Discrete Mathematics with Applications

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Oscar Levin is an Associate Professor at the University of Northern Colorado in the School of Mathematical Sciences. He has taught mathematics at the college level for over 10 years and has received multiple teaching awards. He received his Ph.D. in mathematics from the University of Connecticut in 2009. It's in its third edition and the author mentions making corrections and thanking others for pointing out errors. I didn't find any errors so I would imagine the book is highly accurate. Direct Proof and Counterexample I: Introduction. Direct Proof and Counterexample II: Writing Advice. Direct Proof and Counterexample III: Rational Numbers. Direct Proof and Counterexample IV: Divisibility. Direct Proof and Counterexample V: Division into Cases and the Quotient-Remainder Theorem. Direct Proof and Counterexample VI: Floor and Ceiling. Indirect Argument: Contradiction and Contraposition. Indirect Argument: Two Famous Theorems. Application: Algorithms.

This textbook, “Discrete Mathematics: An Open Introduction”, by Oscar Levin, provides a good overview of topics in Discrete Mathematics. The primary focus of this text is not to provide a rigorous mathematical foundation for Computer Science students; instead, it is targeted towards first and second year undergraduate math majors who will go on to teach middle school and high school mathematics. Discrete Math has applications in many areas including computer science, economics, etc. The topics covered in this book have book have been in existence for a long time and I cannot imagine them to become isolate ever.Flexible organization, allowing instructors the ability to mix core and optional topics easily to suit a wide variety of discrete math course syllabi and topic focus. This is the part I very much like in the book. One can easily move from one part of the book to another. The figures drawn to illustrate graphs etc., are appropriate.

The text has a comprehensive index, and has both a PDF version and a well-designed interactive online format, with a contents tab and expandable solutions (allowing students to attempt a question before unveiling the solution). Set Theory: Definitions and the Element Method of Proof. Properties of Sets. Disproofs and Algebraic Proofs. Boolean Algebras, Russell’s Paradox, and the Halting Problem.The book’s design and interface is well-thought out, particularly the interactive online version, which is cleanly designed, non-distracting, functional and approachable, with simple and straight-forward navigational controls. Some modern textbooks have many more pictures, sidebars, and bells and whistles. This book does not have a lot of that, but the limited numbers of illustrations are clear and do not confuse the reader. The links from the index are excellent. This reviewer tends to think that a lot of textbooks simply distract the reader with all of the pictures and sidebars. The book has a simple clear interface. It is not a fancy book and it does not need to be. I agree with the other reviewers. The textbook is as culturally relevant as a math textbook could be. There are just a few images in the text. Graphics used to illustrate set operations and graph theory concepts are well laid out. Some tree and Venn diagrams might be improved. 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.