Book Reviews

'For Christ's sake don't let's discuss reviews and reviewers. They're the most boring subject on earth. I expect I'll be writing just the same sort of crap myself after a week or two.'

Anthony Powell Books Do Furnish a Room, p. 112 4th Movement in A Dance to the Music of Time University of Chicago Press, 1995

 Roberto Casati and Achille Varzi

Indeed, is it possible to miss the New Year moment? The question is not meant to account for a possible tragic circumstance and is being asked plainly and candidly. Assuming you are in good health on December 31 of one year and remain healthy on January 1 of the next year, is it possible to have missed the New Year moment?

The answer is Yes, and a delightful book Insurmountable Simplicities by Roberto Casati and Achille Varzi, shows how this may happen. Imagine boarding a plane flying from New York to London some time on a New Year's eve, say 10:45 pm. It may so happen that an hour later at 11:45 pm the plane will cross the boundary of a time zone, such that instantaneously you would find yourself in the 00:45 am time zone. Simple? Still curious - the tricks the presence of time zones may play with an uninitiated.

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 William J. Cook

It's a rare pleasure to get a good book ahead of its planned publishing date. In Pursuit of the Traveling Salesman by William Cook that was expected at the beginning of 2012, was delivered yesterday right to my door. My first impression is that this is the sort of a book that are read in one sitting, from cover to cover. The book is clearly intended for the "general audience" and is sweetly written. The author has an obvious writer's streak.

The book narrates the history of the so called "Traveling Salesman Problem", TSP for short. Occasionally (and rather suitably for Christmas time) it is also known as the Santa Claus Problem. In its TSP incarnation, the problem is to find the shortest route that passes through a given number of cities. For Santa Claus it may be important to make the planned visits in the shortest time possible. When it comes to drilling points of contact on a printed board or a computer chip, it's crucial - to make the cheaper chips - that the robot arm that drills the holes moves in a shortest possible path.

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 by C. T. Salkind (I-II), J.M. Earl (III), R. A. Artino et al (IV)

When I was a school boy in Moscow in the 1960s, there were two mathematical olympiads that addressed different audiences of school children. The Moscow City Mathematical Olympiad was intended to attract a broad stratum of middle and high school students. The Moscow State University Mathematical Olympiad was intended for brighter students with interest in mathematics. Problems at the City Olympiad required fluency in the school curriculum and some of them a little ingenuity; all the problems at the University Olympiad went beyond the curriculum and could only be solved with talent and practiced ingenuity. The winners of the latter received certificates and mathematical books - the higher the achievement, the more books have been awarded. A special committee selected the team for the International Olympiad from among the University Olympiad winners. The winners of the City Olympiad received recognition in the form of official certificates and a due respect from their school mates and administration. The participants in the University Olympiad would usually take part in one or two math circles of which there were many; one run by the graduate students at the Mathematics Department of the Moscow State University. The City Olympiad had two streams, one for the middle, the other for the high school. The University Olympiad, while open to all, was realistically intended for high school students.

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 Joseph O'Rourke

How To Fold It is a splendid little book that grew out of the more demanding monograph Geometric Folding Algorithms by J. O'Rourke and E. Demaine. According to the author, both of them had experience presenting aspects of the material in the monograph at various educational levels - from fifth grade to high school. Both found that the tangibility of the topics made them accessible through physical intuition. The book is - in my view - a very successful attempt to capitalize on the readers' intuition in introducing several beautiful facets of contemporary mathematics.

The book, however, should not be perceived as a collection of hands-on activities, nor could it. The author successfully weaves a synergetic combination of do-it-yourself activities and see-why-it-works theory. The do-it-yourself portions could be performed by middle schoolers; and so might some of the mathematical expositions which never require experience beyond common high school curriculum. The author goes to a considerable length to make the book accessible to a broad audience. Some of the ancillary mathematics - vectors, mathematical induction, triangle inequality, the theorem of the incidence of the angle bisectors in a triangle, convexity - are conveniently framed in blue boxes and stand out to be easily found or skipped, depending on the reader's level.

