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課程簡介 Course Introduction
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開課年度學期 Year / Term
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113 學年度 第 2 學期
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開課班級 Department
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應用數學系 應數三
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授課方式 Instructional Method
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課堂教學 、 中英文雙語授課
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課程電腦代號 Course Reference Number
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150053
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課程名稱(中文) Course Title(Chinese)
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組合學
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課程名稱(英文) Course Title(English)
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combinatorics
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學分數/時數 Credit Hours
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3 /
3
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必(選)修 Requirement / Elective Course
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選修
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授課老師 Instructor
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孫新民
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助教 Teaching Assistant
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上課時間 Meeting Time
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星期五，節次3、4、5
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上課教室 Classroom
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A307
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Office Hours
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孫新民：4444/789A
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| 獲獎及補助情形 Awards and Grants |
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| 聯合國永續發展目標 (SDGs跨域類別) Sustainable Development Goals, SDGs |
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SDGs 04.
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優質教育：確保有教無類、公平以及高品質的教育，及提倡終身學習
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課程目標 Learning Objectives
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本課程為對組合學之內容及其應用作學習.###
課程強調問題實作討論,###
及加強相關英文閱讀能力.###
We will focus on combinatorial designs this semester.
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先修 ( 前置 ) 課程 Prerequisite
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| 彈性教學規劃 Flexible Teaching/Planning Schedules |
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課程大綱 Course Syllabus
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| 週次 Week |
課程單元大綱 Unit |
教學方式 Instructional Method/Style/Teaching Style |
參考資料或相關作業 References or Related Materials |
評量方式 Grading |
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1
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Introduction, Basic Results
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2
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放假
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3
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Isomorphisms and Automorphisms, Fisher’s Inequality
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4
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Symmetric BIBDs
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5
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Difference Sets
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6
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Difference Families
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7
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放假
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8
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Resolvable BIBDs
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9
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Mid-Term Exam
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10
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Affine Constructions of Simple BIBDs
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11
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On the Number of Simple BIBDs
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12
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Existence of Simple BIBDs I
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13
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Existence of Simple BIBDs II
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14
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Constructions of Simple BIBDs
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15
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補假
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16
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繳交期末報告, Optimal Constant Weight Codes
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17
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討論期末報告
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18
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討論期末報告
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單一課程對應校能力指標程度 The Degree to Which Single Course Corresponds to School Competence
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| 編號 No. |
校核心能力 School Core Competencies |
符合程度 Degree of conformity |
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1
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公民力 (Citizen)
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3
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2
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自學力 (Self-learning)
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4
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3
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資訊力 (Information)
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4
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4
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創造力 (Creativity)
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4
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5
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溝通力 (Communication)
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5
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6
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就業力(Employability)
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5
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單一課程對應系能力指標程度 The Degree to Which Single Course Corresponds to Department Competence
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| 編號 No. |
類別 Category |
系核心能力 Department Core Competencies |
符合程度 Degree of conformity |
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01
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系所
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學生具備數學思考與推理能力
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5
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02
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系所
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學生擁有數學應用與解決問題能力
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5
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03
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系所
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學生具備代數、離散、統計及科學計算能力
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5
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04
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系所
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學生具有小學數學之專業教學能力
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3
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05
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系所
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學生具有跨領域之科學知識
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4
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06
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系所
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學生擁有閱讀討論與發表之專業能力
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4
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單一課程對應院能力指標程度 The Degree to Which Single Course Corresponds to College Competence
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| 編號 No. |
院核心能力 College Core Competencies |
符合程度 Degree of conformity |
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1
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語文能力
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4
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2
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溝通與合作能力
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4
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3
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創新與實踐能力
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4
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4
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專業知能
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5
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教科書或參考用書 Textbooks or Reference Books
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館藏書名 Library Books
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Handbook of combinatorial designs
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備註 Remarks
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1. 自編教材
2. D.R. Stinson, Combinatorial designs: constructions and analysis, 2004.
• Chapter 1: Sections 1.1–1.3, Section 1.4 (optional), Sections 1.5–1.6
• Chapter 2: Sections 2.1–2.4
• Chapter 3: Sections 3.1–3.4
• Chapter 4: Sections 4.1–4.4, Section 4.5 (optional), Section 4.6
• Chapter 5: Sections 5.1–5.2, Section 5.3 (optional)
• Chapter 6: Sections 6.1, Section 6.2 (optional), Sections 6.3–6.8
• Chapter 7: Sections 7.1–7.3
3. Y.J. Ionin and M.S. Shrikhande, Combinatorics of Symmetric Designs, 2006.
05A Enumerative combinatorics: Stanley2011, Stanley2013, Handbook2015, CombinatoryAnalysis
05B Designs and configurations: Stinson2004_NUTN
05C Graph theory: BR2012, BondyMurtyGTWA
05D Extremal combinatorics
05E Algebraic combinatorics
Analytic Combinatorics
http://algo.inria.fr/flajolet/Publications/books.html
https://ac.cs.princeton.edu/home/
其他參考
Combinatorics e-books
Graph Theory e-books
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R.A. Beeler, How to Count--- An Introduction to Combinatorics and Its Applications, 2015.
R. Balakrishnan and K. Ranganathan, A textbook of graph theory, 2012. 西文電子書, 不能印書
1.1–1.6, 2.1–2.3, 3.1–3.4, 4.1–4.5, 5.1–5.4, 5.5(omitting consequences of Hall’s theorem),5.5 (omitting the Tutte matrix), 6.1–6.3, 7.1, 7.2, 7.5 (omitting Vizing’s theorem), 7.8, 8.1–8.4, and Chap.10.
https://link.springer.com/book/10.1007%2F978-1-4614-4529-6
J.A. Bondy and U.S.R. Murty, Graph Theory with Applications, 1976. (2008. 511.5 B711)
(上學期 Chap.1,2, 3.1, 4.1, 4.2)
B. Korte and J. Vygen, Combinatorial Optimization, 5th ed., Springer, 2012. 西文電子書, 不能印書
https://link.springer.com/book/10.1007%2F978-3-642-24488-9
E.A. Bender and S.G. Williamson, Foundations of Combinatorics with Applications, 2006.
1–3, 4.1, (4.2), 4.3, 5, 6.1, (6.2–6.4), 7, (8) 9.1, (9.2–9.3), 10, (11).
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K.P. Bogart, Combinatorics Through Guided Discovery, 2004.
A. Doerr and K. Levasseur, Applied Discrete Structures, 2013.
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※請尊重智慧財產權，不得非法影印教科書※
※ Please respect intellectual property rights and do not illegally photocopy textbooks. ※
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教學方法 Teaching Method
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教學方法 Teaching Method
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百分比 Percentage
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講述
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70 %
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討論
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30 %
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| 總和 Total |
100 % |
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成績評量方式 Grading
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| 評量方式 Grading |
百分比 Percentage |
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平時成績
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30 %
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期中考
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30 %
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期末報告
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40 %
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| 總和 Total |
100 % |
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成績評量方式補充說明
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平時成績(作業撰寫,其他報告,課堂參與,含習題及點名)(30%)、期中考(30%)、期末報告(40%)
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課程大綱補充資料 Supplementary Material of Course Syllabus
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