Street Fighting Mathematics

Author : Sanjoy Mahajan
Publisher : MIT Press
Page : 152 pages
File Size : 55,8 Mb
Release : 2010-03-05
Category : Education
ISBN : 9780262265591

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Street-Fighting Mathematics by Sanjoy Mahajan Pdf

An antidote to mathematical rigor mortis, teaching how to guess answers without needing a proof or an exact calculation. In problem solving, as in street fighting, rules are for fools: do whatever works—don't just stand there! Yet we often fear an unjustified leap even though it may land us on a correct result. Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions. This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation. In Street-Fighting Mathematics, Sanjoy Mahajan builds, sharpens, and demonstrates tools for educated guessing and down-and-dirty, opportunistic problem solving across diverse fields of knowledge—from mathematics to management. Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool—the general principle—from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest. Street-Fighting Mathematics grew out of a short course taught by the author at MIT for students ranging from first-year undergraduates to graduate students ready for careers in physics, mathematics, management, electrical engineering, computer science, and biology. They benefited from an approach that avoided rigor and taught them how to use mathematics to solve real problems. Street-Fighting Mathematics will appear in print and online under a Creative Commons Noncommercial Share Alike license.

Author : James Carlson,Arthur Jaffe,Andrew Wiles
Publisher : American Mathematical Society, Clay Mathematics Institute
Page : 185 pages
File Size : 45,7 Mb
Release : 2023-09-14
Category : Mathematics
ISBN : 9781470474607

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The Millennium Prize Problems by James Carlson,Arthur Jaffe,Andrew Wiles Pdf

On August 8, 1900, at the second International Congress of Mathematicians in Paris, David Hilbert delivered his famous lecture in which he described twenty-three problems that were to play an influential role in mathematical research. A century later, on May 24, 2000, at a meeting at the Collège de France, the Clay Mathematics Institute (CMI) announced the creation of a US$7 million prize fund for the solution of seven important classic problems which have resisted solution. The prize fund is divided equally among the seven problems. There is no time limit for their solution. The Millennium Prize Problems were selected by the founding Scientific Advisory Board of CMI—Alain Connes, Arthur Jaffe, Andrew Wiles, and Edward Witten—after consulting with other leading mathematicians. Their aim was somewhat different than that of Hilbert: not to define new challenges, but to record some of the most difficult issues with which mathematicians were struggling at the turn of the second millennium; to recognize achievement in mathematics of historical dimension; to elevate in the consciousness of the general public the fact that in mathematics, the frontier is still open and abounds in important unsolved problems; and to emphasize the importance of working towards a solution of the deepest, most difficult problems. The present volume sets forth the official description of each of the seven problems and the rules governing the prizes. It also contains an essay by Jeremy Gray on the history of prize problems in mathematics.

Author : Bonnie Averbach,Orin Chein
Publisher : Courier Corporation
Page : 480 pages
File Size : 54,7 Mb
Release : 2012-03-15
Category : Mathematics
ISBN : 9780486131740

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Problem Solving Through Recreational Mathematics by Bonnie Averbach,Orin Chein Pdf

Fascinating approach to mathematical teaching stresses use of recreational problems, puzzles, and games to teach critical thinking. Logic, number and graph theory, games of strategy, much more. Includes answers to selected problems. Free solutions manual available for download at the Dover website.

Author : Lawrence Weinstein
Publisher : Princeton University Press
Page : 384 pages
File Size : 46,6 Mb
Release : 2012-09-30
Category : Business & Economics
ISBN : 9780691150802

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Guesstimation 2.0 by Lawrence Weinstein Pdf

Simple and effective techniques for quickly estimating virtually anything Guesstimation 2.0 reveals the simple and effective techniques needed to estimate virtually anything—quickly—and illustrates them using an eclectic array of problems. A stimulating follow-up to Guesstimation, this is the must-have book for anyone preparing for a job interview in technology or finance, where more and more leading businesses test applicants using estimation questions just like these. The ability to guesstimate on your feet is an essential skill to have in today's world, whether you're trying to distinguish between a billion-dollar subsidy and a trillion-dollar stimulus, a megawatt wind turbine and a gigawatt nuclear plant, or parts-per-million and parts-per-billion contaminants. Lawrence Weinstein begins with a concise tutorial on how to solve these kinds of order of magnitude problems, and then invites readers to have a go themselves. The book features dozens of problems along with helpful hints and easy-to-understand solutions. It also includes appendixes containing useful formulas and more. Guesstimation 2.0 shows how to estimate everything from how closely you can orbit a neutron star without being pulled apart by gravity, to the fuel used to transport your food from the farm to the store, to the total length of all toilet paper used in the United States. It also enables readers to answer, once and for all, the most asked environmental question of our day: paper or plastic?

