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課程名稱 |
組合學一
Combinatorics (Ⅰ) |
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開課學期 |
107-1 |
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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 |
3.0 |
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全/半年 |
半年 |
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必/選修 |
必修 |
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上課時間 |
星期三8(15:30~16:20)星期五1,2(8:10~10:00) |
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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/1071MATH7701_comb_1 |
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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 some 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 |
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預期每週課後學習時數 |
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Office Hours |
另約時間 備註： gjchang@math.ntu.edu.tw 聯絡。 |
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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 |
待補S. H. M. van Zwam, Lecture Note for MAT377-Combinatorial Mathematics (Fall
2013), Princeton University, April 24, 2014.
J. H. van Lint and R. M. Wilson, A Course in Combinatorics, Second Edition,
Cambridge 2002.
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.
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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No. |
項目 |
百分比 |
說明 |
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1. |
作業 |
32% |
16個作業。 |
2. |
期中考 |
34% |
第9週。 |
3. |
期末考 |
34% |
第18週。 |
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週次 |
日期 |
單元主題 |
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第1週 |
9/12,9/14 |
1. What is Combinatorics?
2. On numbers and counting. |
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第2週 |
9/19,9/21 |
3. Subsets, partitions, permutations. |
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第3週 |
9/26,9/28 |
4. Recurrence reations and generating functions. |
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第4週 |
10/03,10/05 |
5. The Principle of Inclusion and Exclusion. |
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第5週 |
10/10,10/12 |
6. Latin squares and SDRs. |
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第6週 |
10/17,10/19 |
7. Extremal set theory. |
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第7週 |
10/24,10/26 |
8. Steiner triple systems. |
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第8週 |
10/31,11/02 |
9. Finite geometry. |
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第9週 |
11/07,11/09 |
9. Finite geometry.
期中考 |
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第10週 |
11/14,11/16 |
自主學習週 |
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第11週 |
11/21,11/23 |
12. Posets, latices and matroids. |
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第12週 |
11/28,11/30 |
13. More on partitions and permutations. |
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第13週 |
12/05,12/07 |
14. Automorphsim groups and permutation groups. |
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第14週 |
12/12,12/14 |
15. Enumeration under group action. |
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第15週 |
12/19,12/21 |
16. Designs. |
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第16週 |
12/26,12/28 |
17. Error-correcting codes. |
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第17週 |
1/02,1/04 |
19. The infinite.
21. Where to go from here? |
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第18週 |
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期末考 |
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