1.  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

2.  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.  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

4.  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

5.  6.Functions  one to one, onto, one-to-one correspondence  Composite functions and Inverse functions  Cardinality,  0.  Theorems, examples, and exercises

6.  II Combinatorics  1. Pigeonhole principle  Pigeon and pigeonholes  example ， exercise

7.  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

8.  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

9.  Graph theory  P115,4.2;P123 4.3;P290 8.1