Discrete Mathematics for Computing 2nd Edition by Peter Grossman ISBN 0333981111 9780230216112

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ISBN 10: 0333981111 
ISBN 13: 9780230216112
Author: Peter Grossman

Written with a clear and informal style “Discrete Mathematics for Computing” is aimed at first-year undergraduate computing students with very little mathematical background. It is a low-level introductory text which takes the topics at a gentle pace, covering all the essential material that forms the background for studies in computing and information systems. This edition includes new sections on proof methods and recurrences, and the examples have been updated throughout to reflect the changes in computing since the first edition.

 Discrete Mathematics for Computing 2nd Table of contents:

Part 1: Fundamentals

1. Introduction to Discrete Mathematics

   • What is Discrete Mathematics?
   • Applications of Discrete Mathematics
   • Sets and Operations on Sets

2. Logic and Propositional Calculus

   • Propositions and Logical Connectives
   • Truth Tables and Logical Equivalence
   • Predicates and Quantifiers
   • Proofs and Proof Techniques
   • Logical Reasoning and Argumentation

3. Set Theory

   • Definitions and Notations
   • Set Operations and Properties
   • Cartesian Product
   • Venn Diagrams
   • Power Sets and Subsets
   • Relations and Functions

Part 2: Combinatorics

4. Combinatorics and Counting

   • Fundamental Counting Principle
   • Permutations and Combinations
   • Binomial Coefficients
   • Inclusion-Exclusion Principle
   • Pigeonhole Principle
   • Recursion and Recurrence Relations

5. Graph Theory

   • Graphs and Their Representations
   • Types of Graphs: Directed, Undirected, Weighted
   • Graph Traversal: BFS and DFS
   • Eulerian and Hamiltonian Paths
   • Connectivity and Bipartite Graphs
   • Graph Coloring and Planarity

6. Trees

   • Definitions and Properties of Trees
   • Binary Trees and Binary Search Trees
   • Tree Traversals: Pre-order, In-order, Post-order
   • Minimum Spanning Trees (MST)
   • Applications of Trees

Part 3: Algebraic Structures

7. Groups and Semigroups

   • Binary Operations and Closure Property
   • Groups and Subgroups
   • Group Homomorphisms and Isomorphisms
   • Cyclic Groups and Group Applications
   • Semigroups and Monoids

8. Rings and Fields

   • Introduction to Rings and Fields
   • Ring Properties and Operations
   • Polynomials and Their Operations
   • Field Extensions and Applications
   • Division Rings and Field Theory

Part 4: Functions and Relations

9. Functions

   • Types of Functions
   • Composition of Functions
   • Inverse Functions
   • Recursive Functions
   • Function Graphs and Applications

10. Relations

    • Properties of Relations: Reflexive, Symmetric, Transitive
    • Equivalence Relations and Partitions
    • Partial Orders and Lattices
    • Applications of Relations

Part 5: Logic and Automata

11. Boolean Algebra

    • Boolean Functions and Operations
    • Simplification of Boolean Expressions
    • Karnaugh Maps and Logic Gates
    • Boolean Algebra Applications in Computer Systems

12. Automata Theory

    • Finite Automata and Regular Languages
    • Deterministic and Nondeterministic Automata
    • Regular Expressions and Finite State Machines
    • Pushdown Automata and Context-Free Languages

Part 6: Graph Algorithms and Computational Complexity

13. Graph Algorithms

    • Shortest Path Algorithms (Dijkstra, Bellman-Ford)
    • Minimum Spanning Tree Algorithms (Kruskal’s, Prim’s)
    • Network Flow Algorithms
    • Topological Sorting

14. Computational Complexity

    • Time and Space Complexity
    • Big O Notation and Asymptotic Analysis
    • NP-Completeness and Reductions
    • P vs NP Problem
    • Introduction to the Theory of Computation

Part 7: Advanced Topics

15. Recursion and Recurrence Relations

    • Definition and Examples of Recursion
    • Solving Recurrence Relations
    • The Master Theorem
    • Applications of Recursion

16. Cryptography

    • Introduction to Cryptography
    • Classical Encryption Methods
    • Modern Cryptographic Techniques
    • Public-Key Cryptography
    • Cryptographic Protocols

17. Mathematical Logic

    • Propositional and Predicate Logic
    • Formal Proofs and Theorems
    • Formal Systems and Automata
    • Gödel’s Incompleteness Theorem

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