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Targets the general mathematically-interested reader with broad coverage of biographies, history, popular works, and books of general interest.

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23 results in Spectrum

Page 1 of 2

I, Mathematician
  • Edited by Peter Casazza
  • Steven G. Krantz, Randi D. Ruden
  • Published by:
    Mathematical Association of America
    Published online:
    09 June 2017
    Print publication:
    01 April 2015
  • 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.

Half a Century of Pythagoras Magazine
  • Alex van den Brandhof, Jan Guichelaar, Arnout Jaspers
  • Published by:
    Mathematical Association of America
    Published online:
    26 May 2017
    Print publication:
    01 November 2015
  • 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.

How Euler Did Even More
  • C. Edward Sandifer
  • Published by:
    Mathematical Association of America
    Published online:
    05 December 2015
    Print publication:
    01 December 2014
  • 'Read Euler, read Euler, he is master of us all' LaPlace exhorted us. And it is true, Euler writes with unerring grace and ease. He is exceptionally clear thinking and clear speaking. It is a joy and a pleasure to follow him. It is especially so with Ed Sandifer as your guide. Sandifer has been studying Euler for decades and is one of the world's leading experts on his work. This volume is the second collection of Sandifer's 'How Euler Did It' columns. Each is a jewel of historical and mathematical exposition. The sum total of years of work and study of the most prolific mathematician of history, this volume will leave you marveling at Euler's clever inventiveness and Sandifer's wonderful ability to explicate and put it all in context.

Illustrated Special Relativity through its Paradoxes
  • A Fusion of Linear Algebra, Graphics, and Reality
  • Illustrated by John dePillis
  • Jose Wudka
  • Published by:
    Mathematical Association of America
    Published online:
    05 September 2014
    Print publication:
    05 September 2014
  • Illustrated Special Relativity shows that linear algebra is a natural language for special relativity. It illustrates and resolves several apparent paradoxes of special relativity including the twin paradox and train-and-tunnel paradox. Assuming a minimum of technical prerequisites the authors introduce inertial frames and use them to explain a variety of phenomena: the nature of simultaneity, the proper way to add velocities, and why faster-than-light travel is impossible. Most of these explanations are contained in the resolution of apparent paradoxes, including some lesser-known ones: the pea-shooter paradox, the bug-and-rivet paradox, and the accommodating universe paradox. The explanation of time and length contraction is especially clear and illuminating. At the outset of his seminal paper on special relativity, Einstein acknowledges the work of James Clerk Maxwell whose four equations unified the theories of electricity, optics, and magnetism. For this reason, the authors develop Maxwell's equations which lead to a simple calculation for the frame-independent speed of electromagnetic waves in a vacuum. (Maxwell did not realize that light was a special case of electromagnetic waves.) Several chapters are devoted to experiments of Roemer, Fizeau, and de Sitter to measure the speed of light and the Michelson-Morley experiment abolishing the aether. Throughout the exposition is thorough, but not overly technical, and often illustrated by cartoons. The volume might be suitable for a one-semester general-education introduction to special relativity. It is especially well-suited to self-study by interested laypersons or use as a supplement to a more traditional text.

Non-Euclidean Geometry
  • H. S. M. Coxeter
  • Published by:
    Mathematical Association of America
    Published online:
    05 September 2014
    Print publication:
    01 June 1998
  • Throughout most of this book, non-Euclidean geometries in spaces of two or three dimensions are treated as specializations of real projective geometry in terms of a simple set of axioms concerning points, lines, planes, incidence, order and continuity, with no mention of the measurement of distances or angles. This synthetic development is followed by the introduction of homogeneous coordinates, beginning with Von Staudt's idea of regarding points as entities that can be added or multiplied. Tranformations that preserve incidence are called collineations. They lead in a natural way to isometries or 'congruent transformations'. Following a recommendation by Bertrand Russell, continuity is described in terms of order. Elliptic and hyperbolic geometries are derived from real projective geometry by specializing an elliptic or hyperbolic polarity which transforms points into lines (in two dimensions) or planes (in three dimensions) and vice versa.

