Summary: Susanna Epp's DISCRETE MATHEMATICS, THIRD 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 concept...show mores 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.
NEW!-Coverage of new topics suggested by the IEEE/CS and ACM joint committee on computing curriculum, including probability axioms and expected value, conditional probability and Bayes theorem, modular arithmetic, the Chinese remainder theorem, and RSA cryptography. Regular expressions and finite-state automata are also included, as recommended in by the ACM and IEEE-CS joint committee on the software engineering curriculum.
A flow-chart shows the prerequisite relations among the chapters, and most sections are divided into subsections so that instructors can easily tailor the book to meet the needs of their courses.
NEW!-Applications involving the Internet.
NEW!-Refinements to the exposition and exercises for improved pedagogy.
NEW!-Many new problems.
Every concept in the book is applied in at least one and often many different ways to motivate students. Eleven sections are explicitly devoted to applications to computer science, and additional applications are included in most sections.
A spiral approach, in which a number of concepts appear in increasingly more sophisticated forms, provides useful review and develops mathematical maturity in natural stages.
The book presents the unspoken logic and reasoning that underlie mathematical thought in a way that can be understood by typical freshman and sophomore college students.
In showing students how to discover and construct proofs and disproofs, Epp describes the kind of approaches that mathematicians use when confronting challenging problems in their own research.
A wealth of examples written in problem-solution form, and a large variety of exercises at all levels of difficulty are provided.
Logical Form and Logical Equivalence. Conditional Statements. Valid and Invalid Arguments. Application: Digital Logic Circuits. Application: Number Systems and Circuits for Addition.
2. THE LOGIC OF QUANTIFIED STATEMENTS.
Introduction to Predicates and Quantified Statements I. Introduction to Predicates and Quantified Statements II. Statements Containing Multiple Quantifiers. Arguments with Quantified Statements.
3. 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. Direct Proof and Counterexample V: Floor and Ceiling. Indirect Argument: Contradiction and Contraposition. Two Classical Theorems. Application: Algorithms.
4. SEQUENCES AND MATHEMATICAL INDUCTION.
Sequences. Mathematical Induction I. Mathematical Induction II. Strong Mathematical Induction and the Well-Ordering Principle. Application: Correctness of Algorithms.
5. SET THEORY.
Basic Definitions of Set Theory. Properties of Sets. Disproofs, Algebraic Proofs, and Boolean Algebras. Russell''s Paradox and the Halting Problem.
6. COUNTING AND PROBABILITY.
Introduction. Possibility Trees and the Multiplication Rule. Counting Elements of Disjoint Sets: The Addition Rule. Counting Subsets of a Set: Combinations. R-Combinations with Repetition Allowed. The Algebra of Combinations. The Binomial Theorem. Probability Axioms and Expected Value. Conditional Probability, Bayes'' Formula, and Independent Events.
Functions Defined on General Sets. One-to-One and Onto, Inverse Functions. Application: The Pigeonhole Principle. Composition of Functions. Cardinality with Applications to Computability.
Recursively Defined Sequences. Solving Recurrence Relations by Iteration. Second-Order Linear Homogeneous Recurrence Relations with Constant Coefficients. General Recursive Definitions.
9. THE EFFICIENCY OF ALGORITHMS.
Real-Valued Functions of a Real Variable and Their Graphs. O-, Omega-, and Theta-Notations. Application: Efficiency of Algorithms I. Exponential and Logarithmic Functions: Graphs and Orders. Application: Efficiency of Algorithms II.
Relations on Sets. Reflexivity, Symmetry, and Transitivity. Equivalence Relations. Modular Arithmetic with Applications to Cryptography. Partial Order Relations.
11. GRAPHS AND TREES.
Graphs: An Introduction. Paths and Circuits. Matrix Representations of Graphs. Isomorphisms of Graphs. Trees. Spanning Trees.
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