Mathematics

From Eternity to Here: The Quest for the Ultimate Theory of Time

A rising star in theoretical physics offers his awesome vision of our universe and beyond, all beginning with a simple question: Why does time move forward?

Time moves forward, not backward-everyone knows you can't unscramble an egg. In the hands of one of today's hottest young physicists, that simple fact of breakfast becomes a doorway to understanding the Big Bang, the universe, and other universes, too. In From Eternity to Here, Sean Carroll argues that the arrow of time, pointing resolutely from the past to the future, owes its existence to conditions before the Big Bang itself-a period modern cosmology of which Einstein never dreamed. Increasingly, though, physicists are going out into realms that make the theory of relativity seem like child's play. Carroll's scenario is not only elegant, it's laid out in the same easy-to- understand language that has made his group blog, Cosmic Variance, the most popular physics blog on the Net.

From Eternity to Here uses ideas at the cutting edge of theoretical physics to explore how properties of spacetime before the Big Bang can explain the flow of time we experience in our everyday lives. Carroll suggests that we live in a baby universe, part of a large family of universes in which many of our siblings experience an arrow of time running in the opposite direction. It's an ambitious, fascinating picture of the universe on an ultra-large scale, one that will captivate fans of popular physics blockbusters like Elegant Universe and A Brief History of Time.

Cracking the AP Calculus AB & BC Exams, 2010 Edition (College Test Preparation)

If you are preparing for the AP Calculus AB or BC exam, you’ll find all the techniques and information you need in this guide. Cracking the AP Calculus AB & BC Exams, 2010 Edition comes from the test-prep experts at The Princeton Review, and it includes:

•5 full-length AP Calculus practice tests — 3 for Calculus AB and 2 for Calculus BC
•Comprehensive subject review covering the essential test topics: derivatives, logarithmic functions, integrals, and more
•Numerous problem sets for practice and review
•Detailed explanations for answers to all AP Calculus practice and test questions
•List of critical Calculus formulas and prerequisite math

The Visual Display of Quantitative Information, 2nd edition

The Visual Display of Quantitative Information, 2nd edition

A timeless classic in how complex information should be presented graphically. The Strunk & White of visual design. Should occupy a place of honor--within arm's reach--of everyone attempting to understand or depict numerical data graphically. The design of the book is an exemplar of the principles it espouses: elegant typography and layout, and seamless integration of lucid text and perfectly chosen graphical examples. Very Highly Recommended.

Secrets of Mental Math: The Mathemagician's Guide to Lightning Calculation and Amazing Math Tricks

These simple math secrets and tricks will forever change how you look at the world of numbers.

Secrets of Mental Math will have you thinking like a math genius in no time. 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

Kaplan GRE Exam Math Workbook

• NEW! Details and practice for the new question type
• Hundreds of test-like practice questions
• Detailed answer explanations
• Proven score-raising strategies
• Tactics for solving all question types
• Review of core math concepts

Fractal Time: The Secret of 2012 and a New World Age

Godel, Escher, Bach: An Eternal Golden Braid

Twenty years after it topped the bestseller charts, Douglas R. Hofstadter's Gödel, Escher, Bach: An Eternal Golden Braid is still something of a marvel. Besides being a profound and entertaining meditation on human thought and creativity, this book looks at the surprising points of contact between the music of Bach, the artwork of Escher, and the mathematics of Gödel. It also looks at the prospects for computers and artificial intelligence (AI) for mimicking human thought. For the general reader and the computer techie alike, this book still sets a standard for thinking about the future of computers and their relation to the way we think.

Hofstadter's great achievement in Gödel, Escher, Bach was making abstruse mathematical topics (like undecidability, recursion, and 'strange loops') accessible and remarkably entertaining. Borrowing a page from Lewis Carroll (who might well have been a fan of this book), each chapter presents dialogue between the Tortoise and Achilles, as well as other characters who dramatize concepts discussed later in more detail. Allusions to Bach's music (centering on his Musical Offering) and Escher's continually paradoxical artwork are plentiful here. This more approachable material lets the author delve into serious number theory (concentrating on the ramifications of Gödel's Theorem of Incompleteness) while stopping along the way to ponder the work of a host of other mathematicians, artists, and thinkers.

The world has moved on since 1979, of course. The book predicted that computers probably won't ever beat humans in chess, though Deep Blue beat Garry Kasparov in 1997. And the vinyl record, which serves for some of Hofstadter's best analogies, is now left to collectors. Sections on recursion and the graphs of certain functions from physics look tantalizing, like the fractals of recent chaos theory. And AI has moved on, of course, with mixed results. Yet Gödel, Escher, Bach remains a remarkable achievement. Its intellectual range and ability to let us visualize difficult mathematical concepts help make it one of this century's best for anyone who's interested in computers and their potential for real intelligence. --Richard Dragan

Topics Covered: J.S. Bach, M.C. Escher, Kurt Gödel: biographical information and work, artificial intelligence (AI) history and theories, strange loops and tangled hierarchies, formal and informal systems, number theory, form in mathematics, figure and ground, consistency, completeness, Euclidean and non-Euclidean geometry, recursive structures, theories of meaning, propositional calculus, typographical number theory, Zen and mathematics, levels of description and computers; theory of mind: neurons, minds and thoughts; undecidability; self-reference and self-representation; Turing test for machine intelligence.

This groundbreaking Pulitzer Prize-winning book sets the standard for interdisciplinary writing, exploring the patterns and symbols in the thinking of mathematician Kurt Godel, artist M.C. Escher, and composer Johann Sebastian Bach.

Barron's SAT Subject Test Math Level 2, 8th Edition

The newly updated edition of this manual presents a diagnostic test, a review of all Math Level 2 test topics, and six full length model tests with answer keys and answer explanations. Test topics are reviewed in five separate chapters, each containing many practice exercises and answers. Major topics covered include functions and algebra; trigonometry; coordinate geometry; three-dimensional geometry; data analysis, statistics, and probability; and number and operations. Also included is detailed instruction on the use of graphing calculators.

Envisioning Information

A remarkable range of examples for the idea of visual thinking, with beautifully printed pages. A real treat for all who reason and learn by means of images. -- Rudolf Arnheim

Barron's AP Calculus

Both Calculus AB and Calculus BC are covered in this comprehensive AP test preparation manual. Prospective test takers will find four practice exams in Calculus AB and four more in Calculus BC, with all questions answered and solutions explained. The manual also provides a detailed 10-chapter review covering topics for both exams. The authors also offer an overview of the AP Calculus exams, which includes advice to students on making best use of their graphing calculators.