Mathematical Fallacies, Flaws, and Flimflam
  • Edward J. Barbeau
  • Published by:
    Mathematical Association of America
    Published online:
    05 December 2013
    Print publication:
    01 January 2000
  • Through hard experience, mathematicians have learned to subject even the most evident assertions to rigorous scrutiny, as intuition and facile reasoning can often lead them astray. However, the impossibility and impracticality of completely watertight arguments make it possible for errors to slip by the most watchful eye. They are often subtle and difficult of detection. When found, they can teach us a lot and can present a real challenge to straighten out. Presenting students with faulty arguments to troubleshoot can be an effective way of helping them critically understand material, and it is for this reason that I began to compile fallacies and publish them first in the Notes of the Canadian Mathematical Society and later in the College Mathematics Journal in the Fallacies, Flaws and Flimflam section. I hoped to challenge and amuse readers, as well as to provide them with material suitable for teaching and student assignments. This book collects the items from the first eleven years of publishing in the CMJ. One source of such errors is the work of students. Occasionally, a text book will weigh in with a specious result or solution. Nonprofessional sources, such as newspapers, are responsible for a goodly number of mishaps, particularly in arithmetic (especially percentages) and probability; their use in classrooms may help students become critical readers and listeners of the media. Quite a few items come from professional mathematicians. The reader will find in this book some items that are not erroneous but seem to be. These need a fuller analysis to clarify the situation. All the items are presented for your entertainment and use. The mathematical topics covered include algebra, trigonometry, geometry, probability, calculus, linear algebra, and modern algebra.

More Fallacies, Flaws, and Flimflam
  • Edward J. Barbeau
  • Published by:
    Mathematical Association of America
    Published online:
    05 December 2013
    Print publication:
    01 November 2013
  • Here is another collection of Fallacies, Flaws and Flimflam, mostly drawn from the column of this name in the College Mathematics Journal between 2000 and 2008. As in the first volume, there is a variety of items ranging from howlers (outlandish procedures that nonetheless lead to a correct answer) to errors that are deep or subtle often made by strong students. While some are provided for entertainment, others offer a challenge to the reader to determine exactly where things go wrong. There are many proposals to improve the quality of mathematics education, but they seldom address the need for students to pay careful attention to what they do and to check their work. It is through an engagement with meaning that students can avoid the pitfalls that come too naturally. Accordingly, this volume should be useful to teachers at all levels by giving them examples of flawed work they can use in the classroom. Encouraging students to find where someone else went wrong may help them avoid similar errors in the future. The items are sorted according to subject matter. Elementary teachers will not find much of use beyond Chapter 1, while middle and secondary teachers will find items in Chapters 1, 2, 3, 7, 8 that they might use. College teachers should find material in every part of the book. The mathematical topics covered include arithmetic, algebra, trigonometry, geometry, combinatorics, probability, and calculus.

Six Sources of Collapse
  • A Mathematician's Perspective on How Things Can Fall Apart in the Blink of an Eye
  • Charles R. Hadlock
  • Published by:
    Mathematical Association of America
    Published online:
    05 April 2013
    Print publication:
    15 December 2012
  • Beginning with one of the most remarkable ecological collapses of recent time, that of the passenger pigeon, Hadlock goes on to survey collapse processes across the entire spectrum of the natural and man-made world. He takes us through extreme weather events, technological disasters, evolutionary processes, crashing markets and companies, the chaotic nature of Earth's orbit, revolutionary political change, the spread and elimination of disease, and many other fascinating cases. His key thesis is that one or more of six fundamental dynamics consistently show up across this wide range. These six sources of collapse can all be best described and investigated using fundamental mathematical concepts. They include low probability events, group dynamics, evolutionary games, instability, nonlinearity, and network effects, all of which are explained in readily understandable terms. Almost the entirety of the book can be understood by readers with a minimal mathematical background, but even professional mathematicians are likely to get rich insights from the range of examples. The author tells his story with a warmly personal tone and weaves in many of his own experiences, whether from his consulting career of racing around the world trying to head off industrial disasters to his story of watching collapse after collapse in the evolution of an ecosystem on his New Hampshire farm.

