"More concretely," the authors explain, "it is the controlled manipulation of mathematical formulas, using a collection of techniques for solving problems."

    Never again will you order the Poisson Distribution in a French restaurant!This updated version features all new material.

    More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills. This Schaum's Outline gives you:  Practice problems with full explanations that reinforce knowledge Coverage of the most up-to-date developments in your course field In-depth review of practices and applications Fully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time-and get your best test scores! Schaum's Outlines-Problem Solved.

    The novel approach taken here banishes determinants to the end of the book and focuses on the central goal of linear algebra: understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presents - without having defined determinants - a clean proof that every linear operator on a finite-dimensional complex vector space (or an odd-dimensional real vector space) has an eigenvalue. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. This second edition includes a new section on orthogonal projections and minimization problems. The sections on self-adjoint operators, normal operators, and the spectral theorem have been rewritten. New examples and new exercises have been added, several proofs have been simplified, and hundreds of minor improvements have been made throughout the text.

    His aim is to present calculus as the first real encounter with mathematics: it is the place to learn how logical reasoning combined with fundamental concepts can be developed into a rigorous mathematical theory rather than a bunch of tools and techniques learned by rote. Since analysis is a subject students traditionally find difficult to grasp, Spivak provides leisurely explanations, a profusion of examples, a wide range of exercises and plenty of illustrations in an easy-going approach that enlightens difficult concepts and rewards effort. Calculus will continue to be regarded as a modern classic, ideal for honours students and mathematics majors, who seek an alternative to doorstop textbooks on calculus, and the more formidable introductions to real analysis.

    This long-awaited revision contains changes throughout the text. There are new implementations of most of the major programming systems in the book, including the interpreters and compilers, and the authors have incorporated many small changes that reflect their experience teaching the course at MIT since the first edition was published. A new theme has been introduced that emphasizes the central role played by different approaches to dealing with time in computational models: objects with state, concurrent programming, functional programming and lazy evaluation, and nondeterministic programming. There are new example sections on higher-order procedures in graphics and on applications of stream processing in numerical programming, and many new exercises. In addition, all the programs have been reworked to run in any Scheme implementation that adheres to the IEEE standard.

    Working through the book you will develop an arsenal of techniques to help you unlock the meaning of definitions, theorems and proofs, solve problems, and write mathematics effectively. All the major methods of proof - direct method, cases, induction, contradiction and contrapositive - are featured. Concrete examples are used throughout, and you'll get plenty of practice on topics common to many courses such as divisors, Euclidean algorithms, modular arithmetic, equivalence relations, and injectivity and surjectivity of functions. The material has been tested by real students over many years so all the essentials are covered. With over 300 exercises to help you test your progress, you'll soon learn how to think like a mathematician.

    . . Algebra's importance lies in the student's future. . . as essential preparation for the serious study of science, engineering, economics, or for more advanced types of mathematics. . . The primary importance of trigonometry is not in its applications to surveying and navigation, or in making computations about triangles, but rather in the mathematical description of vibrations, rotations, and periodic phenomena of all kinds, including light, sound, alternating currents, and the orbits of the planets around the sun. In this brief, clearly written book, the essentials of geometry, algebra, and trigonometry are pulled together into three complementary and convenient small packages, providing an excellent preview and review for anyone who wishes to prepare to master calculus with a minimum of misunderstanding and wasted time and effort. Students and other readers will find here all they need to pull them through.

    The material is arranged chronologically beginning with archaic origins and covers Egyptian, Mesopotamian, Greek, Chinese, Indian, Arabic and European contributions done to the nineteenth century and present day. There are revised references and bibliographies and revised and expanded chapters on the nineteeth and twentieth centuries.

    As well as lucid descriptions of all the topics and many worked examples, it contains over 800 exercises. New stand-alone chapters give a systematic account of the 'special functions' of physical science, cover an extended range of practical applications of complex variables, and give an introduction to quantum operators. Further tabulations, of relevance in statistics and numerical integration, have been added. In this edition, half of the exercises are provided with hints and answers and, in a separate manual available to both students and their teachers, complete worked solutions. The remaining exercises have no hints, answers or worked solutions and can be used for unaided homework; full solutions are available to instructors on a password-protected web site, www.cambridge.org/9780521679718.