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 Ivan Moscovich

Ivan Moscovich, the author of the two books under review is a well known and much respected puzzlist and toy creator. The books - one of which first appeared in 1994, the other in 2004 - have been recently republished by Dover. Both books are lavishly and beautifully illustrated in full color and would make a memorable present.

Both books are more than mere collections of puzzles. Most of the puzzles are preceded with background information that sometimes is sufficiently comprehensive to occupy a whole page or two. The reader is treated to the shapes of planetary trajectories, a short biography of Leonardo da Vinci, and that of Leonardo of Pisa; the ideas of mechanical linkages and sphere packing; the Golomb rulers; paper-and-pencil games; and the Ramsey theory. The breadth of the collections and occasional depth are quite staggering.

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 Dierk Schleicher and Malte Lackmann

This little book - An Invitation to Mathematics edited by D. Schleicher and M. Lackmann - is a delightful collection of articles from 14 leading mathematicians, each introducing a direction of current mathematical research. The remarkable aspect of all the articles is that they all start at a level that could be appreciated by a curious high school student and then gently lead the reader to the frontiers of the Unknown.

The book is an outgrowth of the events that took place in Germany in 2009 at the 50th International Mathematical Olympiad. During the celebrations of the 50th anniversary six former IMO gold medalists (Béla Bollobás, Timothy Gowers, László Lovász, Stanislav Smirnov, Terence Tao, Jean-Christophe Yoccoz) were invited to give presentations about mathematics, their personal IMO experiences, and their research. All six had accepted the invitations, and their talks have been included in the golden IMO jubilee and the present volumes. Three other contributions (Michael Stoll, Marcel Oliver, Dierk Schleicher) have their roots at the IMO 2009. They grew out of the talks given to the contestants while the solutions were being evaluated. As the editors observe, Whatever their inspirations, all the contributions (to the present book) were specifically written for this occasion.

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 John MacCormick

Computing is transforming our society in ways that are as profound as the changes wrought by physics and chemistry in the previous two centuries. Indeed, there is hardly an aspect of our lives that hasn't already been influenced, or even revolutionized, by digital technology. Given the importance of computing to the modern society, it is therefore somewhat paradoxical that there is so little awareness of the fundamental concepts that make it all possible. The study of these concepts lies at the heart of the computer science, and this new book by MacCormick is one of the relatively few to present them to a general audience.

Chapter-by-chapter, the book covers search engine indexing, the PageRank algorithm, public key cryptography, error-correcting codes, pattern recognition, data compression, databases. These are followed by a general discussion on the limitations and the mundane performance of computers.

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 Donald J. Albers and Gerald L. Alexanderson

This is a beautifully illustrated collection of interviews and biographical etudes of 16 mathematicians of different backgrounds, varied professional interests, diverse level of achievement - all incredibly interesting as human beings. The sixteen interviewees lived and were active in the 1900s, though some are yet alive; the stories throw light - if only in the form of personal perspectives - on many aspects, events and personalities of the 20th century.

Lars Albers came first to the US at the time of the Great Depression (find out how much a Harvard professor was making at the time,) but then at the outset of the WWII felt that his place was at home when his country - Finland - was at war. Towards the end of the war the moods had changed and he and his family were secretly flown to Scotland by the British.

Tom Apostol was the first-born of an immigrant shoemaker father and a mail-order bride. During the Depression his mother took in laundry to help out but also in exchange for piano lessons for him and his sister.

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 P. Diaconis and R. Graham

Many book authors end their book Introduction expressing the hope that readers will enjoy reading the book as much as the author(s) enjoyed writing it. Persi Diaconis and Ron Graham do not. Nonetheless, their book - Magical Mathematics - oozes their enjoyment at writing it. The authors are master storytellers. Movingly, Martin Gardner wrote Foreword in April 2010 - probably just a month before he died - where he highly praised the book.

The book is about mathematics of some card tricks, shuffling and juggling. Curiously, one of the authors started his career as a magician, the other as a juggler. Both were drawn into mathematics while in search of explanation for the artistic acts.

After proving the book's first theorem that explained the workings of a card trick in Chapter 1, the authors remarked,

Did the proof we just gave ruin the trick? For us, it is a beam of light illuminating a fuzzy mystery. It makes us just as happy to see clearly as to be fooled.

