This book is for a basic introduction to the prerequisite mathematics needed for college level math and science courses.

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.

Presents a detailed and critical examination of the available conceptions of set and proposes a novel version.

Mathematical logic grew out of philosophical questions regarding the foundations of mathematics, but logic has now outgrown its philosophical roots, and has become an integral part of mathematics in general. This book is designed for students who plan to specialize in logic, as well as for those who are interested in the applications of logic to other areas of mathematics. Used as a text, it could form the basis of a beginning graduate-level course. There are three main chapters: Set Theory, Model Theory, and Recursion Theory. The Set Theory chapter describes the set-theoretic foundations of all of mathematics, based on the ZFC axioms. It also covers technical results about the Axiom of Choice, well-orderings, and the theory of uncountable cardinals. The Model Theory chapter discusses predicate logic and formal proofs, and covers the Completeness, Compactness, and Lowenheim-Skolem Theorems, elementary submodels, model completeness, and applications to algebra. This chapter also continues the foundational issues begun in the set theory chapter. Mathematics can now be viewed as formal proofs from ZFC. Also, model theory leads to models of set theory. This includes a discussion of absoluteness, and an analysis of models such as H( ) and R( ). The Recursion Theory chapter develops some basic facts about computable functions, and uses them to prove a number of results of foundational importance; in particular, Church's theorem on the undecidability of logical consequence, the incompleteness theorems of Godel, and Tarski's theorem on the non-definability of truth.

Foundations of Mathematics offers the university student or interested reader a unique reference book by covering the basics of algebra, trigonometry, geometry, and calculus. There are many instances in the book to demonstrate the interplay and interconnectedness of these topics. The book presents definitions and examples throughout for clear, easy learning. Numerous exercises are included at the ends of the chapters, and readers are encouraged to complete all of them as an essential part of working through the book. It offers a unique experience for readers to understand different areas of mathematics in one clear, concise text. Instructors’ resources are available upon adoption. Features: •Covers the basics of algebra, trigonometry, geometry, and calculus •Includes all of the mathematics needed to learn calculus •Demonstrates the interplay and interconnectedness of these topics •Uses numerous examples and exercises to reinforce concepts

Explains geometric theories and shows many examples.

This text spans a large range of mathematics, from basic algebra to calculus and Fourier transforms. Its tutorial style bridges the gap between school and university while its conciseness provides a useful reference for the professional.

For courses in Basic Mathematics. The Martin-Gay principle: Every student can succeed Elayn Martin-Gay's student-centric approach is woven seamlessly throughout her texts and MyLab(TM) courses, giving students the optimal amount of support through effective video resources, an accessible writing style, and study skills support built into the program. Elayn's legacy of innovations that support student success include Chapter Test Prep videos and a Video Organizer note-taking guide. Expanded resources in the latest revision bring even more updates to her program, all shaped by her focus on the student - a perspective that has made her course materials beloved by students and instructors alike. The Martin-Gay series offers trusted content written by a preeminent author-educator, tightly integrated with the #1 choice in digital learning: MyLab Math. Also available with MyLab Math MyLab(TM) Math is the teaching and learning platform that empowers you to reach every student. By combining trusted author content with digital tools and a flexible platform, MyLab Math personalizes the learning experience and improves results for each student. Learn more about MyLab Math.

NOTE: Before purchasing, check with your instructor to ensure you select the correct ISBN. Several versions of Pearson's MyLab & Mastering products exist for each title, and registrations are not transferable. To register for and use Pearson's MyLab & Mastering products, you may also need a Course ID, which your instructor will provide. Used books, rentals, and purchases made outside of Pearson If purchasing or renting from companies other than Pearson, the access codes for Pearson's MyLab & Mastering products may not be included, may be incorrect, or may be previously redeemed. Check with the seller before completing your purchase. "This course is ideal for accelerating students as an alternative to the traditional developmental math sequence and preparing them for a college-level statistics, liberal arts math, or STEM-prep course." "MyMathLab for Foundations for Mathematical Reasoning" is the first in a series of MyMathLab courses built to support the New Mathways Project developed by the Charles A. Dana Center. The New Mathways Project embodies the Dana Center s vision for a systemic approach to improving student success and completion through implementation of processes, strategies, and structures built around three mathematics pathways and a supporting student success course. "Foundations for Mathematical Reasoning" is the common starting point for all three mathematics pathways and is designed to build the mathematical skills and understanding necessaryfor success in a quantitative literacy, statistics, or algebra course. "