Engineering professor Barbara Oakley knows firsthand how it feels to struggle with math. She flunked her way through high school math and science courses, before enlisting in the army immediately after graduation. When she saw how her lack of mathematical and technical savvy severely limited her options—both to rise in the military and to explore other careers—she returned to school with a newfound determination to re-tool her brain to master the very subjects that had given her so much trouble throughout her entire life. In A Mind for Numbers, Dr. Oakley lets us in on the secrets to effectively learning math and science—secrets that even dedicated and successful students wish they’d known earlier. Contrary to popular belief, math requires creative, as well as analytical, thinking. Most people think that there’s only one way to do a problem, when in actuality, there are often a number of different solutions—you just need the creativity to see them. For example, there are more than three hundred different known proofs of the Pythagorean Theorem. In short, studying a problem in a laser-focused way until you reach a solution is not an effective way to learn math. Rather, it involves taking the time to step away from a problem and allow the more relaxed and creative part of the brain to take over. A Mind for Numbers shows us that we all have what it takes to excel in math, and learning it is not as painful as some might think!

    With problems and solutions. Includes 99 illustrations.

    Written by two of the field's true pioneers, Spacetime Physics can extend and enhance coverage of specialty relativity in the classroom. This thoroughly up-to-date, highly accessible overview covers microgravity, collider accelerators, satellite probes, neutron detectors, radioastronomy, and pulsars.  The chapter on general relativity with new material on gravity waves, black holes, and cosmology.

    The Clay Mathematics Institute is offering a prize of $1 million to anyone who can discover a general solution to the problem. In this book, Avner Ash and Robert Gross guide readers through the mathematics they need to understand this captivating problem.The key to the conjecture lies in elliptic curves, which are cubic equations in two variables. These equations may appear simple, yet they arise from some very deep--and often very mystifying--mathematical ideas. Using only basic algebra and calculus while presenting numerous eye-opening examples, Ash and Gross make these ideas accessible to general readers, and in the process venture to the very frontiers of modern mathematics. Along the way, they give an informative and entertaining introduction to some of the most profound discoveries of the last three centuries in algebraic geometry, abstract algebra, and number theory. They demonstrate how mathematics grows more abstract to tackle ever more challenging problems, and how each new generation of mathematicians builds on the accomplishments of those who preceded them. Ash and Gross fully explain how the Birch and Swinnerton-Dyer Conjecture sheds light on the number theory of elliptic curves, and how it provides a beautiful and startling connection between two very different objects arising from an elliptic curve, one based on calculus, the other on algebra.

    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.

    Copy veteran Constance Hale is on a mission to make creative communication, both the lyrical and the unlawful, an option for everyone.With its crisp, witty tone, Sin and Syntax covers grammar’s ground rules while revealing countless unconventional syntax secrets (such as how to use—Gasp!—interjections or when to pepper your prose with slang) that make for sinfully good writing. Discover how to:*Distinguish between words that are “pearls” and words that are “potatoes”* Avoid “couch potato thinking” and “commitment phobia” when choosing verbs* Use literary devices such as onomatopoeia, alliteration, and metaphor (and understand what you're doing)Everyone needs to know how to write stylish prose—students, professionals, and seasoned writers alike. Whether you’re writing to sell, shock, or just sing, Sin and Syntax is the guide you need to improve your command of the English language.

    Get ready to amaze your friends—and yourself—with incredible calculations you never thought you could master, as renowned “mathemagician” Arthur Benjamin shares his techniques for lightning-quick calculations and amazing number tricks. This book will teach you to do math in your head faster than you ever thought possible, dramatically improve your memory for numbers, and—maybe for the first time—make mathematics fun.Yes, even you can learn to do seemingly complex equations in your head; all you need to learn are a few tricks. You’ll be able to quickly multiply and divide triple digits, compute with fractions, and determine squares, cubes, and roots without blinking an eye. No matter what your age or current math ability, Secrets of Mental Math will allow you to perform fantastic feats of the mind effortlessly. This is the math they never taught you in school.Also available as an eBook

    Calculus is not a prerequisite, although examples and exercises using very basic calculus are included (labeled Calculus Required.) The most technology-friendly text on the market, Introductory Linear Algebra is also the most flexible. By omitting certain sections, instructors can cover the essentials of linear algebra (including eigenvalues and eigenvectors), to show how the computer is used, and to introduce applications of linear algebra in a one-semester course.

    This introductory text is suitable for use in a course on the subject or for self-study, featuring broad coverage and a readable exposition, with many examples and exercises. The four main chapters present the basics: fundamental group and covering spaces, homology and cohomology, higher homotopy groups, and homotopy theory generally. The author emphasizes the geometric aspects of the subject, which helps students gain intuition. A unique feature is the inclusion of many optional topics not usually part of a first course due to time constraints: Bockstein and transfer homomorphisms, direct and inverse limits, H-spaces and Hopf algebras, the Brown representability theorem, the James reduced product, the Dold-Thom theorem, and Steenrod squares and powers.

