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課程名稱 |
圖論中的拓樸方法
Topological methods for graph theory |
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開課學期 |
105-2 |
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授課對象 |
理學院 數學研究所 |
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授課教師 |
張鎮華 |
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課號 |
MATH5048 |
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課程識別碼 |
221 U7050 |
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班次 |
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學分 |
3.0 |
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全/半年 |
半年 |
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必/選修 |
選修 |
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上課時間 |
星期三1,2(8:10~10:00)星期五4(11:20~12:10) |
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上課地點 |
天數302天數302 |
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備註 |
總人數上限：40人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1052MATH5048_top_gra |
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課程簡介影片 |
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核心能力關聯 |
本課程尚未建立核心能力關連 |
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課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
This course covers simplicial complexes, the Borsuk-Ulam theorem and its applications to combinatorics, the Ky Fan theorem and its application to graph coloring. The attempts to prove the Borsuk-Ulam theorem and the Ky Fan theorem is on the way to possible direct proofs of those results proven by the topological methods. |
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課程目標 |
A number of important results in combinatorics, discrete geometry, and theoretical computer science have been proved by surprising applications of algebraic topology. Lovasz’s striking proof of Kneser’s conjecture from 1978 is among the first and most prominent examples, dealing with a problem about finite sets with no apparent relation to topology.
The aim of this course is to discuss the applications of topological methods to graph coloring, including chromatic numbers and circular chromatic numbers of Kneser graphs.
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課程要求 |
每周要寫作業。 |
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預期每週課後學習時數 |
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Office Hours |
每週三 13:00~17:00 |
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指定閱讀 |
J. Matousek, Using the Borsuk–Ulam Theorem, Springer-Verlage, Berlin, 2003. |
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參考書目 |
J. Matousek, Using the Borsuk–Ulam Theorem, Springer-Verlage, Berlin, 2003. |
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
作業 |
34% |
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2. |
期中考 |
33% |
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3. |
期末考 |
33% |
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週次 |
日期 |
單元主題 |
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第1週 |
2/22,2/24 |
Introduction to Graph Coloring |
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第2週 |
3/01,3/03 |
Simplicial Complexes |
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第3週 |
3/08,3/10 |
Simplicial Complexes |
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第4週 |
3/15,3/17 |
The Borsuk-Ulam Theporem
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第5週 |
3/22,3/24 |
The Borsuk-Ulam Theporem
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第6週 |
3/29,3/31 |
Direct Applications of Borsuk-Ulam
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第7週 |
4/05,4/07 |
Direct Applications of Borsuk-Ulam |
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第8週 |
4/12,4/14 |
Circular Chromatic Number |
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第9週 |
4/19,4/21 |
Circular Chromatic Number
期中考 |
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第10週 |
4/26,4/28 |
Circular Chromatic number |
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第11週 |
5/03,5/05 |
自主學習周 |
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第12週 |
5/10,5/12 |
Genhua Fan's work for \chi_c equals \chi |
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第13週 |
5/17,5/19 |
Ky Fan theorem |
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第14週 |
5/24,5/26 |
Chen's work for circular chromatic number |
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第15週 |
5/31,6/02 |
Related Topics |
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第16週 |
6/07,6/09 |
Related Topics |
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第17週 |
6/14,6/16 |
Related Topics |
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第18週 |
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期末考 |
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第0-0週 |
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Other References |
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第0-1週 |
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J. Matousek, Using the Borsuk-Ulam
Theorem, Springer-Verlage, Berlin, 2003. |
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