基本素養 Basic Literacy無
課程概述 Course Description格羅布納基，布其柏格算法。
Groebner basis, Buchberger's algorithm.
課程學習目標 Course Objectives
課程進度 Course Outline
|週次 Week||進度說明 Progress Description|
|1||Polynomial rings and Ideals [EH: Chap 1]|
|2||Monomial orders and Initial ideals [EH: 2.1-2.2]|
|3||Division algorithm and Buchberger's criterion [EH: 2.3-2.4]|
|4||Buchberger's algorithm and Reduced Grobner bases [EH:2.5-2.6]|
|5||Elimination of variables [EH: 3.1]|
|6||Applications to operations on ideals [EH:3.2]|
|7||Zero dimensional ideals and ideals of initial forms [EH: 3.3-3.4]|
|8||Hilbert's Nullstellensatz and Ideal-variety correspondence [CLO: 4.1~4.4]|
|9||Primary Decomposition [CLO: 4.5~4.7]|
|10||Projective varieties [CLO: 8.2~8.3]|
|11||The Hilbert function and the dimension of a variety [CLO: 9.1~9.3]|
|12||Newton polytopes, State polytopes, and Grobner fans [St: Chap 2]|
|13||Fields with valuations [MS: 2.1], Very affine varieties[MS: 2.2]|
|14||Some polyhedral geometry [MS: 2.3], Grobner bases over fields with valuations [MS: 2.4]|
|15||Grobner complexes and Tropical Bases [MS: 2.5-2.6]|
|16||Fundamental theorem of tropical geometry [MS: 3.1-3.2]|
|17||Structure theorems and the balancing conditions for tropical varieties [MS: 3.3~3.4]|
|18||Students' Final Reports|
有關課程其他調查 Other Surveys of Courses1.本課程是否規劃業界教師參與教學或演講?
Is there any industry specialist invited in this course? How many times?
Are there any internships involved in the course? How many hours?
Is this course recognized as an academic ethics course? In the course how many hours are regarding academic ethics topics?
Is this course recognized as a Community engagement and Service learning course? Which community will be engaged?