Here's the perfect self-teaching guide to help anyone master differential equations--a common stumbling block for students looking to progress to advanced topics in both science and math. Covers First Order Equations, Second Order Equations and Higher, Properties, Solutions, Series Solutions, Fourier Series and Orthogonal Systems, Partial Differential Equations and Boundary Value Problems, Numerical Techniques, and more.
CliffsQuickReview course guides cover the essentials of your toughest classes. Get a firm grip on core concepts and key material, and test your newfound knowledge with review questions. Whether you're looking for an in-depth treatment of the entire subject matter or occasional reinforcement of key algebra concepts, this is the place to find it.
What two things could be more different than numbers and stories? Numbers are abstract, certain, and eternal, but to most of us somewhat dry and bloodless. Good stories are full of life: they engage our emotions and have subtlety and nuance, but they lack rigor and the truths they tell are elusive and subject to debate. As ways of understanding the world around us, numbers and stories seem almost completely incompatible. Once Upon a Number shows that stories and numbers aren't as different as you might imagine, and in fact they have surprising and fascinating connections. The concepts of logic and probability both grew out of intuitive ideas about how certain situations would play out. Now, logicians are inventing ways to deal with real world situations by mathematical means--by acknowledging, for instance, that items that are mathematically interchangeable may not be interchangeable in a story. And complexity theory looks at both number strings and narrative strings in remarkably similar terms.Throughout, renowned author John Paulos mixes numbers and narratives in his own delightful style. Along with lucid accounts of cutting-edge information theory we get hilarious anecdotes and jokes; instructions for running a truly impressive pyramid scam; a freewheeling conversation between Groucho Marx and Bertrand Russell (while they're stuck in an elevator together); explanations of why the statistical evidence against OJ Simpson was overwhelming beyond doubt and how the Unabomber's thinking shows signs of mathematical training; and dozens of other treats. This is another winner from America's favorite mathematician.
The open-ended curve of the spiral gives a sensation of continuous motion -- of life, in fact. In The Curves of Life, Sir Theodore A. Cook (1867-1928), English author and editor, finds that the spiral or helix may lie at the core of life's first principle -- that of growth. The spiral is fundamental to the structure of plants, shells, and the human body; to the periodicity of atomic elements and to an animal's horns; to microscopic DNA (the double helix) and to the Andromeda nebula.
The Curves of Life portrays the significance of the spiral in 426 illustrations, from a Narwhal's tusk to D rer's plan for a cylindrical helix. From the spiral in nature, science, and art, the author suggests ideas on the essence of beauty and man's response to it. "One of the chief beauties of the spiral as an imaginative conception is that it is always growing, yet never covering the same ground, so that it is not merely an explanation of the past, but is also a prophecy of the future."
Martin Gardner, mathematician and author, said of The Curves of Life, "This is the classic reference on how the golden ratio applies to spirals and helices in nature."
This magisterial annotated bibliography of the earliest mathematical works to be printed in the New World challenges long-held assumptions about the earliest examples of American mathematical endeavor. Bruce Stanley Burdick brings together mathematical writings from Mexico, Lima, and the English colonies of Massachusetts, Pennsylvania, and New York. The book provides important information such as author, printer, place of publication, and location of original copies of each of the works discussed.
Burdick's exhaustive research has unearthed numerous examples of books not previously cataloged as mathematical. While it was thought that no mathematical writings in English were printed in the Americas before 1703, Burdick gives scholars one of their first chances to discover Jacob Taylor's 1697 Tenebrae, a treatise on solving triangles and other figures using basic trigonometry. He also goes beyond the English language to discuss works in Spanish and Latin, such as Alonso de la Vera Cruz's 1554 logic text, the Recognitio Summularum; a book on astrology by Enrico Mart nez; books on the nature of comets by Carlos de Sig enza y G ngora and Eusebio Francisco Kino; and a 1676 almanac by Feliciana Ruiz, the first woman to produce a mathematical work in the Americas.
Those fascinated by mathematics, its history, and its culture will note with interest that many of these works, including all of the earliest ones, are from Mexico, not from what is now the United States. As such, the book will challenge us to rethink the history of mathematics on the American continents.
Alternating passages of extraordinarily lucid mathematical exposition with chapters of elegantly composed biography and history, Prime Obsession is a fascinating and fluent account of an epic mathematical mystery that continues to challenge and excite the world.
With Easy as Pi, you'll have instant access to a breadth of knowledge and impress your friends Whether you need homework help or want to win that trivia game, this series is the trusted source for fun facts.Have you ever wondered what makes "seventh heaven" and "cloud nine" so blissful and the number 13 so unlucky? Here's the "4-1-1" on the origins of numerical expressions and the importance of numbers in fiction, film, culture, and religion, including:
Part history, part philosophy, part love letter to the study of mathematics, Everything and More is an illuminating tour of infinity. With his infectious curiosity and trademark verbal pyrotechnics, David Foster Wallace takes us from Aristotle to Newton, Leibniz, Karl Weierstrass, and finally Georg Cantor and his set theory. Through it all, Wallace proves to be an ideal guide--funny, wry, and unfailingly enthusiastic. Featuring an introduction by Neal Stephenson, this edition is a perfect introduction to the beauty of mathematics and the undeniable strangeness of the infinite.
The Cartoon Introduction to Statistics is the most imaginative and accessible introductory statistics course you'll ever take. Employing an irresistible cast of dragon-riding Vikings, lizard-throwing giants, and feuding aliens, the renowned illustrator Grady Klein and the award-winning statistician Alan Dabney teach you how to collect reliable data, make confident statements based on limited information, and judge the usefulness of polls and the other numbers that you're bombarded with every day. If you want to go beyond the basics, they've created the ultimate resource: The Math Cave, where they reveal the more advanced formulas and concepts.Timely, authoritative, and hilarious, The Cartoon Introduction to Statistics is an essential guide for anyone who wants to better navigate our data-driven world.
Thinking Mathematically is perfect for anyone who wants to develop their powers to think mathematically, whether at school, at university or just out of interest. This book is invaluable for anyone who wishes to promote mathematical thinking in others or for anyone who has always wondered what lies at the core of mathematics. Thinking Mathematically reveals the processes at the heart of mathematics and demonstrates how to encourage and develop them. Extremely practical, it involves the reader in questions so that subsequent discussions speak to immediate experience.