Discrete Mathematics and Applications
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Discrete Mathematics and Applications

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Description

This book is intended for a one-semester course in discrete mathematics. Such a course is typically taken by mathematics, mathematics education, and computer science majors, usually in their sophomore year. Calculus is not a prerequisite to use this book. Part one focuses on how to write proofs, then moves on to topics in number theory, employing set theory in the process. Part two focuses on computations, combinatorics, graph theory, trees, and algorithms.
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Product details

  • Hardback | 916 pages
  • 178 x 254 x 50.8mm | 2,064g
  • Productivity Press
  • Portland, United States
  • English
  • New edition
  • 2nd New edition
  • 196 Tables, black and white; 893 Illustrations, black and white
  • 1498730655
  • 9781498730655
  • 1,545,278

Table of contents

I Proofs


Logic and Sets


Statement Forms and Logical Equivalences


Set Notation


Quantifiers


Set Operations and Identities


Valid Arguments


Basic Proof Writing


Direct Demonstration


General Demonstration (Part 1)


General Demonstration (Part 2)


Indirect Arguments


Splitting into Cases


Elementary Number Theory


Divisors


Well-Ordering, Division, and Codes


Euclid's Algorithm and Lemma


Rational and Irrational Numbers


Modular Arithmetic and Encryption


Indexed by Integers


Sequences, Indexing, and Recursion


Sigma Notation


Mathematical Induction, An Introduction


Induction and Summations


Strong Induction


The Binomial Theorem


Relations


General Relations


Special Relations on Sets


Basics of Functions


Special Functions


General Set Constructions


Cardinality


II Combinatorics


Basic Counting


The Multiplication Principle


Permutations and Combinations


Addition and Subtraction


Probability


Applications of Combinations


Correcting for Overcounting


More Counting


Inclusion-Exclusion


Multinomial Coecients


Generating Functions


Counting Orbits


Combinatorial Arguments


Basic Graph Theory


Motivation and Introduction


Special Graphs


Matrices


Isomorphisms


Invariants


Directed Graphs and Markov Chains


Graph Properties


Connectivity


Euler Circuits


Hamiltonian Cycles


Planar Graphs


Chromatic Number


Trees and Algorithms


Trees


Search Trees


Weighted Trees


Analysis of Algorithms (Part 1)


Analysis of Algorithms (Part 2)


A Assumed Properties of Z and R


B Pseudocode


C Answers to Selected Exercises
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