Author : Ian Stewart
Publisher : Profile Books
Page : 335 pages
File Size : 45,7 Mb
Release : 2011-04-07
Category : Mathematics
ISBN : 9781847653505

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Mathematics Of Life by Ian Stewart Pdf

A new partnership of biologists and mathematicians is picking apart the hidden complexity of animals and plants to throw fresh light on the behaviour of entire organisms, how they interact and how changes in biological diversity affect the planet's ecological balance. Mathematics offers new and sometimes startling perspectives on evolution and how patterns of inheritance and population work out over time-scales ranging from millions to hundreds of years - as well as what's going on to change us right now. Ian Stewart, in characteristically clear and entertaining fashion, explores these and a whole range of pertinent issues, including how far genes control behaviour and the nature of life itself. He shows how far mathematicians and biologists are succeeding in tackling some of the most difficult scientific problems the human race has ever confronted and where their research is currently taking us.

Author : D. B. Fuks,Serge Tabachnikov
Publisher : American Mathematical Soc.
Page : 463 pages
File Size : 42,9 Mb
Release : 2007
Category : Mathematics
ISBN : 9780821843161

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Mathematical Omnibus by D. B. Fuks,Serge Tabachnikov Pdf

The book consists of thirty lectures on diverse topics, covering much of the mathematical landscape rather than focusing on one area. The reader will learn numerous results that often belong to neither the standard undergraduate nor graduate curriculum and will discover connections between classical and contemporary ideas in algebra, combinatorics, geometry, and topology. The reader's effort will be rewarded in seeing the harmony of each subject. The common thread in the selected subjects is their illustration of the unity and beauty of mathematics. Most lectures contain exercises, and solutions or answers are given to selected exercises. A special feature of the book is an abundance of drawings (more than four hundred), artwork by an accomplished artist, and about a hundred portraits of mathematicians. Almost every lecture contains surprises for even the seasoned researcher.

Author : Alexandre Borovik,Tony Gardiner
Publisher : Unknown
Page : 398 pages
File Size : 44,8 Mb
Release : 2019-06-11
Category : Mathematics
ISBN : 1783746998

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The Essence of Mathematics Through Elementary Problems by Alexandre Borovik,Tony Gardiner Pdf

Author : Alexandre Borovik
Publisher : American Mathematical Soc.
Page : 317 pages
File Size : 48,5 Mb
Release : 2010
Category : Mathematics
ISBN : 9780821847619

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Mathematics Under the Microscope by Alexandre Borovik Pdf

The author's goal is to start a dialogue between mathematicians and cognitive scientists. He discusses, from a working mathematician's point of view, the mystery of mathematical intuition: why are certain mathematical concepts more intuitive than others? To what extent does the ``small scale'' structure of mathematical concepts and algorithms reflect the workings of the human brain? What are the ``elementary particles'' of mathematics that build up the mathematical universe? The book is saturated with amusing examples from a wide range of disciplines--from turbulence to error-correcting codes to logic--as well as with just puzzles and brainteasers. Despite the very serious subject matter, the author's approach is lighthearted and entertaining. This is an unusual and unusually fascinating book. Readers who never thought about mathematics after their school years will be amazed to discover how many habits of mind, ideas, and even material objects that are inherently mathematical serve as building blocks of our civilization and everyday life. A professional mathematician, reluctantly breaking the daily routine, or pondering on some resisting problem, will open this book and enjoy a sudden return to his or her young days when mathematics was fresh, exciting, and holding all promises. And do not take the word ``microscope'' in the title too literally: in fact, the author looks around, in time and space, focusing in turn on a tremendous variety of motives, from mathematical ``memes'' (genes of culture) to an unusual life of a Hollywood star. --Yuri I. Manin, Max-Planck Institute of Mathematics, Bonn, and Northwestern University

Author : Dirk Jan Struik
Publisher : Princeton University Press
Page : 444 pages
File Size : 48,7 Mb
Release : 2014-07-14
Category : Mathematics
ISBN : 9781400858002

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A Source Book in Mathematics, 1200-1800 by Dirk Jan Struik Pdf

These selected mathematical writings cover the years when the foundations were laid for the theory of numbers, analytic geometry, and the calculus. Originally published in 1986. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Author : Agustin Rayo
Publisher : MIT Press
Page : 321 pages
File Size : 45,8 Mb
Release : 2019-04-02
Category : Mathematics
ISBN : 9780262039413

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On the Brink of Paradox by Agustin Rayo Pdf

An introduction to awe-inspiring ideas at the brink of paradox: infinities of different sizes, time travel, probability and measure theory, and computability theory. This book introduces the reader to awe-inspiring issues at the intersection of philosophy and mathematics. It explores ideas at the brink of paradox: infinities of different sizes, time travel, probability and measure theory, computability theory, the Grandfather Paradox, Newcomb's Problem, the Principle of Countable Additivity. The goal is to present some exceptionally beautiful ideas in enough detail to enable readers to understand the ideas themselves (rather than watered-down approximations), but without supplying so much detail that they abandon the effort. The philosophical content requires a mind attuned to subtlety; the most demanding of the mathematical ideas require familiarity with college-level mathematics or mathematical proof. The book covers Cantor's revolutionary thinking about infinity, which leads to the result that some infinities are bigger than others; time travel and free will, decision theory, probability, and the Banach-Tarski Theorem, which states that it is possible to decompose a ball into a finite number of pieces and reassemble the pieces so as to get two balls that are each the same size as the original. Its investigation of computability theory leads to a proof of Gödel's Incompleteness Theorem, which yields the amazing result that arithmetic is so complex that no computer could be programmed to output every arithmetical truth and no falsehood. Each chapter is followed by an appendix with answers to exercises. A list of recommended reading points readers to more advanced discussions. The book is based on a popular course (and MOOC) taught by the author at MIT.

