Susanna Epp"s DISCRETE MATHEMATICS: AN INTRODUCTION TO MATHEMATICAL REASONING offers a clear advent to discrete mathematics and mathematical thinking in a compact form that concentrates on core topics. Renowned for her lucid, available pincreased, Epp explains facility, abstract ideas with clarity and precision, helping students construct the ability to think abstractly as they study each topic. In doing so, the book offers students through a strong foundation both for computer scientific research and for other upper-level math courses.
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Susanna S. Epp received her Ph.D. in 1968 from the College of Chicearlier, taught briefly at Boston College and the University of Illinois at Chicback, and also is presently Vincent DePaul Professor Emerita of Mathematical Sciences at DePaul College. After initial study in commutative algebra, she came to be interested in cognitive issues connected through teaching analytical thinking and also proof and publiburned a variety of posts related to this topic, one of which was favored for inclusion in The Best Writing on Mathematics 2012. She has actually spoken extensively on discrete math and arranged sessions at nationwide meetings on discrete math instruction. In enhancement to Discrete Mathematics via Applications and Discrete Mathematics: An Review to Mathematical Reasoning, she is co-author of Precalculus and Discrete Mathematics, which was occurred as component of the College of Chicearlier School Mathematics Project. The 3rd edition of Discrete Mathematics via Applications received a Texty Award for Textbook Excellence in June 2005. Epp co-organized an global symposium on teaching logical thinking, sponsored by the Institute for Discrete Mathematics and Theoretical Computer Science (DIMACS), and she was an associate editor of Mathematics Magazine from 1991 to 2001. Long active in the Mathematical Association of America (MAA), she is a co-author of the curricular guidelines for undergraduate mathematics programs: CUPM Curriculum Guide 2004. She received the Hay Award for Contributions to Mathematics Education in 2005 and the Award for Distinguiburned Teaching given by the Illinois Section of the MAA in 2010.
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Table of Contents
1. SPEAKING MATHEMATICALLY. Variables. The Language of Sets. The Language of Relations and Functions. 2. THE LOGIC OF COMPOUND STATEMENTS. Logical Form and Logical Equivalence. Conditional Statements. Valid and Invalid Arguments. 3. THE LOGIC OF QUANTIFIED STATEMENTS. Predicates and also Quantified Statements I. Predicates and also Quantified Statements II. Statements with Multiple Quantifiers. Arguments with Quantified Statements. 4. ELEMENTARY NUMBER THEORY AND METHODS OF PROOF. Direct Proof and also Counterexample I: Overview. Direct Proof and also Counterexample II: Rational Numbers. Direct Proof and Counterexample III: Divisibility. Direct Proof and Counterinstance IV: Division into Cases and also the Quotient-Remainder Theorem. Indirect Argument: Contradiction and Contraplace. Instraight Argument: Two Classical Theorems. 5. SEQUENCES, MATHEMATICAL INDUCTION, AND RECURSION. Sequences. Mathematical Induction I. Mathematical Induction II. Strong Mathematical Induction and also the Well-Ordering Principle. Defining Sequences Recursively. Solving Recurrence Relations by Iteration. 6. SET THEORY. Set Theory: Definitions and the Element Method of Proof. Set Identities. Disproofs and also Algebraic Proofs. Boolean Algebras and Russell"s Paradox. 7. PROPERTIES OF FUNCTIONS. Functions Defined on General Sets. One-to-one, Onto, and Inverse Functions. Composition of Functions. Cardinality and also Sizes of Infinity. 8. PROPERTIES OF RELATIONS. Relations on Sets. Reflexivity, Symmeattempt, and Transitivity. Equivalence Relations. Modular Arithmetic and Zn. The Euclidean Algorithm and also Applications. 9. COUNTING. Counting and also Probcapacity. The Multiplication Rule. Counting Elements of Disjoint Sets: The Addition Rule. The Pigeonhole Principle. Counting Subsets of a Set: Combicountries. Pascal"s Formula and also the Binomial Theorem. 10. GRAPHS AND TREES. Graphs: An Summary. Trails, Paths, and Circuits. Matrix Representations of Graphs. Isomorphisms of Graphs. Trees: Examples and Basic Properties. Rooted Trees.