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 Dusan Djukić et al

The IMO Compendium is in its second edition; the first one appeared in 2006 and covered problems from the Intenational Mathematical Olympiads starting with the very first one (1959) through the 45th IMO (2004). The new edition adds 143 problems submitted in the following 5 years, 2005-2009.

The selection of the problems for an olympiad proceeds in several steps. To start with, the participating countries send their proposals to the IMO organizers. These form the so-called long-listed problems. The Problem Committee selects some of the long-listed problems to submit to the IMO Jury that consists of team leaders. These problems are known as short-listed. From the short-listed problems the Jury chooses 6 problems for the IMO. For most olympiads run in the 1960-1980s, the book includes long-listed, short-listed and the olympiad problems. Starting with 1993, only short-listed (which still form a long list) and olympiad problems have been included. This explains the enormous size of the collection and the strange number - 143 - by which the second edition of the book differs from the first one. All short-listed (in particular, the olympiad) problems come with solutions - many with multiple solutions. More ...

 Michel Balinski and Rida Laraki

The new book by Michel Balinski and Rida Laraki is a veritable encyclopedia of voting methods, even though its declared aim is to advance just one of them - Majority Judgement (MJ). The authors undertake a sweepingly comprehensive effort; not only they introduce and discuss the advantages and drawbacks of their favorite procedure, but also introduce and discuss - for the argument and comparison's sake - the advantages and drawbacks of the competing ones.

The arguments in favor of the MJ are theoretical, empirical and experimental. The author indeed made a thorough study of the voting and grading situations. Chapter 2 is devoted to the social choice methods employed in several countries. In Chapter 7 they gather information on grading used in various competitions: wine contests, figure skating, music contests, and the like. They actually tested their method at the polling stations in the 2007 French presidential election. Their theoretical investigation was even more thorough. Chapters 3-7 cover traditional voting methods and Chapters 17 and 18 the newer approval voting and its extension point-summing methods. One thrust of the investigation is to discern the fallacies built - according to the authors - into the traditional methods. They prove 5 variants of Arrow's Impossibility Theorem and Gibbard-Satterthwaite's theorem as well. The conclusion?. More ...

 Paul H. Nahin

In the preface to his previous book Mrs. Perkins's Electric Quilt author Paul Nahin has advised:

If you think, as I recently heard a TV commentator claim, that you'll save gas by driving as fast as possible because you'll get where you are going sooner, then there is simply no hope for you as an analyst, and you shouldn't buy this book - save the money for the extra gas you'll use!

This advice applies to the book under review which is to a great extent is a continuation of the previous one, with one marked difference.

Concerning the technical side of the books, both deal with mathematics applied to solving physical problems. Nahin includes analysis and calculations that are often skipped over; the level of details reached usually exceeds that of most other books intended for a more or less general audience. More ...

 Keith Devlin

Little is known of the life of Leonardo Pisano that also goes by the names of Leonardo of Pisa and Leonardo Fibonacci. His life has straddled the transition between the 12th and 13th centuries but neither the date of birth or death are known exactly. Leonardo wrote several books in the very first of which Liber Abbaci (dated 1202) he included a recreational puzzle whose solution - the present day Fibonacci numbers - made his name famous in mathematical circles. Fibonacci numbers and the associated Golden Ratio have an uncanny ability to pop up rather unexpectedly in various circumstances. There is even a mathematical periodical (The Fibonacci Quarterly) that is devoted entirely to the properties of the Fibonacci numbers.

Emphatically, Keith Devlin's book is not about the Fibonacci numbers. More ...

 Hans-Dietrich Gronau, Hanns-Heinrich Langmann, Dierk Schleicher

50^th IMO - 50 Years of International Mathematical Olympia is a pleasant, entertaining, and informative volume. This lovely book "is aimed at students in the IMO age group and seeks to demonstrate that mathematics is an active and lively subject, thousands of years old and yet young and fresh, as ever" (Preface). I am pretty sure the book will be enjoyed by a wider audience.

