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Author : Underwood Dudley
Publisher : Unknown
Page : 325 pages
File Size : 41,8 Mb
Release : 2008
Category : Mathematics
ISBN : 1470458624
Author : Underwood Dudley
Publisher : MAA Press
Page : 346 pages
File Size : 50,7 Mb
Release : 2008-04-29
Category : Mathematics
ISBN : STANFORD:36105131792850
This is a collection of gems from the literature of mathematics that shine as brightly today as when they first appeared in print - they deserve to be seen and admired. The selections include two opposing views on the purpose of mathematics, the strong law of small numbers, the treatment of calculus in the 1771 Encyclopaedia Britannica, several proofs that the number of legs on a horse is infinite, a deserved refutation of the ridiculous Euler-Diderot anecdote, the real story of π and the Indiana legislature, the reason why Theodorus stopped proving that square roots were irrational when he got to the square root of 17, an excerpt from Mathematics Made Difficult, a glimpse into the mind of a calculating prodigy, and much more. There will be something here for anyone interested in mathematics.
Author : Philip B Persinger
Publisher : iUniverse
Page : 257 pages
File Size : 41,9 Mb
Release : 2011-10-26
Category : Fiction
ISBN : 9781462014224
What could be worse than losing the love of your life? Getting her back! William Teale is a brilliant professor of mathematics. His theory of inevitability posits that any human action, no matter how insignificant, might result in a disproportionately huge calamity. His wife, Virginia "Faye" Warner, is a world-famous romance novelist who specializes in reuniting soul mates after a tragic and prolonged separation. According to her math, "one past and two hearts plus one love equals four-ever." The Teale-Warner marriage is a thing of geometric and artistic perfection, a melding of the heart and the brain-amour and algebra. But when Faye's ghostwriter suffers a nervous breakdown and shakes all the arrows out of Cupid's quiver, Faye reintroduces her husband to love. Unfortunately, it's not with herself, but with the woman William had loved and lost years ago. Love is about to clash with inevitability, and it's unclear which will emerge victorious. Told in the off-beat voice of William's graduate intern, Roger, Do the Math reveals the curious relationship between logic and love and the delightful consequences of taking a chance.
Author : Jzsef Beck
Publisher : American Mathematical Soc.
Page : 267 pages
File Size : 54,6 Mb
Release : 2009-09-01
Category : Mathematics
ISBN : 9780821847565
Mathematics has been called the science of order. The subject is remarkably good for generalizing specific cases to create abstract theories. However, mathematics has little to say when faced with highly complex systems, where disorder reigns. This disorder can be found in pure mathematical arenas, such as the distribution of primes, the $3n+1$ conjecture, and class field theory. The purpose of this book is to provide examples--and rigorous proofs--of the complexity law: (1) discrete systems are either simple or they exhibit advanced pseudorandomness; (2) a priori probabilities often exist even when there is no intrinsic symmetry. Part of the difficulty in achieving this purpose is in trying to clarify these vague statements. The examples turn out to be fascinating instances of deep or mysterious results in number theory and combinatorics. This book considers randomness and complexity. The traditional approach to complexity--computational complexity theory--is to study very general complexity classes, such as P, NP and PSPACE. What Beck does is very different: he studies interesting concrete systems, which can give new insights into the mystery of complexity. The book is divided into three parts. Part A is mostly an essay on the big picture. Part B is partly new results and partly a survey of real game theory. Part C contains new results about graph games, supporting the main conjecture. To make it accessible to a wide audience, the book is mostly self-contained.
Author : Lena Soler,Emiliano Trizio,Andrew Pickering
Publisher : University of Pittsburgh Press
Page : 401 pages
File Size : 40,9 Mb
Release : 2016-02-19
Category : Science
ISBN : 9780822981152
Could all or part of our taken-as-established scientific conclusions, theories, experimental data, ontological commitments, and so forth have been significantly different? Science as It Could Have Been focuses on a crucial issue that contemporary science studies have often neglected: the issue of contingency within science. It considers a number of case studies, past and present, from a wide range of scientific disciplines—physics, biology, geology, mathematics, and psychology—to explore whether components of human science are inevitable, or if we could have developed an alternative successful science based on essentially different notions, conceptions, and results. Bringing together a group of distinguished contributors in philosophy, sociology, and history of science, this edited volume offers a comprehensive analysis of the contingency/inevitability problem and a lively and up-to-date portrait of current debates in science studies.
