复旦大学赵一鸣离散数学一.ppt

复旦大学赵一鸣离散数学一.pptDiscrete mathematics
Discrete . 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
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%
（英文版·第5版）
作者：Kenneth 著出版社：***出版社
（英文版·第4版）——经典原版书库
作者：（美）布鲁迪（Brualdi,.） 著出版社：***出版社
3,离散数学暨组合数学（英文影印版）
Discrete Mathematics with Combinatorics 
James ,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.
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
Chapter 1 Basic Concepts of Sets
Sets and Subsets
What are Sets?
A collec