The book lists the organizational structure of the olympiad, its regulations and schedule; the latter in a formal table format followed by the colorful newspaper-style Daily News. Chapter 3 explains the source for the official olympiad poster that showed Gauss' 1820 map of the Kingdom of Hanover. This map - together with Gauss' likeness and an image of a sextant - appears also on the 10 Deutsche Mark bill. Along the way, the chapter outlines several of Gauss' contributions, including the Gaussian curvature being an intrinsic property of a surface and Gauss-Bonnet Theorem on the value of the integral over the surface of the Gaussian curvature (which is 2π for closed oriented surfaces homeomorphic to a sphere.) More ...

 Shai Simonson

Shai Simonson begins his book Rediscovering Mathematics: You Do the Math with A Guide for the Reader and an Introduction: How to Read Mathematics, where he lays out the pedagogy behind the book. He writes,

Math can be hard, the fundamentals challenging, and other pursuits are easier and more fun. So why bother?

Significantly, in the answer, he does not mention the everyday utility of mathematics or its importance flashed out by the 21st century technologies:

The answer is because mathematics is an intrinsically beautiful subject. The study and practice of mathematics can raise your spirits, gladden your heart, and put a smile on your face. More ...

 Zvezdelina Stankova and Tom Rike

Math circles are weekly math programs that attract middle and high school students to mathematics by exposing them to intriguing and intellectually stimulating topics, rarely encountered in classrooms.

Math circles are voluntary, extracurricular, after-school programs. The students who are there are much less likely to be motivated by the need to satisfy an academic requirement, prepare to a career, or enhance resumé. They are, for the most part, there because they love mathematics. The teachers encounter students who are willing and hungry to learn, while students encounter teachers with expertise and enthusiasm far beyond the usual classroom experience. Teachers and students look forward with anticipation to the next meeting. More ...

 A. Soifer

The first edition of the book came out with warm recommendations from Paul Erdös, Branko Grünbaum, and Cecil Rousseau. Rousseau is among 10 top Erdös' coauthors. The Russian translation of Grünbaum's own Etudes in Combinatorial Geometry and in the Theory of Convex Sets was a bestseller among young mathematicians when it appeared in 1971, right when Alexander Soifer was an undergraduate student. (Among other accomplishments B. Grünbaum has distinguished himself by detecting in 1985 a defect in the geometry of the MAA logo that was introduced in 1972.) The first edition of the book received a glowing review from Don Chakerian (The American Mathematical Monthly, Vol. 99, No. 5 (May, 1992), pp. 486-489) More ...

 T. Andreescu, D. Andrica, I. Cucurezeanu

Diophantus' Arithmetica is a collection of problems each followed by a solution. My first thought on picking up a book with the subtitle "A Problem-Based Approach" was that this is quite an appropriate way to treat the Diophantine equations: to follow in the footsteps of Diophantus himself. But the book actually goes beyond the classic format. The statements in the book are of the three sorts: theorems, examples, and exercises and problems. All come with solutions (proofs for the theorems) in the spirit of Diophantus, but the distinction makes it easier for a student to grasp the essential followed up by the first applications and then the means to verify his/her understanding of the material. The book also contains some historical information on Diophantus himself (in Preface), occasional remarks, while, in case of Pell's equations, a whole section in the third chapter offers a historic sketch of the treatment of quadratic equations in integers. More ...

 Marc Frantz & Annalisa Crannell

This is a textbook intended for undergraduated mathematics courses with orientation to fine arts majors.

The mathematical content revolves around two subjects: perspective projection and fractal geometry. The brick-and-mortar topics include 2d and 3d coordinates (Ch 1), similarity (Ch 2), central and inscribed angles (Ch 5), existence of orthocenter (Ch 6), self-similarity (Ch 8) and exponents and logarithms (Ch 9). On these, the authors build an edifice of perspective projection (Ch 1-7), with a spacious attic of fractal geometry (Ch 8-9).

Perspective projection is covered gently and at a considerable length. One-, two-, and three-point perspective drawings are treated in separate chapters and extend to anamorphic art (Ch 7) and painting where a sphere replaces the picture plane (Ch 6). More ...

