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· 분류 : 외국도서 > 컴퓨터 > 운영체제(OS) > 일반
· ISBN : 9781439812808
· 쪽수 : 843쪽
· 출판일 : 2009-12-01
목차
Logic
Propositions and Truth Values
Logical Connectives and Truth Tables
Tautologies and Contradictions
Logical Equivalence and Logical Implication
The Algebra of Propositions
Arguments
Formal Proof of the Validity of Arguments
Predicate Logic
Arguments in Predicate Logic
Mathematical Proof
The Nature of Proof
Axioms and Axiom Systems
Methods of Proof
Mathematical Induction
Sets
Sets and Membership
Subsets
Operations on Sets
Counting Techniques
The Algebra of Sets
Families of Sets
The Cartesian Product
Types and Typed Set Theory
Relations
Relations and Their Representations
Properties of Relations
Intersections and Unions of Relations
Equivalence Relations and Partitions
Order Relations
Hasse Diagrams
Application: Relational Databases
Functions
Definitions and Examples
Composite Functions
Injections and Surjections
Bijections and Inverse Functions
More on Cardinality
Databases: Functional Dependence and Normal Forms
Matrix Algebra
Introduction
Some Special Matrices
Operations on Matrices
Elementary Matrices
The Inverse of a Matrix
Systems of Linear Equations
Introduction
Matrix Inverse Method
Gauss?Jordan Elimination
Gaussian Elimination
Algebraic Structures
Binary Operations and Their Properties
Algebraic Structures
More about Groups
Some Families of Groups
Substructures
Morphisms
Group Codes
Introduction to Number Theory
Divisibility
Prime Numbers
Linear Congruences
Groups in Modular Arithmetic
Public Key Cryptography
Boolean Algebra
Introduction
Properties of Boolean Algebras
Boolean Functions
Switching Circuits
Logic Networks
Minimization of Boolean Expressions
Graph Theory
Definitions and Examples
Paths and Cycles
Isomorphism of Graphs
Trees
Planar Graphs
Directed Graphs
Applications of Graph Theory
Introduction
Rooted Trees
Sorting
Searching Strategies
Weighted Graphs
The Shortest Path and Traveling Salesman Problems
Networks and Flows
References and Further Reading
Hints and Solutions to Selected Exercises
Index
