课程大纲
COURSE SYLLABUS
1.
课程代码/名称
Course Code/Title
MAT7080 组合数学专题 Topics in Combinatorics
2.
课程性质
Compulsory/Elective
选修 Elective
3.
课程学分/学时
Course Credit/Hours
3
4.
授课语言
Teaching Language
英文
English
5.
授课教师 Instructor(s)
向青教授，李才恒教授，刘博辰副教授
Qing Xiang, Professor; Caiheng Li, Professor; Bochen Liu, Associate Professor
6.
是否面向本科生开放
Open to undergraduates
or not
是 Yes
7.
先修要求
Pre-requisites
MA103b 线性代数 I & II，MA214 抽象代数
MA103b Linear Algebra, MA214 Abstract Algebra
8.
教学目标 Course Objectives
本课程介绍组合数学的几个分支的前沿研究，主要内容包括关联几何（特别是有限几何），极值组
合，代数编码，代数/极值图论。
This course will introduce cutting edge research in several areas of combinatorics. The main topics will
involve incidence geometry (in particular, finite geometry), extremal combinatorics, algebraic coding
theory and algebraic/extremal graph theory.
9.
教学方法 Teaching Methods
将采用传统方式教授此课(版书，课堂讨论，作业，课外答疑，闭卷考试)
The course will be taught in the standard way (“chalk and board”, in-class discussion, homework, office
hours, closed-book exams).
10.
教学内容 Course Contents
Section 1
Introduction
Section 2
Vector Spaces
Section 3
Forms
Section 4
Geometries
Section 5
Combinatorial Applications (e.g. The finite field Kakeya problem)
Section 6
Turan numbers of bipartite graphs
Section 7
Erdos-Ko-Rado type theorems
Section 8
MDS codes
Section 9
Spread and ovoids in polar spaces
Section 10
Generalized quadrangles/polygons
Section 11
Incidence graphs of generalized polygons
Section 12
LDPC codes from geometries
Section 13
Section 14
11.
课程考核 Course Assessment
作业（40%）+期末考试（60%）
Assignment (40%) + Final Exam (60%)
12.
教材及其它参考资料 Textbook and Supplementary Readings
1. Finite geometry and combinatorial applications, by Simeon Ball
2. Polynomial Methods in Combinatorics, by Larry Guth
3
. Incidence Geometry, Eric Moorhouse
