组合数学 (Spring 2013): Difference between revisions
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*[[组合数学 (Spring 2013)/Problem Set 1|Problem Set 1]], due on April 4, Thursday, in class. | *[[组合数学 (Spring 2013)/Problem Set 1|Problem Set 1]], due on April 4, Thursday, in class. | ||
*[[组合数学 (Spring 2013)/Problem Set 2|Problem Set 2]], due on April 25, Thursday, in class. | *[[组合数学 (Spring 2013)/Problem Set 2|Problem Set 2]], due on April 25, Thursday, in class. | ||
*[[组合数学 (Spring 2013)/Problem Set 3|Problem Set 3]], due on May 23, Thursday, in class. | |||
= Lecture Notes = | = Lecture Notes = | ||
Revision as of 15:04, 8 May 2013
| Instructor | |
|---|---|
| 尹一通 | |
| yitong.yin@gmail.com yinyt@nju.edu.cn | |
| office | 计算机系 804 |
| Class | |
| Class meetings |
Thursday, 8am-10am 仙 I-103 |
| Office hours |
Wednesday, 2-4pm 计算机系 804 |
| Textbook | |
 | |
|
van Lint and Wilson. A course in Combinatorics, 2nd ed., Cambridge Univ Press, 2001. | |
 | |
|
Jukna. Extremal Combinatorics: With Applications in Computer Science, 2nd ed., Springer, 2011. | |
This is the page for the class Combinatorics for the Spring 2013 semester. Students who take this class should check this page periodically for content updates and new announcements.
Announcement
- The second homework assignment is out, due in ONE week.
- 由于清明假期，作业提交时间推迟一周（4月11日课上交）。
- The first homework assignment is out, due in two weeks.
Course info
- Instructor : 尹一通
- email: yitong.yin@gmail.com, yinyt@nju.edu.cn,
- office: 804
- Teaching fellow: 金宇
- email: jinyu1122@hotmail.com
- Class meeting: Thursday 8am-10am, 仙 I-103.
- Office hour: Wednesday 2-4pm, 计算机系 804.
Syllabus
先修课程 Prerequisites
- 离散数学（Discrete Mathematics）
- 线性代数（Linear Algebra）
- 概率论（Probability Theory）
Course materials
成绩 Grades
- 课程成绩：本课程将会有六次作业和一次期末考试。最终成绩将由平时作业成绩和期末考试成绩综合得出。
- 迟交：如果有特殊的理由，无法按时完成作业，请提前联系授课老师，给出正当理由。否则迟交的作业将不被接受。
学术诚信 Academic Integrity
学术诚信是所有从事学术活动的学生和学者最基本的职业道德底线，本课程将不遗余力的维护学术诚信规范，违反这一底线的行为将不会被容忍。
作业完成的原则：署你名字的工作必须由你完成。允许讨论，但作业必须独立完成，并在作业中列出所有参与讨论的人。不允许其他任何形式的合作——尤其是与已经完成作业的同学“讨论”。
本课程将对剽窃行为采取零容忍的态度。在完成作业过程中，对他人工作（出版物、互联网资料、其他人的作业等）直接的文本抄袭和对关键思想、关键元素的抄袭，按照 ACM Policy on Plagiarism的解释，都将视为剽窃。剽窃者成绩将被取消。如果发现互相抄袭行为， 抄袭和被抄袭双方的成绩都将被取消。因此请主动防止自己的作业被他人抄袭。
学术诚信影响学生个人的品行，也关乎整个教育系统的正常运转。为了一点分数而做出学术不端的行为，不仅使自己沦为一个欺骗者，也使他人的诚实努力失去意义。让我们一起努力维护一个诚信的环境。
Assignments
- Problem Set 1, due on April 4, Thursday, in class.
- Problem Set 2, due on April 25, Thursday, in class.
- Problem Set 3, due on May 23, Thursday, in class.
Lecture Notes
- Basic enumeration | slides1 | slides2
- Generating functions | slides1 | slides2
- Sieve methods | slides1 | slides2
- Cayley's formula | slides
- Pólya's theory of counting | slides1 | slides2
- Existence problems | slides1
- The probabilistic method
- Extremal graph theory
- Extremal set theory
- Ramsey theory
- Matching theory
- Flow and matching
Concepts
- Binomial coefficient
- Composition of a number
- Combinations with repetition, [math]\displaystyle{ k }[/math]-multisets on a set
- Stirling number of the second kind
- Partition of a number
- Ferrers diagram (and the MathWorld link)
- The twelvefold way
- Generating function and formal power series
- Fibonacci number
- Newton's formula
- Catalan number
- The principle of inclusion-exclusion (and more generally the sieve method)
- Möbius inversion formula
- Derangement, and Problème des ménages
- Ryser's formula
- Euler totient function
- Cayley's formula
- Double counting and the handshaking lemma