复旦大学：《离散数学 Discrete Mathematics（上）》英文课件（赵一鸣）30/30

I Introduction to Set Theory ◆1. Sets and subsets Representation of set: o Listing elements Set builder notion, Recursive definition ◆∈,c,C ◆P(A) 2. Operations on Sets o Operations and their properties ◆A=?B ◆AB, and bca ◆ Properties o Theorems, examples, and exercises

 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  Properties  Theorems, examples, and exercises

+3. Relations and Properties of relations ◆ reflexive, irreflexive o symmetric, asymmetric ,antisymmetric ◆ Transitive Closures of relations ◆r(R),s(R),t(R)=? Theorems, examples, and exercises 44. Operations on relations Inverse relation, Composition o 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

紫◆5. Equivalence relations o Equivalence relations ◆ equivalence class .6.Partial order relations and Hasse Diagrams Extremal elements of partially ordered sets: maximal element. minimal element o greatest element, least element o upper bound, lower bound least upper bound, greatest lower bound o Theorems examples. and exercises

 5. Equivalence Relations  Equivalence Relations  equivalence class  6.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

◆7. Functions ◆ one to one,onto, o one-to-one correspondence 4 Composite functions and Inverse functions ◆ Cardinality,Np o Theorems, examples, and exercises

 7.Functions  one to one, onto,  one-to-one correspondence  Composite functions and Inverse functions Cardinality, 0 .  Theorems, examples, and exercises

tII Combinatorics 1. Pigeonhole principle Pigeon and pigeonholes example, exercise

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