Combinatorics (Fall 2010): Difference between revisions
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* [http://en.wikipedia.org/wiki/Partition_(number_theory) Partition of a number] | * [http://en.wikipedia.org/wiki/Partition_(number_theory) Partition of a number] | ||
* [http://en.wikipedia.org/wiki/Twelvefold_way The twelvefold way] | * [http://en.wikipedia.org/wiki/Twelvefold_way The twelvefold way] | ||
* [http://en.wikipedia.org/wiki/Partition_(number_theory)#Ferrers_diagram Ferrers diagram] (and the MathWorld [http://mathworld.wolfram.com/FerrersDiagram.html link]) | |||
* [http://en.wikipedia.org/wiki/Inclusion-exclusion_principle The principle of inclusion-exclusion] (and more generally the [http://en.wikipedia.org/wiki/Sieve_theory sieve method]) | |||
* [http://en.wikipedia.org/wiki/Derangement Derangement] | |||
* [http://en.wikipedia.org/wiki/M%C3%A9nage_problem problème des ménages] |
Revision as of 07:02, 10 September 2010
This is the page for the class Combinatorics for the Fall 2010 semester. Students who take this class should check this page periodically for content updates and new announcements.
Announcement
- 9月3日第一次课。时间:上午三、四节;地点:馆I-105。
Course info
- Instructor : 尹一通,
- email: yitong.yin@gmail.com, yinyt@nju.edu.cn, yinyt@lamda.nju.edu.cn
- office: MMW 406.
- Class meeting: 10am-12 am, Friday; 馆I-105.
- Office hour: 2-5pm, Saturday; MMW 406.
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
Policies
Assignments
- To be announced.
Lecture Notes
A tentative list of topics:
- Basic enumeration | slides
- Partitions, Sieve methods | slides
- Generating functions
- The probabilistic method
- Random graphs
- Extremal graph theory
- Finite set systems
- Extremal set theory
- Ramsey theory
- Optimization
- Duality
- Flow and matching
- Matroid
- Spectra of graphs
- Harmonic analysis of boolean functions
- The Szemeredi regularity lemma
- Sum-product theorems, Kakeya set
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
- The twelvefold way
- Ferrers diagram (and the MathWorld link)
- The principle of inclusion-exclusion (and more generally the sieve method)
- Derangement
- problème des ménages