An invitation to discrete mathematics 2nd Edition by Matousek J, Nesetril J ISBN 0198570430 9780198570431

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ISBN 10: 0198570430 
ISBN 13: 9780198570431
Author: Matousek J, Nesetril J

This book is a clear and self-contained introduction to discrete mathematics. Aimed mainly at undergraduate and early graduate students of mathematics and computer science. It is written with the goal of stimulating interest in mathematics and an active, problem-solving approach to the presented material. The reader is led to an understanding of the basic principles and methods of actually doing mathematics (and having fun at that). Being more narrowly focused than many discrete mathematics textbooks and treating selected topics in an unusual depth and from several points of view, the book reflects the conviction of the authors, active and internationally renowned mathematicians, that the most important gain from studying mathematics is the cultivation of clear and logical thinking and habits useful for attacking new problems. More than 400 enclosed exercises with a wide range of difficulty, many of them accompanied by hints for solution, support this approach to teaching. The readers will appreciate the lively and informal style of the text accompanied by more than 200 drawings and diagrams. Specialists in various parts of science with a basic mathematical education wishing to apply discrete mathematics in their field can use the book as a useful source, and even experts in combinatorics may occasionally learn from pointers to research literature or from presentations of recent results. Invitation to Discrete Mathematics should make a delightful reading both for beginners and for mathematical professionals

An invitation to discrete mathematics 2nd Table of contents:

Chapter 1: Introduction to Discrete Mathematics
1.1 What is Discrete Mathematics?
1.2 Applications in Computer Science and Beyond
1.3 Sets, Logic, and Proof Techniques

Chapter 2: Logic and Proofs
2.1 Propositional Logic
2.2 Predicate Logic
2.3 Methods of Proof: Direct, Contradiction, and Induction
2.4 Proof Strategies in Discrete Mathematics

Chapter 3: Sets, Functions, and Relations
3.1 Set Theory Basics
3.2 Functions: One-to-One, Onto, and Inverse
3.3 Relations and Their Properties
3.4 Equivalence Relations and Partial Orders

Chapter 4: Combinatorics
4.1 Counting Principles: Addition and Multiplication Rules
4.2 Permutations and Combinations
4.3 Pigeonhole Principle
4.4 Advanced Counting Techniques

Chapter 5: Recursion and Recurrence Relations
5.1 Introduction to Recursion
5.2 Solving Recurrence Relations
5.3 Generating Functions
5.4 Applications in Computer Science

Chapter 6: Graph Theory
6.1 Basic Concepts and Terminology
6.2 Special Graphs and Properties
6.3 Graph Algorithms: Paths, Cycles, and Connectivity
6.4 Trees and Applications

Chapter 7: Algebraic Structures
7.1 Groups, Rings, and Fields
7.2 Applications in Cryptography and Coding Theory
7.3 Boolean Algebra and Logic Circuits

Chapter 8: Probability in Discrete Mathematics
8.1 Basic Probability Principles
8.2 Conditional Probability and Independence
8.3 Discrete Random Variables
8.4 Applications in Algorithms and Networks

Chapter 9: Advanced Topics
9.1 Network Flows and Matching
9.2 Discrete Optimization
9.3 Complexity and Algorithm Analysis
9.4 Emerging Applications in Computer Science

Chapter 10: Conclusion and Further Reading
10.1 Summary of Key Concepts
10.2 Directions for Further Study
10.3 Suggested Exercises and Projects

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Tags: Matousek J, Nesetril J, discrete mathematics