Author : Hal Hellman
Publisher : Turner Publishing Company
Page : 292 pages
File Size : 50,8 Mb
Release : 2010-12-17
Category : Mathematics
ISBN : 9781118040119

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Great Feuds in Mathematics by Hal Hellman Pdf

Praise for Hal Hellman Great Feuds in Mathematics "Those who think that mathematicians are cold, mechanical proving machines will do well to read Hellman's book on conflicts in mathematics. The main characters are as excitable and touchy as the next man. But Hellman's stories also show how scientific fights bring out sharper formulations and better arguments." -Professor Dirk van Dalen, Philosophy Department, Utrecht University Great Feuds in Technology "There's nothing like a good feud to grab your attention. And when it comes to describing the battle, Hal Hellman is a master." -New Scientist Great Feuds in Science "Unusual insight into the development of science . . . I was excited by this book and enthusiastically recommend it to general as well as scientific audiences." -American Scientist "Hellman has assembled a series of entertaining tales . . . many fine examples of heady invective without parallel in our time." -Nature Great Feuds in Medicine "This engaging book documents [the] reactions in ten of the most heated controversies and rivalries in medical history. . . . The disputes detailed are . . . fascinating. . . . It is delicious stuff here." -The New York Times "Stimulating." -Journal of the American Medical Association

Author : Lillian R. Lieber
Publisher : Paul Dry Books
Page : 238 pages
File Size : 42,7 Mb
Release : 2007-06-01
Category : Literary Collections
ISBN : 9781589880337

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The Education of T.C. MITS by Lillian R. Lieber Pdf

Whether you are stumped by the "commutative law" in algebra or a whiz at multiplying three-digit numbers in your head, this book opens the door to the wonders of mathematical imagining. By using simple language and intriguing illustrations drawn by her husband, Hugh, Lillian Lieber presents subtle mathematical concepts in an easy-to-understand way. Over sixty years after its release, this whimsical exploration of how to think in a mathematical mood will continue to delight math-lovers of all ages. Barry Mazur's new introduction is a tribute to the Liebers' influence on generations of mathematicians.

Author : BATHUL, SHAHNAZ
Publisher : PHI Learning Pvt. Ltd.
Page : 376 pages
File Size : 49,7 Mb
Release : 2015-04-01
Category : Mathematics
ISBN : 9788120350991

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REMEDIAL MATHEMATICS by BATHUL, SHAHNAZ Pdf

Primarily intended to serve as a textbook for undergraduate students of pharmacy, this new edition deals with the basic concepts of mathematics. The primary objective of this text is to solidify the mathematical skills of even those students who do not have any mathematical background. The text discusses progressions, binomial theorem, trigonometric functions, matrices and determinants, Cramer's rule, differentiations, integrations, differential equations and their applications in an easy-to-understand style that creates interest in the subject. The text is supported by a number of solved and unsolved examples to enhance the problem-solving skills of the students. Besides, various universities' examination questions and quiz are also provided with answers. KEY FEATURES Simple and clear explanation of the concepts. Multiple choice questions and exercise problems at the end of each chapter. Numerous worked-out problems.

Author : Sanjoy Mahajan
Publisher : Cambridge University Press
Page : 215 pages
File Size : 49,5 Mb
Release : 2020-06-18
Category : Science
ISBN : 9781108471145

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A Student's Guide to Newton's Laws of Motion by Sanjoy Mahajan Pdf

Master Newton's laws of motion, the basis of modern science and engineering, with this intuitive and accessible text.

Author : Thomas William Körner
Publisher : Cambridge University Press
Page : 548 pages
File Size : 43,8 Mb
Release : 1996-12-05
Category : Mathematics
ISBN : 0521568234

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The Pleasures of Counting by Thomas William Körner Pdf

What is the connection between the outbreak of cholera in Victorian Soho, the Battle of the Atlantic, African Eve and the design of anchors? One answer is that they are all examples chosen by Dr Tom Körner to show how a little mathematics can shed light on the world around us, and deepen our understanding of it. Dr Körner, an experienced author, describes a variety of topics which continue to interest professional mathematicians, like him. He does this using relatively simple terms and ideas, yet confronting difficulties (which are often the starting point for new discoveries) and avoiding condescension. If you have ever wondered what it is that mathematicians do, and how they go about it, then read on. If you are a mathematician wanting to explain to others how you spend your working days (and nights), then seek inspiration here.