Discrete Mathematics for New Technology by R Garnier and Taylor is a comprehensive textbook designed for students and professionals who are studying discrete mathematics and its applications in technology and engineering. The book covers the fundamental concepts of discrete mathematics, including graph theory, combinatorics, algorithms, and coding theory, among others.
This textbook is notable for its focus on real-world applications of discrete mathematics, which helps students to understand the relevance of the subject to their future careers. The authors, R Garnier and Taylor, are experts in the field of mathematics and technology, and they have written this book in a clear and concise manner that makes the material easy to understand and follow.
TABLE OF CONTENTS
Chapter 1 Logic
- Propositions and Truth Values
- Logical Connectives and Truth Tables
- Tautologies and Contradictions
- Logical Equivalance and Logical Implication
- The Algebra of Propositions
- More about Conditionals
- Arguments
- Predicate Logic
- Arguments in Predicate Logic
Chapter 2 Mathematical Proof
The Nature of Proof
Axioms and Axiom System
Methods of Proof
Mathematical Induction
Chapter3 Sets
Sets and Membership
Subsets
Operations on Sets
Counting Techniques
The Algebra of Sets
Families of Sets
The Cartesian product
Types and Types Set Theory
Chapter4 Relations
Relations and Their Representations
Properties of Relations
Intersections and Unions of Relations
Order Relations
Hasse Diagrams
Application: Relational Database
Chapter 5 Functions
Definitions and Examples
Composite Functions
Injections and Surjections
Bijections and Inverse Functions
More on Cardinality
Database: Functional Dependence and Normal Forms
Chapter 6 Matrix Algebra
Introduction
Some Special Matrices
Operations on Matrices
Elementry Matrices
The Inverse of a Matrix
Chapter7 Systems of Linear Equations
Matrix Inverse Method
Gauss-Jordan Elimination
Gaussian Elimination
Chapter8 Algebraic Structures
Binary Operations and their Properties
Algebraic Structures
More about Groups
Some Families of Groups
Substructures
Morphisms
Group Codes
Chapter9 Boolean Algebra
Introduction
Properties of Boolean Algebras
Boolean Functions
Switching Circuits
Logic Networks
Minimization of Boolean Expressions
Chapter10 Graph Theory
Definitions and Examples
Paths and Cycles
Isomorphism of Graphs
Trees
Planar Graphs
Directed Graphs
Chapter11 Applications of Graph Theory
Introduction
Rooted Trees
Sorting
Searching Strategies
Weighted Graphs
The Shortest Path and Travelling Salesman Problems
Networks and Flows
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Discrete Mathematics for New Technology covers a wide range of topics, including graph theory, trees, networks, coding theory, and algorithms. Additionally, the book includes numerous examples and exercises, which provide opportunities for students to practice what they have learned and apply the concepts covered in the book to new problems.
The book is designed to be used as a course textbook or as a reference for professionals who are interested in learning about discrete mathematics. Whether you are a student just starting out in your mathematical journey or a professional looking to refresh your knowledge of discrete mathematics, Discrete Mathematics for New Technology by R Garnier and Taylor is an excellent resource that is sure to meet your needs.
Overall, Discrete Mathematics for New Technology is a comprehensive textbook that provides a solid foundation in discrete mathematics and its applications in technology and engineering. With its clear writing style, focus on real-world applications, and comprehensive coverage of the subject, this textbook is sure to provide a valuable resource for anyone interested in learning about discrete mathematics.
