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2010年度前期「MMA数学特論I」
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担当教員： Xavier Dahan 教員
開講時限： 木曜2限（10:30～12:00）
対象学年： MMA修士およびその他の数理学修士
特記事項： 講義やその他の伝達はすべて英語で行われます。
Mathematica のインストール
- Mathematica Download Page (Virtual Office, Not accessible from outside)
配布資料・ファイル一覧
Apr. 15, 2010 / #1 Introduction & Motivation
Apr. 22, 2010 / #2 Univariate Polynomial's GCD: Bezout Identity
May. 6, 2010 / #3 About Univariate Polynomial and intro. to Multivariate
May. 13, 2010 / #4 About Multivariate Polynomial and Division Algorithm
- #3 Continued...
May. 20, 2010 / #5 About unicity and Introduction to Groebner basis I
- Lecture Sildes IV
- Practice Test I: Monomial Order and Division Algorithm
- TA's Handout 4: Easy Exercises
May. 27, 2010 / #6 Introduction to Groebner basis II
- TA's Handout Extra: Remarks for P.T. I in Japanese
- Practice Test II: Division equality and monomial ideals
Jun. 3, 2010 / #7 Buchberger's algorithm
Jun. 10, 2010 / #8 Syzygies and Overview of Resultants
- #7 Continued...
Jun. 17, 2010 / #9 Resultants I
- Lecture Sildes VI
- Practice Test III: Around the Buchberger algorithm
- 6/29 modified: Here is the CORRECTED version, especially the following.
- CORRECTION 1: Ex.5-Q2. "Next, select the pair (1,3)" → NO! It is (2,3).
- CORRECTION 2: Ex.5-Q3. "Next the pair (2,3)" → NO! It is (1,3).
- CORRECTION 3: It is written "There are 2 pairs above [1,l] and [3,l] such that Test 2 works" but it doesn't work. However, it is not so serious because actually we have S(f1,f3) --> 0 so the other questions are correct.
- CORRECTION 4: Ex.6-Q3, It is not correct, but there is a homogeneous syzygy of multi-degree X^\gamma, so it is not "too incorrect".
- For students who have difficulties, it is highly recommended to come to the office hours, Monday from 2pm to 4pm.
Jun. 24, 2010 / #10 Resultants II + Elimination and Nullstellensatz I
- Resultant and Applications
- TA's Handout 5: Examples and Remarks
- Mathematica File: Syl-2.nb
- Sylvester matrix, intersection of 2 plane curves, Eulidean algorithm for the resultant
- Mathematica File: VanishOnAlgNbr.nb
- Contains 3 examples of computation of a vanishing polynomial of some algebraic numbers