 C. Alsina and R. B. Nelsen

The aim of this book is to present a collection of remarkable proofs in elementary mathematics (numbers, geometry, inequalities, functions, origami, tilings, ...) that are exceptionally elegant, full of ingenuity, and succinct. By means of surprising argument or a powerful visual representation, we hope the charming proofs in our collection will invite readers to enjoy the beauty of mathematics, to share their discoveries with others, and to become involved in the process of creating new proofs.

I can confidently confirm that the authors have achieved the stated goal admirably. They put together in access of 100 mostly elementary mathematics facts--quite curious in their own right--proved by elegant and often surprising arguments. More ...

 G. Szpiro

Until about 20 years ago, the 1-2 math courses the Liberal Arts majors had to take as a requirement for graduation came traditionally from the Calculus sequence: Precalculus or Calculus I, at best. The dismal retention rate for Calculus topics led to a reevaluation of course offerings. Mathematics does not lack in more current and relevant topics that require minimum preparation and offer insight into the depth and beauty of the subject. Among these are the theories of Social Choice. Voting systems, the problem of seat apportionment in national assemblies, and power and ability to form coalitions among parties and popular representatives became a staple of Liberal Arts Mathematics. George Szpiro's recent book covers in depth the theories of voting and apportionment.

Szpiro's volume is far from being a textbook that usually would include a greater variety of topics, come in sizes that exceed 700-800 pages and at a hefty price in a vicinity of $100, if not more. The book may of course be used as supplement in a Liberal Arts course. Both instructors and students will find it a rich source of information, with a sensibly exhaustive coverage of main topics. But completeness of coverage is not the strongest point of the book. The author skillfully placed the development and evolution of the Social Choice theories in a broad historical context. The book shines in weaving the emergent math theories with historical circumstances. More ...

 P. Lockhart

The best recommendation I can make for a book is to say that every one should own it and read it. Paul Lockhart's A Mathematician's Lament is one such book that I unreservedly recommend to teachers, math educators, state and federal senators and congressmen, parents and even children.

The author decries on the state of math education, focusing on school mathematics. His point of departure is the idea that mathematics is the purest form of art and should be taught as such. What he proposes is not another reform but a revamping of the whole of the educational system. Realizing that the system is part and parcel of the cultural atmosphere, he soberly laments the impossibility of achieving his goal.

However, Paul's view is only partially utopian. A professional mathematician, he left a university professorship to devote himself to teaching K-12 level students. He taught at St.Ann's School in Brooklyn, NY since 2000. In the book he not only offers his passionate critique of the state of education but also shares his experience as a teacher and outlines his view of what teaching of mathematics should be. More ...

 T. Gowers, J. Barrow-Green, I. Leader (eds)

This is an unusual book targeting a broad audience ranging from (even young) fans curious about the present state of mathematics to the professional mathematicians seeking to have a glimpse at the areas of mathematics not directly related to their special interests. The book is unusual in many respects and, first of all, in its composition.

It is not an encyclopedia, but rather like The World of Mathematics by James R. Newman is a huge collection of essays on various aspects of mathematics, its history, important concepts, evolution, including biographies of its movers and shakers and its relevance to and impact on other branches of sciences and human culture. Unlike Newman's book which is a collection of excerpts from mathematical literature, all articles in The Companion have been written specifically for that book. More ...

 Adapted from Russian by Alexander Givental 

The book under review is an expanded translation of a unique phenomenon in the Russian mathematical literature. If nothing else, its staying power may serve an enticement to anyone interested in, or involved with, high school geometry. First published in 1892 by A. P. Kiselev as Elementary Geometry, by 1940 it underwent more than 40 revisions and eventually became a measuring rod for geometry education in Russia against which all other textbooks had to be judged. Its introduction to the English speaking student and teacher is more than welcome. The effort by Professor A. Givental who translated the book from Russian and combined pieces of the many editions of the original deserves a wholehearted recognition and sincere praise.

The early history of the book is murky. In the Tsarist Russia Kiselev's Geometry competed successfully against other textbooks. Its 23nd (1914) is available online. The upheaval of 1917 brought an overhaul of the education system based more on revolutionary zeal than on evolutionary societal demands. More ...

