His Contemporary Abstract Algebra, 6/e, includes challenging topics in abstract algebra as well as numerous figures, tables, photographs, charts, biographies, computer exercises, and suggested readings that give the subject a current feel and makes the content interesting and relevant for students.

    The Calculus Lifesaver provides students with the essential tools they need not only to learn calculus, but to excel at it.All of the material in this user-friendly study guide has been proven to get results. The book arose from Adrian Banner's popular calculus review course at Princeton University, which he developed especially for students who are motivated to earn A's but get only average grades on exams. The complete course will be available for free on the Web in a series of videotaped lectures. This study guide works as a supplement to any single-variable calculus course or textbook. Coupled with a selection of exercises, the book can also be used as a textbook in its own right. The style is informal, non-intimidating, and even entertaining, without sacrificing comprehensiveness. The author elaborates standard course material with scores of detailed examples that treat the reader to an inner monologue--the train of thought students should be following in order to solve the problem--providing the necessary reasoning as well as the solution. The book's emphasis is on building problem-solving skills. Examples range from easy to difficult and illustrate the in-depth presentation of theory.The Calculus Lifesaver combines ease of use and readability with the depth of content and mathematical rigor of the best calculus textbooks. It is an indispensable volume for any student seeking to master calculus.Serves as a companion to any single-variable calculus textbookInformal, entertaining, and not intimidatingInformative videos that follow the book--a full forty-eight hours of Banner's Princeton calculus-review course--is available at Adrian Banner lecturesMore than 475 examples (ranging from easy to hard) provide step-by-step reasoningTheorems and methods justified and connections made to actual practiceDifficult topics such as improper integrals and infinite series covered in detailTried and tested by students taking freshman calculus

    This work includes differential forms and the elegant forms of Maxwell's equations, and a chapter on probability and statistics. It also illustrates and proves mathematical relations.

    Over 100 problems at ends of chapters. Answers in back of book. 1962 edition.

    Subsequent sections deal with integrating factors; dilution and accretion problems; linearization of first order systems; Laplace Transforms; Newton's Interpolation Formulas, more.

    But that doesn’t mean that mathematics isn’t a crucial tool for understanding love. Love, like most things in life, is full of patterns. And mathematics is ultimately the study of patterns—from predicting the weather to the fluctuations of the stock market, the movement of planets or the growth of cities. These patterns twist and turn and warp and evolve just as the rituals of love do. In The Mathematics of Love, Dr. Hannah Fry takes the reader on a fascinating journey through the patterns that define our love lives, applying mathematical formulas to the most common yet complex questions pertaining to love: What’s the chance of finding love? What’s the probability that it will last? How do online dating algorithms work, exactly? Can game theory help us decide who to approach in a bar? At what point in your dating life should you settle down? From evaluating the best strategies for online dating to defining the nebulous concept of beauty, Dr. Fry proves—with great insight, wit, and fun—that math is a surprisingly useful tool to negotiate the complicated, often baffling, sometimes infuriating, always interesting, mysteries of love.

    Since its first appearance in 1956 there have been eight editions as well as translations from the original Russian into Ukrainian, Estonian, Lettish, and Lithuanian. Almost a million copies of the Russian version alone have been sold.Part of the reason for the book's success is its marvelously varied assortment of brainteasers ranging from simple "catch" riddles to difficult problems (none, however, requiring advanced mathematics). Many of the puzzles will be new to Western readers, while some familiar problems have been clothed in new forms. Often the puzzles are presented in the form of charming stories that provide non-Russian readers with valuable insights into contemporary Russian life and customs. In addition, Martin Gardner, former editor of the Mathematical Games Department, Scientific American, has clarified and simplified the book to make it as easy as possible for an English-reading public to understand and enjoy. He has been careful, moreover, to retain nearly all the freshness, warmth, and humor of the original.Lavishly illustrated with over 400 clear diagrams and amusing sketches, this inexpensive edition of the first English translation will offer weeks or even months of stimulating entertainment. It belongs in the library of every puzzlist or lover of recreational mathematics.

    The new edition provides invitations - not requirements - to use technology, as well as new conceptual problems, and new projects that focus on writing and working in teams.

