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Developed for an introductory course in mathematical analysis at MIT, this text focuses on concepts, principles, and methods. Its introductions to real and complex analysis are closely formulated, and they constitute a natural introduction to complex function theory. Starting with an overview of the real number system, the text presents results for subsets and functions related to Euclidean space of n dimensions. It offers a rigorous review of the...
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This collection of yummy recipes and fun math facts is sure to tempt taste buds and make you hungry for more. Explore patterns in nature while you chomp on Fibonacci Stack Sticks. Amaze your friends with delicious Variable Pizza Pi! Wash down your geometry assignment with some Milk and Tangram Cookies. Topics covered include probability, Fibonacci numbers, tessellations, variability, and more.
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A comprehensive text on matrix theory and its applications, this book is intended for a broad range of students in mathematics, engineering, and other areas of science at the university level. Author Alexander Graham avoids a simple catalogue of techniques by exploring the concepts' underlying principles as well as their numerous applications. Many problems elucidate the text, which includes a substantial answer section at the end. The treatment explores...
84) Modern Algebra
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This standard text, written for junior and senior undergraduates, is unusual in that its presentation is accessible enough for the beginner, yet its thoroughness and mathematical rigor provide the more advanced student with an exceptionally comprehensive treatment of every aspect of modern algebra. It especially lends itself to use by beginning graduate students unprepared in modern algebra. The presentation opens with a study of algebraic structures...
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Mathematics has come a long way indeed in the last 2,000 years, and this guide to modern mathematics traces the fascinating path from Euclid's Elements to contemporary concepts. No background beyond elementary algebra and plane geometry is necessary to understand and appreciate author Constance Reid's simple, direct explanations of the arithmetic of the infinite, the paradoxes of point sets, the "knotty" problems of topology, and "truth tables" of...
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In Part One of this comprehensive and frequently cited treatment, the authors develop Euclidean and Bolyai-Lobachevskian geometry on the basis of an axiom system due, in principle, to the work of David Hilbert. Part Two develops projective geometry in much the same way. An Introduction provides background on topological space, analytic geometry, and other relevant topics, and rigorous proofs appear throughout the text. Topics covered by Part One include...
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Soccer may be considered a low-scoring sport by some, but learning its intricacies allows readers to see the world of math that is hidden inside what is known as The Beautiful Game. Readers will learn basics like goals and assists as well as higher numbers like caps. They'll even learn how league standings work, and how more complex equations like goal differential can sometimes determine league champions.
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This ultimate parents' guide to elementary school math features projects, games, and activities children and parents can do together to increase their understanding of basic math concepts. Fun activities such as mapping a child's bedroom for practice in measurements or keeping a diary of numeric items like vacation mileage and expenses reinforce the math skills outlined in each lesson. Using the standards issued by the National Council of Teachers...
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This advanced text explores a category of mathematical problems that occur frequently in physics and other sciences. Five preliminary chapters make the book accessible to students without extensive background in this area. Topics include Hamiltonian systems, symplecticness, numerical methods, order conditions, and implementation. The heart of the book, chapters 6 through 10, explores simplistic integration, simplistic order conditions, available simplistic...
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Julian Havil is a former Master at Winchester College, England, where he taught mathematics for more than thirty years. He is the author of Gamma: Exploring Euler's Constant and Impossible?: Surprising Solutions to Counterintuitive Conundrums (both Princeton).
Math-the application of reasonable logic to reasonable assumptions-usually produces reasonable results. But sometimes math generates astonishing paradoxes-conclusions that seem completely...
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Marc Chamberland is professor of mathematics and natural sciences at Grinnell College. He is the creator of the YouTube channel Tipping Point Math, which strives to make mathematics accessible to everyone.
The remarkable properties of the numbers one through nine
In Single Digits, Marc Chamberland takes readers on a fascinating exploration of small numbers, from one to nine, looking at their history, applications, and connections to various areas...
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Historically, many of the most important mathematical concepts arose from problems that were recreational in origin. This book takes advantage of that fact, using recreational mathematics - problems, puzzles and games - to teach students how to think critically. Encouraging active participation rather than just observation, the book focuses less on mathematical results than on how these results can be applied to thinking about problems and solving...
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How big is your vocabulary?
How heavy is your house?
Do the dead outnumber the living?
What are the best words to use in a personal ad?
We humans are a curious species, prone to think, ruminate, reflect, cogitate, mull over, and philosophize. We long to explain away the world around us, to answer all those seeming unanswerables: Why are we here? Is there a God? Is there life after death? And, above all, how many houseflies does it take...
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"Fascinating facts and stories behind inventions based on mathematics -- from search engines to streaming video to self-correcting golf balls. How do dating sites match compatible partners? What do cell phones and sea coasts have in common? And why do computer scientists keep ant colonies? Jeff Suzuki answers these questions and more in Patently Mathematical , which explores the mathematics behind some of the key inventions that have changed our world....
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School mathematics sometimes excite and sometimes scare, and sadly, sometimes bore. In fact, elementary school arithmetic seems to get us through most situations. So why all the rest? This book aspires to give a glimpse into how things started and evolved, and how math can help us today, from simple measurements to navigating using mathematically simplified maps. The accompanying activities (some easier and some more challenging ones) aim to engage...
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This concise introduction to the methods and techniques of vector analysis is suitable for college undergraduates in mathematics as well as students of physics and engineering. Rich in exercises and examples, the straightforward presentation focuses on physical ideas rather than mathematical rigor. The treatment begins with a chapter on vectors and vector addition, followed by a chapter on products of vector. Two succeeding chapters on vector calculus...
100) The Theory of Groups
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\"Mastering the contents of Hall's book will lead a student to the frontiers of group theory. He will be well equipped to read any recent literature and start original research himself in this field ... This remarkable book undoubtedly will become a standard text on group theory.\" Eugene Guth, American Scientist \"This is a book which I wish I could put in the hands of every graduate student who has shown an interest in the elements of group theory....
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