Author : Richard Courant,Herbert Robbins
Publisher : Oxford University Press, USA
Page : 596 pages
File Size : 41,5 Mb
Release : 1996
Category : Juvenile Nonfiction
ISBN : 0195105192
The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but not real understanding or greater intellectual independence. The new edition of this classic work seeks to address this problem. Its goal is to put the meaning back into mathematics. "Lucid . . . easily understandable".--Albert Einstein. 301 linecuts.
Author : Nathan Carter
Publisher : American Mathematical Soc.
Page : 462 pages
File Size : 50,8 Mb
Release : 2016-12-31
Category : Mathematics
ISBN : 9781614441229
This text, by an award-winning [Author];, was designed to accompany his first-year seminar in the mathematics of computer graphics. Readers learn the mathematics behind the computational aspects of space, shape, transformation, color, rendering, animation, and modeling. The software required is freely available on the Internet for Mac, Windows, and Linux. The text answers questions such as these: How do artists build up realistic shapes from geometric primitives? What computations is my computer doing when it generates a realistic image of my 3D scene? What mathematical tools can I use to animate an object through space? Why do movies always look more realistic than video games? Containing the mathematics and computing needed for making their own 3D computer-generated images and animations, the text, and the course it supports, culminates in a project in which students create a short animated movie using free software. Algebra and trigonometry are prerequisites; calculus is not, though it helps. Programming is not required. Includes optional advanced exercises for students with strong backgrounds in math or computer science. Instructors interested in exposing their liberal arts students to the beautiful mathematics behind computer graphics will find a rich resource in this text.
Author : Gregory Chaitin
Publisher : Vintage
Page : 242 pages
File Size : 51,8 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9781400077977
Gregory Chaitin, one of the world’s foremost mathematicians, leads us on a spellbinding journey, illuminating the process by which he arrived at his groundbreaking theory. Chaitin’s revolutionary discovery, the Omega number, is an exquisitely complex representation of unknowability in mathematics. His investigations shed light on what we can ultimately know about the universe and the very nature of life. In an infectious and enthusiastic narrative, Chaitin delineates the specific intellectual and intuitive steps he took toward the discovery. He takes us to the very frontiers of scientific thinking, and helps us to appreciate the art—and the sheer beauty—in the science of math.
Author : Alex Van Den Brandhof,Jan Guichelaar,Arnout Jaspers
Publisher : The Mathematical Association of America
Page : 319 pages
File Size : 41,6 Mb
Release : 2015-09-29
Category : Mathematics
ISBN : 9780883855874
Half a Century of Pythagoras Magazine is a selection of the best and most inspiring articles from this Dutch magazine for recreational mathematics. Founded in 1961 and still thriving today, Pythagoras has given generations of high school students in the Netherlands a perspective on the many branches of mathematics that are not taught in schools. The book contains a mix of easy, yet original puzzles, more challenging - and at least as original – problems, as well as playful introductions to a plethora of subjects in algebra, geometry, topology, number theory and more. Concepts like the sudoku and the magic square are given a whole new dimension. One of the first editors was a personal friend of world famous Dutch graphic artist Maurits Escher, whose 'impossible objects' have been a recurring subject over the years. Articles about his work are part of a special section on 'Mathematics and Art'. While many books on recreational mathematics rely heavily on 'folklore', a reservoir of ancient riddles and games that are being recycled over and over again, most of the puzzles and problems in Half a Century of Pythagoras Magazine are original, invented for this magazine by Pythagoras' many editors and authors over the years. Some are no more than cute little brainteasers which can be solved in a minute, others touch on profound mathematics and can keep the reader entranced indefinitely. Smart high school students and anyone else with a sharp and inquisitive mind will find in this book a treasure trove which is rich enough to keep his or her mind engaged for many weeks and months.
