An Introduction to Discrete Mathematics

By Steven Roman

An Introduction to Discrete Mathematics, Second Edition by Steven Roman is once again available, now from Innovative Textbooks. This text was the leading seller in earlier days before it got unceremoniously kicked from publisher to publisher, in some cases without the author's knowledge! Nevertheless, it is still a perfect text for a course in elementary discrete mathematics. (A permutation in 1995 is still a permutation today.)

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Please note that the book is a spiral bound (so it will lay flat) photocopy of the Second Edition, published originally by HBJ. Any pages that contain color that is important for the exposition are copied in color. The remaining pages are black and white.

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Table of Contents

• Sets, Functions and Proof Techniques
  • The Language of Sets
  • One-to-one Correspondences
  • Countable and Uncountable Sets (Optional)
  • Functions
  • Inductive Proofs and Inductive Definitions
  • Proof by Contradiction
• Logic and Logic Circuits
  • Statements, Connectives and Symbolic Language
  • Truth Tables, Tautologies and Contradictions
  • Logical Equivalence
  • Valid Arguments
  • Boolean Functions and Disjunctive Normal Form
  • Logic Circuits
  • Karnaugh Maps
• Relations on Sets
  • Relations
  • Properties of Relations
  • Equivalence Relations
  • Partially Ordered Sets
  • More on Partially Ordered Sets; Maximal and Minimal Elements and Topological Sorting
  • Order Isomorphisms
• Combinatorics‐The Art of Counting
  • Introduction
  • The Multiplication Rule
  • The Pigeonhole Principle
  • Permutations
  • More on Permutations
  • Combinations
  • Properties of the Binomial Coefficients
  • The Multinomial Coefficient
  • An Introduction to Recurrence Relations
  • Second Order Linear Homogeneous Recurrence Relations with Constant Coefficients
  • Second Order Linear Nonhomogeneous Recurrence Relations with Constant Coefficients
  • Generating Functions and Recurrence Relations
• More on Combinatorics
  • Permutations with Repetitions
  • Combinations with Repetitions
  • Linear Equations with Unit Coefficients
  • Distributing Balls into Boxes
  • The Principle of Inclusion-Exclusion‐I
  • The Principle of Inclusion-Exclusion‐II
  • The Principle of Inclusion-Exclusion‐III
  • An Introduction to Probability
• An Introduction to Graph Theory
  • Introduction
  • paths and Connectedness
  • Eulerian and Hamiltonian Graphs
  • Graph Isomorphisms; Planar Graphs
  • Trees: The Depth First Search
  • Two Applications of Trees: Binary Search and Huffman Codes
  • Undirected Networks: The Minimal Spanning Tree Problem
  • Directed Graphs: Strong Connectivity
  • Directed Networks: The Shortest Path Problem
  • Finite State Machines