复旦大学：《离散数学》PPT教学课件（赵一鸣）01/28

Discrete mathematics Discrete ie no continuous Set theory, Combinatorics, Graphs, Modern Algebra(Abstract algebra, Algebraic structures), Logic, classic probability, number theory, Automata and Formal Languages, Computability and decidability etc

Discrete mathematics Discrete i.e. no continuous Set theory, Combinatorics, Graphs, Modern Algebra(Abstract algebra, Algebraic structures), Logic, classic probability, number theory, Automata and Formal Languages, Computability and decidability etc

Before the 18th century, Discrete, quantity and space astronomy, physics Example: planetary orbital, Newton 's laws in Three Dimensions continuous mathematics: calculus Equations of Mathematical Physics, Functions of Real Variable Functions of complex variable Discrete ? stagnancy

Before the 18th century, Discrete， quantity and space astronomy, physics Example: planetary orbital, Newton's Laws in Three Dimensions continuous mathematics: calculus, Equations of Mathematical Physics, Functions of Real Variable,Functions of complex Variable Discrete ? stagnancy

in the thirties of the twentieth century Turing Machines Finite Discrete Data Structures and Algorithm Design Database Compilers Design and Analysis of Algorithms Computer Networks Software information security and cryptography the theory of computation New generation computers

in the thirties of the twentieth century, Turing Machines Finite Discrete Data Structures and Algorithm Design Database Compilers Design and Analysis of Algorithms Computer Networks Software information security and cryptography the theory of computation New generation computers

Set theory Introductory Combinatorics, Graphs, Algebtaic structures, ogIc This term: Set theory, Introductory Combinatorics Graphs, Algebtaic structures(Group, Ring, Field) Next term: Algebtaic structures(Lattices and Boolean Algebras) ogIc

Set theory, Introductory Combinatorics, Graphs, Algebtaic structures, Logic. This term: Set theory, Introductory Combinatorics , Graphs, Algebtaic structures(Group,Ring，Field). Next term: Algebtaic structures(Lattices and Boolean Algebras), Logic

每周三交作业,作业成绩占总成绩的15%; 平时不定期的进行小测验,占总成绩的 15 期中考试成绩占总成绩的20%;期终考试成绩 占总成绩的50% zhym@fudanedu.cn 张宓13212010027 fudan,edu,cn BBS id: abchjsabc软件楼1039 杨侃10302010007 fudan edu. cn

每周三交作业，作业成绩占总成绩的15%； 平时不定期的进行小测验，占总成绩的 15%； 期中考试成绩占总成绩的20%；期终考试成绩 占总成绩的50% zhym@fudan.edu.cn 张宓 13212010027@fudan.edu.cn BBS id:abchjsabc 软件楼1039 杨侃 10302010007@fudan.edu.cn

1离散数学及其应用(英文版) 作者: Kenneth H. rosen著出版社:机械工业出 版社 2组合数学(英文版)经典原版书库 作者:(美)布鲁迪( Brualdi,R.A.)著出版社: 机械工业出版社 3离散数学暨组合数学(英文影印版) Discrete Mathematics with Combinatorics James A Anderson, University of South Carolina, Spartanburg 大学计算机教育国外著名教材系列(影印 版)清华大学出版社

1.离散数学及其应用（英文版） 作者：Kenneth H.Rosen 著出版社：机械工业出 版社 2.组合数学（英文版）——经典原版书库 作者：（美）布鲁迪（Brualdi,R.A.） 著出版社： 机械工业出版社 3.离散数学暨组合数学（英文影印版） Discrete Mathematics with Combinatorics James A.Anderson,University of South Carolina,Spartanburg 大学计算机教育国外著名教材系列（影印 版） 清华大学出版社

I Introduction to Set Theory The objects of study of Set Theory are sets. As sets are fundamental objects that can be used to define all other concepts in mathematics. Georg Cantor(1845--1918) is a German mathematician Cantor's 1874 paper, On a Characteristic Property of All Real Algebraic Numbers marks the birth of set theory. paradox

ⅠIntroduction to Set Theory The objects of study of Set Theory are sets. As sets are fundamental objects that can be used to define all other concepts in mathematics. Georg Cantor(1845--1918) is a German mathematician. Cantor's 1874 paper, "On a Characteristic Property of All Real Algebraic Numbers", marks the birth of set theory. paradox

twentieth century axiomatic set theory naive set theory Concept Relation. function. cardinal number paradox

twentieth century axiomatic set theory naive set theory Concept Relation,function,cardinal number paradox

Chapter 1 Basic Concepts of Sets 1.1 Sets and subsets What are sets? A collection of different objects is called a set SA The individual objects in this collection are called the elements of the set We write“teA” to say that t is an element ofa, and we write“tgA” to say that t is not an element ofA

Chapter 1 Basic Concepts of Sets 1.1 Sets and Subsets What are Sets? A collection of different objects is called a set S,A The individual objects in this collection are called the elements of the set We write “tA” to say that t is an element of A, and We write “tA” to say that t is not an element of A

Example: The set of all integers, Z Then3∈Z,-8∈Z,6.5gZ These sets, each denoted using a boldface letter, play an important role in discrete mathematics: N=0, 1, 2,, the set of natural number FF(,2, -1, 0, 1, 2 ., the set of integers F=Z=1, 2, ., the set of positive integers Z=1, -2,, the set of negative integers Q={p/qlp∈Z2q∈Z,q≠0}, the set of rational numbers Q, the set of positive rational numbers Q, the set of negative rational numbers

Example:The set of all integers, Z. Then 3Z, -8Z, 6.5Z These sets, each denoted using a boldface letter, play an important role in discrete mathematics: N={0,1,2,…}, the set of natural number I=Z={…,-2,-1,0,1,2,…}, the set of integers I +=Z+={1,2,…}, the set of positive integers I -=Z-={-1,-2,…}, the set of negative integers Q={p/q|pZ,qZ,q0}, the set of rational numbers Q+ , the set of positive rational numbers Q- , the set of negative rational numbers