In the Dark on the Sunny Side
  • A Memoir of an Out-of-Sight Mathematician
  • Larry Baggett
  • Published by:
    Mathematical Association of America
    Published online:
    05 November 2012
    Print publication:
    30 September 2012
  • Misfortune struck one June day in 1944, when a five-year-old boy was forever blinded following an accident he suffered with a paring knife. Few people become internationally recognized research mathematicians and famously successful university professors of that erudite subject, and not surprisingly a minuscule number of those few are visually impaired. In the Dark on the Sunny Side tells the story of one such individual. Larry Baggett was main-streamed in school long before main-streaming was at all common. On almost every occasion he was the first blind person involved in whatever was going on - the first blind student enrolled in the Orlando Public School System, the first blind student admitted to Davidson College, and the first blind doctoral student in mathematics at the University of Washington. Besides describing the various successes and failures Baggett experienced living in the dark on the sunny side, he displays in this volume his love of math and music by interspersing short musings on both topics, such as discussing how to figure out how many dominoes are in a set, the intricacies of jazz chord progressions, and the mysterious Comma of Pythagoras.

Sophie's Diary
  • A Mathematical Novel
  • Dora Musielak
  • Published by:
    Mathematical Association of America
    Published online:
    05 June 2012
    Print publication:
    15 April 2012
  • Sophie's Diary: A Mathematical Novel is a work of fiction inspired by French mathematician Sophie Germain. It chronicles the coming of age of a teenager learning mathematics on her own, growing up during the most turbulent years of the French Revolution. The fictionalized diary uses mathematics, intertwined with historically-accurate accounts of the social chaos that reigned in Paris between 1789 and 1794, to describe the learning journey of a remarkable girl that became the first and only woman in history to make a substantial contribution to the proof of Fermat’s Last Theorem. Sophie Germain was born in Paris in 1776. Little is known about her childhood or about her initiation into mathematics. Her first biographers wrote that, as a young woman, she assumed the name of a male student at the Ecole Polytechnique to submit her own work to Lagrange. Yet, no biography has explained how Germain studied mathematics before that time to encourage such boldness. Sophie's Diary is an attempt to put in perspective how a self-taught girl could have acquired the knowledge to enter the world of Lagrange's analysis.

Calculus and Its Origins
  • David Perkins
  • Published by:
    Mathematical Association of America
    Published online:
    05 April 2012
    Print publication:
    15 February 2012
  • Calculus and Its Origins is primarily a collection of results that show how calculus came to be, beginning in ancient Greece and climaxing with the discovery of calculus. Other books have traveled these paths, but they presuppose knowledge of calculus. This book requires only a basic knowledge of high school geometry and algebra. Exercises introduce further historical figures and their results, and make it possible for a professor to use this book in class.

A Mathematician Comes of Age
  • Steven G. Krantz
  • Published by:
    Mathematical Association of America
    Published online:
    05 March 2012
    Print publication:
    15 December 2011
  • A Mathematician Comes of Age discusses the maturation process for a mathematics student. It describes and analyzes how a student develops from a neophyte who can manipulate simple arithmetic problems to a sophisticated thinker who can understand abstract concepts, can think rigorously, and can analyze and manipulate proofs. Most importantly, mature mathematics students can create proofs and know when the proofs that they have created are correct. Mathematics is distinct from other disciplines in the nature of its intellectual development. The book lays out these differences and discusses their significance.

