期中测验时间： 10 月 31 日上午 9 ： 40—11 ： 30 第一到第四章 即，集合，关系，函数，组合数学
Ⅰ Introduction to Set Theory 1. Sets and Subsets Representation of set: Listing elements, Set builder notion, Recursive definition , , P(A) 2. Operations on Sets Operations and their Properties A=?B A B, and B A Or Properties Theorems, examples, and exercises
3. Relations and Properties of relations reflexive,irreflexive symmetric, asymmetric,antisymmetric Transitive Closures of Relations r(R),s(R),t(R)=? Theorems, examples, and exercises 4. Operations on Relations Inverse relation, Composition Theorems, examples, and exercises
5. Equivalence Relation and Partial order relations Equivalence Relation equivalence class Partial order relations and Hasse Diagrams Extremal elements of partially ordered sets: maximal element, minimal element greatest element, least element upper bound, lower bound least upper bound, greatest lower bound Theorems, examples, and exercises
6.Functions one to one, onto, one-to-one correspondence Composite functions and Inverse functions Cardinality, 0. Theorems, examples, and exercises
II Combinatorics 1. Pigeonhole principle Pigeon and pigeonholes example ， exercise
2. Permutations and Combinations Permutations of sets, Combinations of sets circular permutation Permutations and Combinations of multisets Formulae inclusion-exclusion principle generating functions integral solutions of the equation
Applications of Inclusion-Exclusion principle example,exercise Applications generating functions and Exponential generating functions e x =1+x+x 2 /2!+…+x n /n!+…; x+x 2 /2!+…+x n /n!+…=e x -1; e -x =1-x+x 2 /2!+…+(-1) n x n /n!+…; 1+x 2 /2!+…+x 2n /(2n)!+…=(e x +e -x )/2; x+x 3 /3!+…+x 2n+1 /(2n+1)!+…=(e x -e -x )/2; examples, and exercises 3. recurrence relation Using Characteristic roots to solve recurrence relations Using Generating functions to solve recurrence relations examples, and exercises
Graph theory P115,4.2;P ;P