 Adapted from Russian by Alexander Givental 

The Stereometry book adapted from Russian by A. Givental is the second part of the legendary Kiselev's Geometry. It first appeared in 1892 as a second half of a single textbook and, for a long time, the two co-existed between the same covers. Indeed, the idea of a plane was introduced on page 1 while the last chapter of the book (that followed the stereometry part) was devoted to the geometric constructions in two dimensions. Kiselev's Geometry has demonstrated an unusual staying power, being in an uninterrupted circulation for a good part of a century. (For the historic outline, see the review of the first part.) As a matter of fact, the first part of the book met with stiffer competition so that, while its rule was weakened in the 1960s, the second part reigned in the textbook market well into the 1970s.

The combined 1980 edition came out under the title Elementary Geometry for teacher colleges with a Forward by A. N. Tikhonov who observed, albeit with some reservations, that the pedagogical mastery with which the book was written, the simplicity and consistency of the exposition, kept the book from becoming obsolete. More ...

 Ron Aharoni

The book is an outcome of a rare experiment: an university math professor (a high caliber professor at that from one of the best universities in the world) who has responded to a challenge to teach in elementary school shares the acquired insights about teaching young children and their mathematics. The book is a very enjoyable read, the advice proffered is sound, the pedagogy is illustrated by numerous examples. I highly recommend the book to the grown ups concerned with young children education. (The subtitle A Book for Grownups about Children's Mathematics reflects better than the title Arithmetic for Parents on the intended audience.)

The book includes Foreward, Introduction, three Parts (Elements, Principles of Teaching, Aritmetic from First to Sixth Grades) and an Appendix. In the Foreward, the author explains the structure of the book ... More ...

 Jerry Slocum and Dic Sonneveld 

The book adds intrigue to the humanistic background of Sam Loyd's puzzle: as the authors have found, Sam Loyd has not invented the puzzle, but managed to fool the contemporaries and following generations into believing otherwise. It took five quarters of a century for the truth to be revealed. By painstakingly wading through thousands of newspapers found in dozens of locations throughout the United States and Europe, the authors uncovered the true origins of the puzzle and its winding itinerary to the market and into the history.

The book itself is of the gift quality, well written and exquisitely illustrated. The text is authenticated with photographs and newspaper clips. Interspersed among bits and pieces related to the puzzle, many illustrations build up the historic background and help recreate and sense the cultural atmosphere of the last two decades of the 19^th century. More ...

 Chris K. Caldwell, G. L. Honaker Jr.

This is a dictionary of prime number trivia, an eclectic collage of miscellaneous facts. A few of these tidbits have deep mathematical significance, but many are simple observations which require no mathematics.

For example, in what year did England make it illegal to jail a jury for returning the "wrong" decision? What was Jenny's phone number in Tommy Tutone's hit song? What is the highest number of votes a candidate received for the U.S. Presidency while incarcerated? The answers are all prime, and in this book. Other results are quasi-mathematical, such as those having to do with the shape or representation of a number. Consider the prime 18181: This number is the same forwards, backwards, and even upside down--do you know how many of these primes there are? Can a prime be small and even, and at the same time, large and odd? More ...

 G. Suri and H. Singh Bal 

A mathematical novel!

Is this a new genre? Is there any justification for such a subtitle? Well, this is a novel and a novel with a captivating plot at that. Then it is also a book about mathematics, about its philosophy, its beauty and about its relevance to the human understanding of the surrounding world. There is not a page where mathematics or mathematicians are not mentioned. Mathematics is woven inextricably into the story line itself and I would say that the plot evolves with the mathematical precision.

The story begins with a nostalgic flashback experienced by the main character, Ravi Kapoor, to the time his mathematician grandfather gave him a math problem to try on a calculator. The manner in which the problem was given suggests gentleness in the grandfather's relationship with his grandson and appreciation of the magical effect a solution might have on the boy. The grandfather died the next day, but the reader is left with the realization of the importance the memory of the grandfather played in Ravi's life. It is noteworthy that in the absence of the grandfather's wise guidance the boy grows indifferent to mathematics. More ...