Sherlock Holmes in Babylon
  • And Other Tales of Mathematical History
  • Edited by Marlow Anderson, Victor Katz, Robin Wilson
  • Published by:
    Mathematical Association of America
    Published online:
    05 January 2012
    Print publication:
    01 August 2003
  • This book is a collection of 44 articles on the history of mathematics, published in MAA journals over the past 100 years. Covering a span of almost 4000 years, from the ancient Babylonians to the eighteenth century, it chronicles the enormous changes in mathematical thinking over this time, as viewed by distinguished historians of mathematics from the past (Florian Cajori, Max Dehn, David Eugene Smith, Julian Lowell Coolidge, and Carl Boyer etc.) and the present. Each of the four sections of the book (Ancient Mathematics, Medieval and Renaissance Mathematics, The Seventeenth Century, The Eighteenth Century) is preceded by a Foreword, in which the articles are put into historical context, and followed by an Afterword, in which they are reviewed in the light of current historical scholarship. In more than one case, two articles on the same topic are included, to show how knowledge and views about the topic changed over the years. This book will be enjoyed by anyone interested in mathematics and its history—and in particular by mathematics teachers at secondary, college, and university levels.

Mathematics in Historical Context
  • Jeff Suzuki
  • Published by:
    Mathematical Association of America
    Published online:
    05 January 2012
    Print publication:
    03 January 2011
  • What would Newton see if he looked out his bedroom window? Mathematics in Historical Context describes the world around the important mathematicians of the past, and explores the complex interaction between mathematics, mathematicians, and society. It takes the reader on a grand tour of history from the ancient Egyptians to the twentieth century to show how mathematicians and mathematics were affected by the outside world, and at the same time how the outside world was affected by mathematics and mathematicians. Part biography, part mathematics, and part history, this book provides the interested layperson the background to understand mathematics and the history of mathematics, and is suitable for supplemental reading in any history of mathematics course.

Mathematical Reminiscences
  • Howard Eves
  • Published by:
    Mathematical Association of America
    Published online:
    05 January 2012
    Print publication:
    30 June 2001
  • Long known as a mathematical storyteller, Howard Eves here writes his personal reminiscences—mostly mathematical, some not. The cast of characters includes Albert Einstein, Norbert Wiener, Julian Lowell Coolidge, Maurice Fréchet, Nathan Altschiller-Court, G. H. Hardy, and many other interesting figures whom he encountered in a long and active life in mathematics. In Mathematical Reminiscences we read of Eves' famous mathematical museum, with its lock of Einstein's hair, Hardy's scarf, Veblen's bright yellow lead pencil, Wiener's hat, and much, much more.

Beautiful Mathematics
  • Martin Erickson
  • Published by:
    Mathematical Association of America
    Published online:
    05 January 2012
    Print publication:
    01 December 2011
  • Beautiful Mathematics is about beautiful mathematical concepts and creations. Mathematical ideas have an aesthetic appeal that can be appreciated by those who have the time and dedication to investigate. Mathematical topics are presented in the categories of words, images, formulas, theorems, proofs, solutions, and unsolved problems. Readers will investigate exciting mathematical topics ranging from complex numbers to arithmetic progressions, from Alcuin's sequence to the zeta function, and from hypercubes to infinity squared. Do you know that a lemniscate curve is the circular inversion of a hyperbola?   That Sierpiński’s triangle has fractal dimension 1.585… .?   That a regular septagon can be constructed with straightedge, compass, and an angle trisector?   Do you know how to prove Lagrange’s theorem that every positive integer is the sum of four squares?   Can you find the first three digits of the millionth Fibonacci number?  Discover the keys to these and many other mathematical problems.  In each case, the mathematics is compelling, elegant, simple, and beautiful. Who should read Beautiful Mathematics? There is something new for any mathematically-minded person. High school and college students will find motivation for their mathematical studies. Professional mathematicians will find fresh examples of mathematical beauty to pass along to others. Within each chapter, the topics require progressively more prerequisite knowledge. An appendix gives background definitions and theorems, while another gives challenging exercises (with solutions).

