Discrete Mathematics with Applications – Metric Version (5th Edition)


Download Discrete Mathematics with Applications – Metric Version (5th Edition) written by Susanna S. Epp in PDF format. This book is under the category Mathematics and bearing the isbn/isbn13 number 0357114086; 0357121465/9780357114087; 9780357121467. You may reffer the table below for additional details of the book.


Discrete Mathematics With Applications; fifth Edition; Metric Version; (PDF) explains complicated; summary ideas with readability and precision and provides a robust basis for laptop science and higher-stage arithmetic programs of the pc age. Expert writer Susanna Epp supplies not solely the main themes of discrete arithmetic; but in addition the reasoning that brings about mathematical thought. Students develop the ability to suppose abstractly as they examine the concepts of proof and logic. While studying about such ideas as algorithm evaluation; logic circuits and laptop addition; computability; automata; recursive considering; cryptography and combinatorics; college college students be taught that the concepts of discrete arithmetic underlie and are important to in the present day’s science and know-how.

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Additional information


Susanna S. Epp


CENGAGE Publishing; 5th Metric Edition




984 pages




0357114086; 0357121465


9780357114087; 9780357121467

Table of contents

Table of contents :
Chapter 1: Speaking Mathematically
1.1 Variables
1.2 The Language of Sets
1.3 The Language of Relations and Functions
1.4 The Language of Graphs
Chapter 2: The Logic of Compound Statements
2.1 Logical Form and Logical Equivalence
2.2 Conditional Statements
2.3 Valid and Invalid Arguments
2.4 Application: Digital Logic Circuits
2.5 Application: Number Systems and Circuits for Addition
Chapter 3: The Logic of Quantified Statements
3.1 Predicates and Quantified Statements I
3.2 Predicates and Quantified Statements II
3.3 Statements with Multiple Quantifiers
3.4 Arguments with Quantified Statements
Chapter 4: Elementary Number Theory and Methods of Proof
4.1 Direct Proof and Counterexample I: Introduction
4.2 Direct Proof and Counterexample II: Writing Advice
4.3 Direct Proof and Counterexample III: Rational Numbers
4.4 Direct Proof and Counterexample IV: Divisibility
4.5 Direct Proof and Counterexample V: Division into Cases and the Quotient-Remainder Theorem
4.6 Direct Proof and Counterexample VI: Floor and Ceiling
4.7 Indirect Argument: Contradiction and Contraposition
4.8 Indirect Argument: Two Famous Theorems
4.9 Application: The Handshake Theorem
4.10 Application: Algorithms
Chapter 5: Sequences, Mathematical Induction, and Recursion
5.1 Sequences
5.2 Mathematical Induction I: Proving Formulas
5.3 Mathematical Induction II: Applications
5.4 Strong Mathematical Induction and the Well-Ordering Principle for the Integers
5.5 Application: Correctness of Algorithms
5.6 Defining Sequences Recursively
5.7 Solving Recurrence Relations by Iteration
5.8 Second-Order Linear Homogeneous Recurrence Relations with Constant Coefficients
5.9 General Recursive Definitions and Structural Induction
Chapter 6: Set Theory
6.1 Set Theory: Definitions and the Element Method of Proof
6.2 Properties of Sets
6.3 Disproofs and Algebraic Proofs
6.4 Boolean Algebras, Russell’s Paradox, and the Halting Problem
Chapter 7: Properties of Functions
7.1 Functions Defined on General Sets
7.2 One-to-One, Onto, and Inverse Functions
7.3 Composition of Functions
7.4 Cardinality with Applications to Computability
Chapter 8: Properties of Relations
8.1 Relations on Sets
8.2 Reflexivity, Symmetry, and Transitivity
8.3 Equivalence Relations
8.4 Modular Arithmetic with Applications to Cryptography
8.5 Partial Order Relations
Chapter 9: Counting and Probability
9.1 Introduction to Probability
9.2 Possibility Trees and the Multiplication Rule
9.3 Counting Elements of Disjoint Sets: The Addition Rule
9.4 The Pigeonhole Principle
9.5 Counting Subsets of a Set: Combinations
9.6 r-Combinations with Repetition Allowed
9.7 Pascal’s Formula and the Binomial Theorem
9.8 Probability Axioms and Expected Value
9.9 Conditional Probability, Bayes’ Formula, and Independent Events
Chapter 10: Theory of Graphs and Trees
10.1 Trails, Paths, and Circuits
10.2 Matrix Representations of Graphs
10.3 Isomorphisms of Graphs
10.4 Trees: Examples and Basic Properties
10.5 Rooted Trees
10.6 Spanning Trees and a Shortest Path Algorithm
Chapter 11: Analysis of Algorithm Efficiency
11.1 Real-Valued Functions of a Real Variable and Their Graphs
11.2 Big-O, Big-Omega, and Big-Theta Notations
11.3 Application: Analysis of Algorithm Efficiency I
11.4 Exponential and Logarithmic Functions: Graphs and Orders
11.5 Application: Analysis of Algorithm Efficiency II
Chapter 12: Regular Expressions and Finite-State Automata
12.1 Formal Languages and Regular Expressions
12.2 Finite-State Automata
12.3 Simplifying Finite-State Automata
Appendix A: Properties of the Real Numbers
Appendix B: Solutions and Hints to Selected Exercises

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