(eBook PDF) Discrete Mathematics with Applications 4th by Susanna – Digital Ebook – Instant Delivery Download

**Product details:**

- ISBN-10 : 0495391328
- ISBN-13 : 978-0495391326
- Author: Susanna S. Epp

Susanna Epp’s DISCRETE MATHEMATICS WITH APPLICATIONS, FOURTH EDITION provides a clear introduction to discrete mathematics. Renowned for her lucid, accessible prose, Epp explains complex, abstract concepts with clarity and precision. This book presents not only the major themes of discrete mathematics, but also the reasoning that underlies mathematical thought. Students develop the ability to think abstractly as they study the ideas of logic and proof. While learning about such concepts as logic circuits and computer addition, algorithm analysis, recursive thinking, computability, automata, cryptography, and combinatorics, students discover that the ideas of discrete mathematics underlie and are essential to the science and technology of the computer age. Overall, Epp’s emphasis on reasoning provides students with a strong foundation for computer science and upper-level mathematics courses.

**Table contents:**

Chapter 1: SPEAKING MATHEMATICALLY

1.1 Variables

1.2 The Language of Sets

1.3 The Language of Relations and Functions

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: Rational Numbers

4.3 Direct Proof and Counterexample III: Divisibility

4.4 Direct Proof and Counterexample IV: Division Into Cases and the Quotient-Remainder Theorem

4.5 Direct Proof and Counterexample V: Floor and Ceiling

4.6 Indirect Argument: Contradiction and Contraposition

4.7 Indirect Argument: Two Classical Theorems

4.8 Application: Algorithms

Chapter 5: SEQUENCES, MATHEMATICAL INDUCTION, AND RECURSION

5.1 Sequences

5.2 Mathematical Induction I

5.3 Mathematical Induction II

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, Algebraic Proofs, and Boolean Algebras

6.4 Boolean Algebras, Russell’s Paradox, and the Halting Problem

Chapter 7: FUNCTIONS

7.1 Functions Defined on General Sets

7.2 One-to-One and Onto, Inverse Functions

7.3 Composition of Functions

7.4 Cardinality with Applications to Computability

Chapter 8: 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

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: GRAPHS AND TREES

10.1 Graphs: Definitions and Basic Properties

10.2 Trails, Paths, and Circuits

10.3 Matrix Representations of Graphs

10.4 Isomorphisms of Graphs

10.5 Trees

10.6 Rooted Trees

10.7 Spanning Trees and Shortest Paths

Chapter 11: ANALYSIS OF ALGORITHM EFFICIENCY

11.1 Real-Valued Functions of a Real Variable and Their Graphs

11.2 O-, Ω-, and Θ-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

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