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課程名稱 |
組合學一
Combinatorics (Ⅰ) |
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開課學期 |
103-1 |
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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 |
MATH7701 |
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課程識別碼 |
221 U3290 |
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班次 |
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學分 |
3 |
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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 |
星期三5(12:20~13:10)星期五3,4(10:20~12:10) |
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上課地點 |
天數102天數101 |
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備註 |
總人數上限：60人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1031MATH7701_comb_I |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
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課程大綱
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課程概述 |
This course contains two parts, one on counting theory and the other on design theory. For the part of counting theory, we will cover pigeonhole principle, permutation, generating function, inclusion-exclusion principle, Polya counting, and some advanced topics. For the part of design theory, we will cover PBD design, finite geometry, Hadamard matrices, orthogonal Latin squares, as well as the applications of design theory. |
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課程目標 |
Combinatorics is concerned with arrangements of the objects of a set into patterns satisfying specified rules. Two general types of problems occur repeatedly: existence of arrangement, enumeration or classification of the arrangements. The goal of this course is to introduce counting theory and design theory. |
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課程要求 |
＊Grading scheme：
作業、期中考、期末考各占三分之一成績。
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預期每週課後學習時數 |
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Office Hours |
每週五 14:30~17:00 |
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指定閱讀 |
P. J. Cameron, Combinatorics: Topics, Techniques, Algorithms, Cambridge
University Press, 1994.
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參考書目 |
R.A. Brualdi, Introductory Combinatorics, Third Edition, Prentice Hall, Upper
saddle River, 1999.
L. Lovasz, Combinatorial Problems and Exercises, North-Holland Pub. Comp.,
Amsterdam, 1979.
R.P. Stanley, Enumerative Combinatorics, Volume I, Wadsworth & Brooks,
Monterey, CA, 1986.
J.H. van Lint and R.M. Wilson, A Course in Combinatorics, Second Edition,
Cambridge 2002.
沈灝，組合設計理論，第二版，上海角通大學出版社，2008。 |
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評量方式
(僅供參考) |
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週次 |
日期 |
單元主題 |
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第1週 |
9/17,9/19 |
Counting |
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第2週 |
9/24,9/26 |
Subsets, partitions, permuttaions (see the book by Peter J. Cameron, Chapter 3) |
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第3週 |
10/01,10/03 |
Recurrence relations, permutations |
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第4週 |
10/08,10/10 |
The principle of inclusuion and exclusion |
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第5週 |
10/15,10/17 |
Latin squares |
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第6週 |
10/22,10/24 |
Extremal set theory |
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第7週 |
10/29,10/31 |
Steiner triple systems |
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第8週 |
11/05,11/07 |
Finite geometry |
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第9週 |
11/12,11/14 |
期中考 (11/14 Friday in class, up to Steiner triple systems) |
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第10週 |
11/19,11/21 |
學習自主週，停課。 |
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第11週 |
11/26,11/28 |
Ramsey's theory |
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第12週 |
12/03,12/05 |
Posets, lattices, matroids |
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第13週 |
12/10,12/12 |
More on partitions and permutations |
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第14週 |
12/17,12/19 |
Automorphism gropus and permutation groups |
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第15週 |
12/24,12/26 |
Enumeration under group action |
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第16週 |
12/31,1/02 |
Designs |
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第17週 |
1/07,1/09 |
Codes |
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第18週 |
1/16 |
期末考 (After Steiner triple systems) |
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