    For the media, statistics are routinely 'damning', 'horrifying', or, occasionally, 'encouraging'. Yet, for all their ubiquity, most of us really don't know what to make of statistics. Exploring the history, mathematics, philosophy and practical use of statistics, Eileen Magnello - accompanied by Bill Mayblin's intelligent graphic illustration - traces the rise of statistics from the ancient Babylonians, Egyptians and Chinese, to the censuses of Romans and the Greeks, and the modern emergence of the term itself in Europe. She explores the 'vital statistics' of, in particular, William Farr, and the mathematical statistics of Karl Pearson and R.A. Fisher.She even tells how knowledge of statistics can prolong one's life, as it did for evolutionary biologist Stephen Jay Gould, given eight months to live after a cancer diagnoses in 1982 - and he lived until 2002. This title offers an enjoyable, surprise-filled tour through a subject that is both fascinating and crucial to understanding our world.

    Taken literally, it implies that there are many universes “parallel” to the one we see around us. This multiplicity of universes, according to Deutsch, turns out to be the key to achieving a new worldview, one which synthesizes the theories of evolution, computation, and knowledge with quantum physics. Considered jointly, these four strands of explanation reveal a unified fabric of reality that is both objective and comprehensible, the subject of this daring, challenging book. The Fabric of Reality explains and connects many topics at the leading edge of current research and thinking, such as quantum computers (which work by effectively collaborating with their counterparts in other universes), the physics of time travel, the comprehensibility of nature and the physical limits of virtual reality, the significance of human life, and the ultimate fate of the universe. Here, for scientist and layperson alike, for philosopher, science-fiction reader, biologist, and computer expert, is a startlingly complete and rational synthesis of disciplines, and a new, optimistic message about existence.

    Cox and Forshaw's contention? There is no need for quantum mechanics to be viewed this way. There is a lot of mileage in the 'weirdness' of the quantum world, and it often leads to confusion and, frankly, bad science. The Quantum Universe cuts through the Wu Li and asks what observations of the natural world made it necessary, how it was constructed, and why we are confident that, for all its apparent strangeness, it is a good theory.The quantum mechanics of The Quantum Universe provide a concrete model of nature that is comparable in its essence to Newton’s laws of motion, Maxwell’s theory of electricity and magnetism, and Einstein’s theory of relativity.

    Full of insights, arguments and philosophical perspectives, the book covers an amazing array of topics. Beginning in antiquity with Democritus, it progresses through logic and set theory, computability and complexity theory, quantum computing, cryptography, the information content of quantum states and the interpretation of quantum mechanics. There are also extended discussions about time travel, Newcomb's Paradox, the anthropic principle and the views of Roger Penrose. Aaronson's informal style makes this fascinating book accessible to readers with scientific backgrounds, as well as students and researchers working in physics, computer science, mathematics and philosophy.

    In studying number theory from such a perspective, mathematics majors are spared repetition and provided with new insights, while other students benefit from the consequent simplicity of the proofs for many theorems.Among the topics covered in this accessible, carefully designed introduction are multiplicativity-divisibility, including the fundamental theorem of arithmetic, combinatorial and computational number theory, congruences, arithmetic functions, primitive roots and prime numbers. Later chapters offer lucid treatments of quadratic congruences, additivity (including partition theory) and geometric number theory.Of particular importance in this text is the author's emphasis on the value of numerical examples in number theory and the role of computers in obtaining such examples. Exercises provide opportunities for constructing numerical tables with or without a computer. Students can then derive conjectures from such numerical tables, after which relevant theorems will seem natural and well-motivated..

    Drawing heavily on the author's own real-world experiences, the book stresses design and analysis. Coverage is divided into two parts, the first being a general guide to techniques for the design and analysis of computer algorithms. The second is a reference section, which includes a catalog of the 75 most important algorithmic problems. By browsing this catalog, readers can quickly identify what the problem they have encountered is called, what is known about it, and how they should proceed if they need to solve it. This book is ideal for the working professional who uses algorithms on a daily basis and has need for a handy reference. This work can also readily be used in an upper-division course or as a student reference guide. THE ALGORITHM DESIGN MANUAL comes with a CD-ROM that contains: * a complete hypertext version of the full printed book. * the source code and URLs for all cited implementations. * over 30 hours of audio lectures on the design and analysis of algorithms are provided, all keyed to on-line lecture notes.

    It reveals the attraction that has drawn leading mathematicians and amateurs alike to number theory over the course of history.