DISCRETE MATHEMATICS WITH APPLICATIONS, 5th Edition, Metric Edition explains complex, abstract concepts with clarity and precision and provides a strong foundation for computer science and upper-level mathematics courses of the computer age. Author Susanna Epp 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 today's science and technology.

This book introduces the mathematics that supports advanced computer programming and the analysis of algorithms. The primary aim of its well-known authors is to provide a solid and relevant base of mathematical skills - the skills needed to solve complex problems, to evaluate horrendous sums, and to discover subtle patterns in data. It is an indispensable text and reference not only for computer scientists - the authors themselves rely heavily on it! - but for serious users of mathematics in virtually every discipline. Concrete Mathematics is a blending of CONtinuous and disCRETE mathematics. "More concretely," the authors explain, "it is the controlled manipulation of mathematical formulas, using a collection of techniques for solving problems." The subject matter is primarily an expansion of the Mathematical Preliminaries section in Knuth's classic Art of Computer Programming, but the style of presentation is more leisurely, and individual topics are covered more deeply. Several new topics have been added, and the most significant ideas have been traced to their historical roots. The book includes more than 500 exercises, divided into six categories. Complete answers are provided for all exercises, except research problems, making the book particularly valuable for self-study. Major topics include: Sums Recurrences Integer functions Elementary number theory Binomial coefficients Generating functions Discrete probability Asymptotic methods This second edition includes important new material about mechanical summation. In response to the widespread use of the first edition as a reference book, the bibliography and index have also been expanded, and additional nontrivial improvements can be found on almost every page. Readers will appreciate the informal style of Concrete Mathematics. Particularly enjoyable are the marginal graffiti contributed by students who have taken courses based on this material. The authors want to convey not only the importance of the techniques presented, but some of the fun in learning and using them.

"Approaching Precalculus Mathematics Discretely introduces concepts of discrete mathematics through the computer, making them easier to teach and more fun to learn. Philip Lewis shows how this can be accomplished using the Logo language to apply and explore much of the material in standard high school advanced algebra and precalculus programs. He develops sophisticated programming techniques in conjunction with mathematical concepts that make the book a model for teachers looking for ways to integrate computers into the mathematics curriculum. The opening chapter introduces the use of Logo to express a variety of basic mathematical functions. The next four chapters broaden the discussion to include elementary vector operations, in the plane and linear transformations and matrix operations defined as vector-valid functions. Chapter 4 applies the theory of linear transformations to the mapping of two dimensional geometric objects drawn on the computer screen. Chapter 5 takes up mathematical induction and recursion. This allows the transformation theory of chapter 4 to be extended to wire frame objects in space that are projected on the computer screen. Chapter 7 constructs a graphing utility that is used in subsequent chapters to examine the graphs of a variety of functions and to introduce the concept of a limit. This extends to an intuitive introduction to slope and the derivative in order to establish a territory for the calculus. The two chapters that follow examine the traditional cyclic functions from a graphic and transformational point of view. The book concludes by outlining explorations of topics from earlier chapters. Philip G. Lewis teaches mathematics and computer science atLincoln Sudbury Regional High School in Sudbury Massachusetts. "Approaching Precalculus Mathematics Discretely" is included in the series Exploring with Logo, edited by E. Paul Goldenberg.

Offers ways of presenting and developing three topics emphasised in Principles and Standards for School Mathematics: counting, vertex-edge graphs and iterative and recursive processes.

Discrete mathematics is the basis of much of computer science, from algorithms and automata theory to combinatorics and graph theory. Essential Discrete Mathematics for Computer Science aims to teach mathematical reasoning as well as concepts and skills by stressing the art of proof. It is fully illustrated in color, and each chapter includes a concise summary as well as a set of exercises.

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"Precalculus is intended for college-level precalculus students. Since precalculus courses vary from one institution to the next, we have attempted to meet the needs of as broad an audience as possible, including all of the content that might be covered in any particular course. The result is a comprehensive book that covers more ground than an instructor could likely cover in a typical one- or two-semester course; but instructors should find, almost without fail, that the topics they wish to include in their syllabus are covered in the text. Many chapters of OpenStax College Precalculus are suitable for other freshman and sophomore math courses such as College Algebra and Trigonometry; however, instructors of those courses might need to supplement or adjust the material. OpenStax will also be releasing College Algebra and Algebra and trigonometry titles tailored to the particular scope, sequence, and pedagogy of those courses."--Preface.

Stein/Drysdale/Bogart's Discrete Mathematics for Computer Scientists is ideal for computer science students taking the discrete math course. Written specifically for computer science students, this unique textbook directly addresses their needs by providing a foundation in discrete math while using motivating, relevant CS applications. This text takes an active-learning approach where activities are presented as exercises and the material is then fleshed out through explanations and extensions of the exercises.