    It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity. Topics include sets, logic, counting, methods of conditional and non-conditional proof, disproof, induction, relations, functions and infinite cardinality.

    These themes include mathematical reasoning, combinatorial analysis, discrete structures, algorithmic thinking, and enhanced problem-solving skills through modeling. Its intent is to demonstrate the relevance and practicality of discrete mathematics to all students. The Fifth Edition includes a more thorough and linear presentation of logic, proof types and proof writing, and mathematical reasoning. This enhanced coverage will provide students with a solid understanding of the material as it relates to their immediate field of study and other relevant subjects. The inclusion of applications and examples to key topics has been significantly addressed to add clarity to every subject. True to the Fourth Edition, the text-specific web site supplements the subject matter in meaningful ways, offering additional material for students and instructors. Discrete math is an active subject with new discoveries made every year. The continual growth and updates to the web site reflect the active nature of the topics being discussed. The book is appropriate for a one- or two-term introductory discrete mathematics course to be taken by students in a wide variety of majors, including computer science, mathematics, and engineering. College Algebra is the only explicit prerequisite.

    By presenting actual experiences and analyzing them as they are described, the author conveys the developmental thought processes employed and shows a style of thinking that leads to successful results is something that can be learned. Along with spectacular successes, the author also conveys how failures contributed to shaping the thought processes. Provides the reader with a style of thinking that will enhance a person's ability to function as a problem-solver of complex technical issues. Consists of a collection of stories about the author's participation in significant discoveries, relating how those discoveries came about and, most importantly, provides analysis about the thought processes and reasoning that took place as the author and his associates progressed through engineering problems.

    . . Nothing less than a major contribution to the scientific culture of this world." — The New York Times Book ReviewThis major survey of mathematics, featuring the work of 18 outstanding Russian mathematicians and including material on both elementary and advanced levels, encompasses 20 prime subject areas in mathematics in terms of their simple origins and their subsequent sophisticated developement. As Professor Morris Kline of New York University noted, "This unique work presents the amazing panorama of mathematics proper. It is the best answer in print to what mathematics contains both on the elementary and advanced levels."Beginning with an overview and analysis of mathematics, the first of three major divisions of the book progresses to an exploration of analytic geometry, algebra, and ordinary differential equations. The second part introduces partial differential equations, along with theories of curves and surfaces, the calculus of variations, and functions of a complex variable. It furthur examines prime numbers, the theory of probability, approximations, and the role of computers in mathematics. The theory of functions of a real variable opens the final section, followed by discussions of linear algebra and nonEuclidian geometry, topology, functional analysis, and groups and other algebraic systems.Thorough, coherent explanations of each topic are further augumented by numerous illustrative figures, and every chapter concludes with a suggested reading list. Formerly issued as a three-volume set, this mathematical masterpiece is now available in a convenient and modestly priced one-volume edition, perfect for study or reference."This is a masterful English translation of a stupendous and formidable mathematical masterpiece . . ." — Social Science

    Just about everyone has at least heard of Albert Einstein's formulation of 1905, which came into the world as something of an afterthought. But far fewer can explain his insightful linkage of energy to mass. David Bodanis offers an easily grasped gloss on the equation. Mass, he writes, "is simply the ultimate type of condensed or concentrated energy," whereas energy "is what billows out as an alternate form of mass under the right circumstances." Just what those circumstances are occupies much of Bodanis's book, which pays homage to Einstein and, just as important, to predecessors such as Maxwell, Faraday, and Lavoisier, who are not as well known as Einstein today. Balancing writerly energy and scholarly weight, Bodanis offers a primer in modern physics and cosmology, explaining that the universe today is an expression of mass that will, in some vastly distant future, one day slide back to the energy side of the equation, replacing the "dominion of matter" with "a great stillness"--a vision that is at once lovely and profoundly frightening. Without sliding into easy psychobiography, Bodanis explores other circumstances as well; namely, Einstein's background and character, which combined with a sterling intelligence to afford him an idiosyncratic view of the way things work--a view that would change the world. --Gregory McNamee