Discrete Mathematics Introduction to Mathematical Reasoning

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  • Edition: 1st
  • Format: Hardcover
  • Copyright: 2011-02-07
  • Publisher: Cengage Learning

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Susanna Epp's DISCRETE MATHEMATICS: AN INTRODUCTION TO MATHEMATICAL REASONING provides a clear introduction to discrete mathematics and mathematical reasoning in a compact form that focuses on core topics. Renowned for her lucid, accessible prose, Epp explains complex, abstract concepts with clarity and precision, helping students develop the ability to think abstractly as they study each topic. In doing so, the book provides students with a strong foundation both for computer science and for other upper-level mathematics courses.

Table of Contents

Speaking Mathematically
The Language of Sets
The Language of Relations and Functions
The Logic of Compound Statements
Logical Form and Logical Equivalence
Conditional Statements
Valid and Invalid Arguments
The Logic of Quantified Statements
Predicates and Quantified Statements I
Predicates and Quantified Statements II
Statements with Multiple Quantifiers
Arguments with Quantified Statements
Elementary Number Theory and Methods of Proof
Direct Proof and Counterexample I: Introduction
Direct Proof and Counterexample II: Rational Numbers
Direct Proof and Counterexample III: Divisibility
Direct Proof and Counterexample IV: Division into Cases and the Quotient-Remainder Theorem
Indirect Argument: Contradiction and Contraposition
Indirect Argument: Two Classical Theorems
Sequences, Mathematical Induction, and Recursion
Mathematical Induction I
MathematicalInduction II
Strong Mathematical Induction and the Well-Ordering Principle
Defining Sequences Recursively
Solving Recurrence Relations by Iteration
Set Theory
Set Theory: Definitions and the Element Method of Proof
Set Identities
Disproofs and Algebraic Proofs
Boolean Algebras and Russell's Paradox
Properties of Functions
Functions Defined on General Sets
One-to-one, Onto, and Inverse Functions
Composition of Functions
Cardinality and Sizes of Infinity
Properties of Relations
Relations on Sets
Reflexivity, Symmetry, and Transitivity
Equivalence Relations
Modular Arithmetic and Zn
The Euclidean Algorithm and Applications
Counting and Probability
The Multiplication Rule
Counting Elements of Disjoint Sets: The Addition Rule
The Pigeonhole Principle
Counting Subsets of a Set: Combinations
Pascal's Formula and the Binomial Theorem
Graphs and Trees
Graphs: An Introduction
Trails, Paths, and Circuits
Matrix Representations of Graphs
Isomorphisms of Graphs
Trees: Examples and Basic Properties
Rooted Trees
Table of Contents provided by Publisher. All Rights Reserved.

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