 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
 ⅠIntroduction 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
 ex=1+x+x2/2!+…+xn/n!+…;
 x+x2/2!+…+xn/n!+…=ex-1;
 e-x=1-x+x2/2!+…+(-1)nxn/n!+…;
 1+x2/2!+…+x2n/(2n)!+…=(ex+e-x)/2;
 x+x3/3!+…+x2n+1/(2n+1)!+…=(ex-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;P123 4.3;P290 8.1