Author : Peter Casazza,Steven G. Krantz,Randi D. Ruden
Publisher : The Mathematical Association of America
Page : 289 pages
File Size : 50,8 Mb
Release : 2015-03-10
Category : Mathematics
ISBN : 9780883855850
Mathematicians have pondered the psychology of the members of our tribe probably since mathematics was invented, but for certain since Hadamard’s The Psychology of Invention in the Mathematical Field. The editors asked two dozen prominent mathematicians (and one spouse thereof) to ruminate on what makes us different. The answers they got are thoughtful, interesting and thought-provoking. Not all respondents addressed the question directly. Michael Atiyah reflects on the tension between truth and beauty in mathematics. T.W. Körner, Alan Schoenfeld and Hyman Bass chose to write, reflectively and thoughtfully, about teaching and learning. Others, including Ian Stewart and Jane Hawkins, write about the sociology of our community. Many of the contributions range into philosophy of mathematics and the nature of our thought processes. Any mathematician will find much of interest here.
Author : Raymond L. Wilder
Publisher : Elsevier
Page : 195 pages
File Size : 46,7 Mb
Release : 2014-05-20
Category : Social Science
ISBN : 9781483100616
Mathematics as a Cultural System discusses the relationship between mathematics and culture. The book is comprised of eight chapters discussing topics that support the concept of mathematics as a cultural system. Chapter I deals with the nature of culture and cultural systems, while Chapter 2 provides examples of cultural patterns observable in the evolution of mechanics. Chapter III treats historical episodes as a laboratory for the illustration of patterns and forces that have been operative in cultural change. Chapter IV covers hereditary stress, and Chapter V discusses consolidation as a force and process. Chapter VI talks about the singularities in the evolution of mechanics, while Chapter 7 deals with the laws governing the evolution of mathematics. Chapter VIII tackles the role and future of mathematics. The book will be of great interest to readers who are curious about how mathematics relates to culture.
Author : Jeff Suzuki
Publisher : MAA
Page : 432 pages
File Size : 52,7 Mb
Release : 2009-08-27
Category : Mathematics
ISBN : 0883855704
An exploration of the interaction between mathematics, mathematicians and society. What would Newton see if he looked out his window?
Author : Dr. Thomas Stark
Publisher : Magus Books
Page : 395 pages
File Size : 44,7 Mb
Release : 2024-07-03
Category : Mathematics
ISBN : 8210379456XXX
So, you know what mathematics is, right? Well, if you do, you're a smarter person than Nobel laureates Albert Einstein and Eugene Wigner, who were baffled by what mathematics is and how it relates to science and the world. Wigner wrote a famous paper entitled "The Unreasonable Effectiveness of Mathematics in the Natural Sciences." No scientist has ever explained why mathematics is so uncannily appropriate to describing Nature. Galileo said, "The Book of Nature is written in mathematical language, and its characters are triangles, circles and other geometric figures, without which it is impossible to humanly understand a word; without these, one is wandering in a dark labyrinth." Do you want to escape from the dark labyrinth? Then you must discover what mathematics really is. The answer will blow your mind. Guaranteed. Come on the greatest detective adventure of them all, where you do nothing but exercise pure deduction. Come and be a cosmic Sherlock Holmes. Put on your deerstalker and practice the pristine science of deduction. Determining the true nature of mathematics is the No. 1 problem facing humanity. To explain mathematics is to explain reality itself.
Author : E. Brian Davies
Publisher : OUP Oxford
Page : 272 pages
File Size : 42,6 Mb
Release : 2010-07-09
Category : Science
ISBN : 9780191591563
In the follow-up to his acclaimed Science in the Looking Glass, Brian Davies discusses deep problems about our place in the world, using a minimum of technical jargon. The book argues that 'absolutist' ideas of the objectivity of science, dating back to Plato, continue to mislead generations of both theoretical physicists and theologians. It explains that the multi-layered nature of our present descriptions of the world is unavoidable, not because of anything about the world, but because of our own human natures. It tries to rescue mathematics from the singular and exceptional status that it has been assigned, as much by those who understand it as by those who do not. Working throughout from direct quotations from many of the important contributors to its subject, it concludes with a penetrating criticism of many of the recent contributions to the often acrimonious debates about science and religions.
Author : F. William Lawvere,Robert Rosebrugh
Publisher : Cambridge University Press
Page : 280 pages
File Size : 54,9 Mb
Release : 2003-01-27
Category : Mathematics
ISBN : 0521010608
In this book, first published in 2003, categorical algebra is used to build a foundation for the study of geometry, analysis, and algebra.