 Arturo Sangalli

A mathematical mystery

Pythagoras - a mystic, a philosopher, a brilliant mathematician, a secretive, religious leader - who lived 2500 years ago left no written work and still his name is remembered today as it is sure to be remembered yet for many generations to come. Who did not hear of the Pythagorean theorem, a theorem that fascinated young children, mature mathematicians and grown-ups from all walks of life, the US presidents included? A theorem that gathered more proofs that any other known to the mankind. Such a man left no written works, or so we learn from history books. But what if? What if a man like that were to write a book? What mystery, what message to the future generations would it contain? Just try to don Pythagoras' hat and put on his shoes, or rather sandals. This probably what the author Arturo Sangalli did when devising a plot that spans 2500 years of history.

A math Ph.D. and a freelance science author, Sangalli weaves a story in which mathematics places an integral part. More ...

 Fukagawa Hidetoshi and Tony Rothman

A result of an unusual collaboration of two authors who never met, this is a glamorous book which will be treasured by all mathematics fans and especially by lovers of geometry.

The period that began in the early seventeenth century and lasted a little past the mid-nineteenth holds fascination for any student of Japanese history. During this period of roughly 200 years the country was almost entirely closed to foreign influence; travel to and from the West was banned and considered a capital offence. Trade with the West was channeled through the man-made miniature island of Deshima in Nagasaki harbor. (However, trade with China and Korea was not so obstructed.) Deshima was surrounded by a wall and joined to the mainland by a guarded bridge. More ...

 Joseph Mazur

The book which I enjoyed reading left me with a mixed feeling. For, it reminded me of a homeschooling mother who assigned her children to learn by heart a list of words that they should not be using. The author powerfully and passionately forwards the thesis of utter unreasonableness of the expectations to win and the sense of control over one's fortunes and fate commonly proclaimed by individual gamblers. The author is quite unequivocal and outspoken about gambling being obsessive and destructive. And yet the reader gets so much information about the gambling and specifics of the games that it undoubtedly might compete with other volumes exclusively devoted to presenting particular games.

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 B. S. Everitt & A. Skrondal

I am glad to have this handy reference on my bookshelves. The fourth edition has been revised and expanded; in its present state the book is a reasonably complete collection of definitions, with a good deal of illustrations, examples, formulas and equations where necessary. Also included are short biographies of mathematicians and statisticians who made an impact on the development of theory of probability and statistics. The book also contains descriptions of pertinent software packages. Almost all entries have source references to follow up if so desired.

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 William Dunham

Have you ever tried to plough through the early Calculus texts, say, those of the founding fathers, I. Newton and G. W. Leibniz? Truly, this undertaking is not for a light hearted. Derek Whiteside, editor of Newton's mathematical papers, aptly characterized a proof that the area under the graph of y = x^m/n is (m + n)/n x^{(m + n)/n} as "a brief, scarcely comprehensible appearance of fluxions" [Dunham, p. 15] ...

Come The Calculus Gallery: Masterpieces from Newton to Lebesgue by William Dunham, the master storyteller. More ...

 Ross Honsberger (editor)

Mathematical Plums is the fourth book in the Dolciani Mathematical Expositions series. The first three have been authored by Ross Honsberger; for this one, he served as an editor. The book consists of 10 chapters by various authors. The chapters are absolutely independent; some have been probably plucked by Honsberger from periodical publications, some may have been written specifically for the book. I can't say. Except for the Chapters 3, 8, and 10 by R. P. Boas that at least partly came from the MAA magazines, and Chapter 9 that grew out of the notes Honsberger took at a lecture given by A. W. Tucker, I am not aware of other sources. More ...

 David Ruelle

A philosopher would like to see how the human mind, or we may say the mathematician's mind, comes to grips with mathematical reality.

My ambition is to present here a view of mathematics and mathematicians that will interest those without training in mathematics, as well as the many who are mathematically literate.

The author achieves the set goal admirably providing a very enjoyable read along the way. At the outset, I was misled by the title into expecting an attempt to explain how a mathematician's mind works. And, in a sense, the reader does get a glimpse into the working of a mathematician's mind, albeit indirectly.

As the author - a notable mathematical physicist, an expert in non-linear dynamics (chaos and turbulence) - wrote in the first chapter... More ...

 K. Bezdek

Discrete and Combinatorial Geometry are two (often interchangeable) designations of a branch of mathematics that deals with finite combinations of geometric objects. If there is any distinction, the appellation "discrete" is associated more with the subject of optimal combinatorics than with the combinatorial questions per se.