    But in spirit, the title is apt, as the book does cover a much broader range of topics than a typical introductory book on mathematical statistics. This book is for people who want to learn probability and statistics quickly. It is suitable for graduate or advanced undergraduate students in computer science, mathematics, statistics, and related disciplines. The book includes modern topics like nonparametric curve estimation, bootstrapping, and clas- sification, topics that are usually relegated to follow-up courses. The reader is presumed to know calculus and a little linear algebra. No previous knowledge of probability and statistics is required. Statistics, data mining, and machine learning are all concerned with collecting and analyzing data. For some time, statistics research was con- ducted in statistics departments while data mining and machine learning re- search was conducted in computer science departments. Statisticians thought that computer scientists were reinventing the wheel. Computer scientists thought that statistical theory didn't apply to their problems. Things are changing. Statisticians now recognize that computer scientists are making novel contributions while computer scientists now recognize the generality of statistical theory and methodology. Clever data mining algo- rithms are more scalable than statisticians ever thought possible. Formal sta- tistical theory is more pervasive than computer scientists had realized.

    The stories she loves most follow other organic patterns found in nature―spirals, meanders, and explosions, among others. Alison’s manifesto for new modes of narrative will appeal to serious readers and writers alike. As Jane Alison writes in the introduction to her insightful and appealing book about the craft of writing: “For centuries there’s been one path through fiction we’re most likely to travel―one we’re actually told to follow―and that’s the dramatic arc: a situation arises, grows tense, reaches a peak, subsides. . . . But: something that swells and tautens until climax, then collapses? Bit masculo-sexual, no? So many other patterns run through nature, tracing other deep motions in life. Why not draw on them, too?”W. G. Sebald’s The Emigrants was the first novel to show Alison how forward momentum can be created by way of pattern, rather than the traditional arc―or, in nature, wave. Other writers of nonlinear prose considered in her “museum of specimens” include Nicholson Baker, Anne Carson, Marguerite Duras, Jamaica Kincaid, Clarice Lispector, Gabriel García Márquez, Susan Minot, David Mitchell, Caryl Phillips, and Mary Robison.Meander, Spiral, Explode is a singular and brilliant elucidation of literary strategies that also brings high spirits and wit to its original conclusions. It is a liberating manifesto that says, Let’s leave the outdated modes behind and, in thinking of new modes, bring feeling back to experimentation. It will appeal to serious readers and writers alike.

    We spin fantasies. We devour novels, films, and plays. Even sporting events and criminal trials unfold as narratives. Yet the world of story has long remained an undiscovered and unmapped country. It’s easy to say that humans are “wired” for story, but why?In this delightful and original book, Jonathan Gottschall offers the first unified theory of storytelling. He argues that stories help us navigate life’s complex social problems—just as flight simulators prepare pilots for difficult situations. Storytelling has evolved, like other behaviors, to ensure our survival.Drawing on the latest research in neuroscience, psychology, and evolutionary biology, Gottschall tells us what it means to be a storytelling animal. Did you know that the more absorbed you are in a story, the more it changes your behavior? That all children act out the same kinds of stories, whether they grow up in a slum or a suburb? That people who read more fiction are more empathetic?Of course, our story instinct has a darker side. It makes us vulnerable to conspiracy theories, advertisements, and narratives about ourselves that are more “truthy” than true. National myths can also be terribly dangerous: Hitler’s ambitions were partly fueled by a story.But as Gottschall shows in this remarkable book, stories can also change the world for the better. Most successful stories are moral—they teach us how to live, whether explicitly or implicitly, and bind us together around common values. We know we are master shapers of story. The Storytelling Animal finally reveals how stories shape us.

    W. R. Dedekind. The first presents Dedekind's theory of the irrational number-the Dedekind cut idea-perhaps the most famous of several such theories created in the 19th century to give a precise meaning to irrational numbers, which had been used on an intuitive basis since Greek times. This paper provided a purely arithmetic and perfectly rigorous foundation for the irrational numbers and thereby a rigorous meaning of continuity in analysis.The second essay is an attempt to give a logical basis for transfinite numbers and properties of the natural numbers. It examines the notion of natural numbers, the distinction between finite and transfinite (infinite) whole numbers, and the logical validity of the type of proof called mathematical or complete induction.The contents of these essays belong to the foundations of mathematics and will be welcomed by those who are prepared to look into the somewhat subtle meanings of the elements of our number system. As a major work of an important mathematician, the book deserves a place in the personal library of every practicing mathematician and every teacher and historian of mathematics. Authorized translations by "Vooster " V. Beman.

    The approach taken here uses elementary versions of modern methods found in sophisticated mathematics. The formal prerequisites include only a term of linear algebra, a nodding acquaintance with the notation of set theory, and a respectable first-year calculus course (one which at least mentions the least upper bound (sup) and greatest lower bound (inf) of a set of real numbers). Beyond this a certain (perhaps latent) rapport with abstract mathematics will be found almost essential.

    This free Kindle book features interviews, essays, excerpts, and other fun extras about the year’s top 20 titles: Donna Tartt talks about her eating habits while writing The Goldfinch; Khaled Hosseini’s publicist discusses what it’s like to be on a national tour with him; David Finkel discusses the emotional impact following the 2-16 infantry battalion in Thank You for Your Service; and much more.