《組合數學》課程介紹
《組合數學》（又稱組合學）是計算機科學與技術專業的模塊限制選修課。它是為培養學生的組合思維能力而設置的，是一門研究離散對象的非常有趣和有用的課程。
通過本課程的學習，學生将做到：
1. 用容斥原理、生成函數和波利亞定理等求解線性（或圓）排列、集合分劃、整數分拆等計數問題；
2. 掌握遞推關系的計數方法以及常系數線性非齊次遞推關系的求解方法；
3. 了解組合數學的存在性證明和恒等式證明的基本方法。
4. 了解組合算法進行組合構造和最優化求解。
課程内容主要以計數為主，還涉及到組合數學的存在性、構造和優化問題。主要包括鴿巢原理、牛頓二項式定理、容斥原理、生成函數、遞推關系、波利亞定理等理論、方法及其應用，特殊計數序列，以及排列與組合的生成算法、組合優化算法。
通過本課程的學習，使學生系統地掌握組合數學的基本理論和方法，了解組合算法，培養學生的組合計算能力、發散思維能力，為計算機科學中其他課程的學習奠定必要的數學基礎。
The introduction of course –Combinatorics
Combinatorics is a foundational and limited-optional specialty course for undergraduates majoring in computer science and technology,; this course is a very interesting and useful course which involves discrete structures and builds up a good combinatorial thinking for computer science students.
Through this course, students will:
1. Use inclusion-exclusion principle, generating functions, Polya counting etc. to solve the problems such as permutation combination, set partition, integer partitions.
2. Master the counting technique of recurrence relations and how to solve the linear nonhomogeneous Recursive Relation with constant coefficients.
3. Learn the basics of existence proof and combinatorial identity proof.
4. Learn the constructive algorithms and optimization algorithms.
This course emphasizes on combinatorial counting techniques. The contents contain the Pigeonhole principle, the binomial coefficients, the inclusion-exclusion principle, recurrence relations, generating functions, Polya counting and their applications, special counting sequences, generating permutations and combinations and combinatorial optimization algorithms.
Study of this course makes students to grasp the basic theorems, principles and algorithms of Combinatorics, and improve the ability to combinatorial thinking and skill in solving the practical problems.