I still own a small 1965 paperback Theorems and Problems of Combinatorial Geometry by V. G. Boltyanski and I. Z. Gohberg that I was fascinated with in high school. Most of the problems admitted simple formulations, with a minimum of mathematical jargon, and were of engagingly visual character. The simplicity of the formulations was rather deceptive. Even though the book was intended for high school students, it ended up with a list of unsolved problems. More ...

 H. M. Enzensberger 

Hans Magnus Enzensberger is a well known German poet and essayist, author of The Number Devil which is, in my view, one of the best mathematics books ever written for children. His small book Drawbridge Up: Mathematics - a Cultural Anathema is based on the invited talk he gave at the 1998 International Congress of Mathematicians in Berlin. In the book, he laments the current state of education whose ills he sees as a cultural phenomenon. Instead of focusing, as quite common, on specific math topics or educational technology, he deplores the culture tolerant of the proud display of innumeracy. Enzensberger's ideas are very close to what I wrote years ago in my Manifesto. The author offer no quick fixes but sees the need in overhaul of the educational framework that confines a teacher to operate at the end of a bureaucratic tether. On the whole, it is a beautifully written essay that should be read and pondered over by all math educators.

 L. Hathout

Crimes and Mathdemeanors is a collection of 14 math problems framed into entertaining yarns featuring a teenage math prodigy Ravi. Each comes that a complete and well explained solution. In every story Ravi manages to reduce a complicated crime to a math problem. Each chapter consists of a story, followed by analysis and motivation for the solution, solution and occasionally extension where the author looks into possible generalizations. Remarkably the author himself is a high school student from California who began participating in math competitions from the age of 9. He won numerous awards in the national competitions and achieved a perfect score at the California Math League exam. The problems are entertaining, explanations clear, and the book is a pleasure to read. The book should inspire a high school student bored with classroom word problems. It is a valuable resource for high school teachers as well.

 T. Andreescu and D. Andrica 

The book reaches to about the same audience of (I quote from the back cover) "undergraduates, high school students and their teachers, mathematical contestants ... and their coaches, as well as anyone interested in essential mathematics," as some other books on the market, notably L.-s. Hahn's Complex Numbers & Geometry from the MAA, with which it has a nonempty overlap, naturally. ... The book is a real treasure trove of nontrivial elementary key concepts and applications of complex numbers developed in a systematic manner with a focus on problem solving techniques. Much of the book goes to geometric applications, of course, but there are also sections on polynomial equations, trigonometry, combinatorics ... More ...

 C. Pritchard 

The book is an expanded collection of 57 articles published in Mathematical Gazette and Mathematics in School — two journals of The Mathematical Association, a British organization for teachers of mathematics — over about one hundred years. The Mathematical Association is the name taken by the Association for the Improvement of Geometrical Teaching in 1897. The latter was created in 1871. At the time, school and university geometry curricula were entirely based on Euclid's Elements and geometry was universally "viewed as the ideal vehicle for developing an understanding of formal proof". More ...

 Paul. J. Nahin 

The book is a collection of 21 essays, each built around one or two probability problems. The author plays with the problems: solving them, modifying them, simulating them on a computer. Indeed simulations constitute a considerable part of the book. (MATLAB scripts take up 65 out of 270 pages, with additional 22 pages devoted to the history and theory of random number generators.) All discussed problems come with solutions - some with solutions at the text proper, some at the end of the book.

Most of the essays follow a definite plan: a problem, its solution, a modification, its solution. More ...

 Paul. J. Nahin 

This is a wonderful book - a sequel to Nahin's earlier An Imaginary Tale: the Story of √-1. This one is more advanced. And the author clearly sets up requirements: "... two years of calculus, a first course in differential equations, and perhaps some preliminary acquittance with matrix algebra and elementary probability. Third year math majors would certainly haev the required background." I would low the bar if a little. An intelligent second year student will enjoy the book, even if it takes a little more effort. Doubt not: the extra effort will pay off.

The scope of the book is astonishing. True, the starting point is indeed the formula e^iπ + 1 = 0 but ... More ...