CS0901: Combinatorics

Shanghai Jiao Tong University, Fall 2025

 

Course Information

InstructorKuan Yang
Lecture timesTuesday 12 : 55 - 16 : 40     (Week 1 - 16)
LocationEast Lower Hall 309 (东下院 309)
Teaching assistant(s)Zhidan Li (李至丹)
Office hoursTo be determined

 

News and Announcements

 

Textbook and References

 

Syllabus

  1. Counting
  1. Structures
  1. Existence and Extremal Problems
  1. The Probabilistic Method
  1. Linear Algebraic Methods

 

Lecture Schedule

WeekDateTopicsLecture notes
109/16Introduction, the twelvefold way, binomial coefficients,
double counting, combinatorial identities, Catalan numbers
Lecture 01
209/23Generating functionsLecture 02
 09/28Principle of Inclusion and exclusion, Möbius inversionLecture 03
309/30Posets, chains and antichains, Möbius inversion on posetsLecture 04
510/14Graph theory basicsLecture 05
610/21Colorings, bipartite graph matchingsLecture 06
710/28Pigeonhole principle, happy ending problem, Ramsey theoryLecture 07
811/04Extremal graph theoryLecture 08
911/11Discrete geometry; Mid-term QuizLecture 09
1011/18Extremal set theoryLecture 10
1111/25Basic probabilistic arguments, linearity of expectationLecture 11
1212/02Alterations, Markov's inequality, second moment methodLecture 12
1312/09Threshold in random graph theory, Lovász local lemmaLecture 13
1412/16Algorithmic local lemma, intro to linear algebra methodLecture 14
1512/23Dimensions of linear spaces, eigenvalues of graphsLecture 15
1612/30Final Quiz