Harmony of the World
  • 75 Years of Mathematics Magazine
  • Edited by Gerald L. Alexanderson
  • Assisted by Peter Ross
  • Published by:
    Mathematical Association of America
    Published online:
    05 January 2012
    Print publication:
    01 June 2007
  • Who would expect to find in Mathematics Magazine an interview by Mike Wallace of 60 Minutes of a 12-year-old boy in New York who had published an article on a number system with an irrational base and who would go on to a significant career as a professor of mathematics at the University of California, Berkeley? And who would expect to find in the pages of the Magazine the first full treatment of one of the more important and oft-cited twentieth century theorems in analysis, the Stone-Weierstrass Theorem-in an article by Marshall Stone himself. Where else would one look for proofs of trigonometric identities using commutative ring theory? Or one of the earliest and best expository articles on the then new Jones knot polynomials, an article that won the prestigious Chauvenet Prize? Or an amusing article purporting to show that the value of phas been time dependent over the years? This and much more is in this collection of the 'best' from Mathematics Magazine. The list of authors is star-studded: E.T. Bell, Otto Neugebaur, D.H. Lehmer, Morris Kline, Einar Hille, Richard Bellman, Judith Grabiner, Paul Erdös, B.L. van der Waerden, Paul R. Halmos, Doris Schattschneider, J.J. Burckhardt, Branko Grübaum, and many more. Eight of the articles included have received the Carl L. Allendoerfer or Lester R. Ford Awards.

500 Mathematical Challenges
  • Edward J. Barbeau, Murray S. Klamkin, William O. J. Moser
  • Published by:
    Mathematical Association of America
    Published online:
    05 January 2012
    Print publication:
    01 June 1995
  • This book contains 500 problems that range over a wide spectrum of areas of high school mathematics and levels of difficulty. Some are simple mathematical puzzlers while others are serious problems at the Olympiad level. Students of all levels of interest and ability will be entertained and taught by the book. For many problems, more than one solution is supplied so that students can see how different approaches can be taken to a problem and compare the elegance and efficiency of different tools that might be applied. Teachers at both the college and secondary levels will find the book useful, both for encouraging their students and for their own pleasure. Some of the problems can be used to provide a little spice in the regular curriculum by demonstrating the power of very basic techniques. This collection provides a solid base for students who wish to enter competitions at the Olympiad level. They can begin with easy problems and progress to more demanding ones. A special mathematical tool chest summarizes the results and techniques needed by competition-level students.

The Words of Mathematics
  • An Etymological Dictionary of Mathematical Terms used in English
  • Steven Schwartzman
  • Published by:
    Mathematical Association of America
    Published online:
    05 January 2012
    Print publication:
    01 June 1994
  • The Words of Mathematics explains the origins of over 1500 mathematical terms used in English. While other dictionaries of mathematics define technical terms, this book concentrates on where those terms came from and what their literal meanings are. The words included here range from simple to advanced. This dictionary is easy to use. Although some of the entries are highly technical, the book explains them in plain English. The introduction gives an overview of how the ancient language known as Indo-European developed into Latin, Greek, French, and English, the languages from which most of our mathematical vocabulary has been derived. Another section discusses the many ways in which mathematicians have borrowed and created their specialized vocabulary over the centuries. A glossary explains historical and linguistic terms used throughout the book.

Proof and Other Dilemmas
  • Mathematics and Philosophy
  • Edited by Bonnie Gold, Roger A. Simons
  • Published by:
    Mathematical Association of America
    Published online:
    05 November 2011
    Print publication:
    03 January 2008
  • Has the advent of computers changed the nature of mathematical knowledge? Should it? Is the importance of proof decreasing? Is there an empirical aspect to mathematics after all? To what extent is mathematics socially constructed? Is mathematics the "science of patterns?" Recently emerging questions like these are discussed in this book along with some recent thinking about classical questions. This book of 16 essays, all written specifically for this volume, is the first to explore this range of new developments in a language accessible to mathematicians. Approximately half the essays were written by mathematicians, and consider questions that philosophers are not yet discussing. The other half, written by philosophers of mathematics, summarize the discussion in that community during the last 35 years. In each case, a connection is made (in the article itself, or in its introduction) to issues relevant to the teaching of mathematics.

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