zero divisors</ins>, <ins style="font-weight: bold; text-decoration: none;">nilpotent and idempotent elements. Ideals</ins>. <ins style="font-weight: bold; text-decoration: none;">Description </ins>of <ins style="font-weight: bold; text-decoration: none;">ideals in Z and Z_n</ins>. <ins style="font-weight: bold; text-decoration: none;">Homomorphisms </ins>and <ins style="font-weight: bold; text-decoration: none;">isomorphisms of rings</ins>. <ins style="font-weight: bold; text-decoration: none;">The Chinese remainder theorem for rings</ins>. The <ins style="font-weight: bold; text-decoration: none;">kernel and the image </ins>of a <ins style="font-weight: bold; text-decoration: none;">homomorphism, their properties</ins>.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>'''Lecture&amp;nbsp;<del style="font-weight: bold; text-decoration: none;">2</del>''' (<del style="font-weight: bold; text-decoration: none;">13</del>.04.2026). <del style="font-weight: bold; text-decoration: none;">Classification of cyclic groups</del>. <del style="font-weight: bold; text-decoration: none;">The subgroups of the group of integers</del>. The <del style="font-weight: bold; text-decoration: none;">subgroups of the group Z_n. Left and right cosets, examples</del>. <del style="font-weight: bold; text-decoration: none;">Normal subgroups. The Lagrange theorem and its corollaries</del>.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>'''Lecture&amp;nbsp;<ins style="font-weight: bold; text-decoration: none;">4</ins>''' (<ins style="font-weight: bold; text-decoration: none;">27</ins>.04.2026). <ins style="font-weight: bold; text-decoration: none;">Cryptography</ins>. <ins style="font-weight: bold; text-decoration: none;">Exponentiation by squaring (fast raising to a power algorithm)</ins>. The <ins style="font-weight: bold; text-decoration: none;">discrete logarithm problem</ins>. <ins style="font-weight: bold; text-decoration: none;">Diffie-Hellman key exchange</ins>.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&#039;&#039;&#039;Lecture&amp;nbsp;3&#039;&#039;&#039; (20.04.2026). Homomorphisms and Isomorphisms of groups. Image and kernel of a homomorphism. Normal subgroups. Direct product of groups. Finite Abelian Groups. The Chinese Remainder Theorem. Structure of a finite abelian group.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&#039;&#039;&#039;Lecture&amp;nbsp;3&#039;&#039;&#039; (20.04.2026). Homomorphisms and Isomorphisms of groups. Image and kernel of a homomorphism. Normal subgroups. Direct product of groups. Finite Abelian Groups. The Chinese Remainder Theorem. Structure of a finite abelian group.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>'''Lecture&amp;nbsp;<del style="font-weight: bold; text-decoration: none;">4</del>''' (<del style="font-weight: bold; text-decoration: none;">27</del>.04.2026). <del style="font-weight: bold; text-decoration: none;">Cryptography</del>. <del style="font-weight: bold; text-decoration: none;">Exponentiation by squaring </del>(<del style="font-weight: bold; text-decoration: none;">fast raising to </del>a <del style="font-weight: bold; text-decoration: none;">power algorithm)</del>. The <del style="font-weight: bold; text-decoration: none;">discrete logarithm problem. Diffie-Hellman key exchange</del>.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>'''Lecture&amp;nbsp;<ins style="font-weight: bold; text-decoration: none;">2</ins>''' (<ins style="font-weight: bold; text-decoration: none;">13</ins>.04.2026). <ins style="font-weight: bold; text-decoration: none;">Classification of cyclic groups</ins>. <ins style="font-weight: bold; text-decoration: none;">The subgroups of the group of integers. The subgroups of the group Z_n. Left and right cosets, examples. Normal subgroups. The Lagrange theorem and its corollaries.</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">'''Lecture&amp;nbsp;1''' </ins>(<ins style="font-weight: bold; text-decoration: none;">06.04.2026). Binary operations. Associativity, neutral element, inverse element, commutativity. Definition of </ins>a <ins style="font-weight: bold; text-decoration: none;">group. Additive and multiplicative notations. Subgroups and cyclic subgroups</ins>. The <ins style="font-weight: bold; text-decoration: none;">order of an element of a group</ins>.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>= Problem sheets =</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>= Problem sheets =</div></td></tr> </table>

Mazhuga.A.M.