Discrete Mathematics Proofs Structures and Applications 1st Edition by Rowan Garnier, John Taylor 9781439812808 1439812802

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Product details:

ISBN 10: 1439812802

ISBN 13: 9781439812808

Author: Rowan Garnier; John Taylor

Offers an exposition of discrete mathematics, including the core mathematical foundation of computer science. This book includes a section on the formal proof of the validity of arguments in propositional logic and predicate logic. It also contains a chapter on elementary number theory and congruences.

Table of contents:

Part I: Logic
Chapter 1: Propositions and Truth Values
Chapter 2: Logical Connectives and Truth Tables
Chapter 3: Tautologies and Contradictions
Chapter 4: Logical Equivalence and Logical Implication
Chapter 5: The Algebra of Propositions
Chapter 6: Arguments
Chapter 7: Formal Proof of the Validity of Arguments
Chapter 8: Predicate Logic
Chapter 9: Arguments in Predicate Logic

Part II: Mathematical Proof
Chapter 10: The Nature of Proof
Chapter 11: Axioms and Axiom Systems
Chapter 12: Methods of Proof
Chapter 13: Mathematical Induction

Part III: Sets
Chapter 14: Sets and Membership
Chapter 15: Subsets
Chapter 16: Operations on Sets
Chapter 17: Counting Techniques
Chapter 18: The Algebra of Sets
Chapter 19: Families of Sets
Chapter 20: The Cartesian Product
Chapter 21: Types and Typed Set Theory

Part IV: Relations
Chapter 22: Relations and Their Representations
Chapter 23: Properties of Relations
Chapter 24: Intersections and Unions of Relations
Chapter 25: Equivalence Relations and Partitions
Chapter 26: Order Relations
Chapter 27: Hasse Diagrams
Chapter 28: Application: Relational Databases

Part V: Functions
Chapter 29: Definitions and Examples
Chapter 30: Composite Functions
Chapter 31: Injections and Surjections
Chapter 32: Bijections and Inverse Functions
Chapter 33: More on Cardinality
Chapter 34: Databases: Functional Dependence and Normal Forms

Part VI: Matrix Algebra
Chapter 35: Introduction
Chapter 36: Some Special Matrices
Chapter 37: Operations on Matrices
Chapter 38: Elementary Matrices
Chapter 39: The Inverse of a Matrix

Part VII: Systems of Linear Equations
Chapter 40: Introduction
Chapter 41: Matrix Inverse Method
Chapter 42: Gauss–Jordan Elimination
Chapter 43: Gaussian Elimination

Part VIII: Algebraic Structures
Chapter 44: Binary Operations and Their Properties
Chapter 45: Algebraic Structures
Chapter 46: More about Groups
Chapter 47: Some Families of Groups
Chapter 48: Substructures
Chapter 49: Morphisms
Chapter 50: Group Codes

Part IX: Introduction to Number Theory
Chapter 51: Divisibility
Chapter 52: Prime Numbers
Chapter 53: Linear Congruences
Chapter 54: Groups in Modular Arithmetic
Chapter 55: Public Key Cryptography

Part X: Boolean Algebra
Chapter 56: Introduction
Chapter 57: Properties of Boolean Algebras
Chapter 58: Boolean Functions
Chapter 59: Switching Circuits
Chapter 60: Logic Networks
Chapter 61: Minimization of Boolean Expressions

Part XI: Graph Theory
Chapter 62: Definitions and Examples
Chapter 63: Paths and Cycles
Chapter 64: Isomorphism of Graphs
Chapter 65: Trees
Chapter 66: Planar Graphs
Chapter 67: Directed Graphs
Chapter 68: Applications of Graph Theory
Chapter 69: Introduction
Chapter 70: Rooted Trees
Chapter 71: Sorting
Chapter 72: Searching Strategies
Chapter 73: Weighted Graphs
Chapter 74: The Shortest Path and Traveling Salesman Problems
Chapter 75: Networks and Flows

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Tags: Rowan Garnier, John Taylor, Discrete, Mathematics