Discrete mathematics Discrete i.e. no continuousSet theory, .ppt

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, Newtons 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 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 每周一交作业，作业成绩占总成绩的10%； 平时不定期的进行小测验，占总成绩的20%； 期中考试成绩占总成绩的20%；期终考试成绩占总成绩的50% 1.离散数学及其应用（英文版·第5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·第4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 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. Cantors 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 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 in