'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.'
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 19th century. 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 ...
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 = xm/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 ...
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. 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 eiπ + 1 = 0 but ... More ...
There are many conversations, committee meetings, etc., today about the modernization of the undergraduate calculus course; but all too often the attack on the problem falls short of being comprehensive. So begins a 1958 article Bringing Calculus Up-to-date (AMM, 65 (1958), pp. 81-90) by M. E. Munroe. Too young at the time to be interested in Calculus, I first ran into the article while browsing the first volume of the collection A Century of Calculus. It's a remarkable two-volume set -- a small library in fact. A library of 310 papers selected from the American Mathematical Monthly, Mathematics Magazine and College Mathematics Journal. More ...
The book combines concepts and results from mathematics and computer science related to the generation of sequences by simple computational model called the finite automaton. More ...
The book is intended for teachers of mathematics in professional development and preservice settings. This is one part of a triptych that also includes the Facilitator's Guide and the Further Explorations CD-ROM. In the absence of the latter two pieces, the review relates only to the one book at hand. More ...
This laptop of a handbook is a tremendous collection of 65 articles on discrete and computational geometry. The second edition, at 1539 pages, is more than 500 pages longer than the first. The organization of the book is superb. Each article/chapter begins with an introduction and ends with lists of recommended surveys and related chapters, as well as comprehensive references. In addition, each chapter contains one or more glossaries. More ...
The title of the book, A Course in the Geometry of n Dimensions, is a misnomer on two accounts. First, the book is too small -- 63 pages in all -- for even a 1-semester course. Second, the book is not about geometry per se. A longer title, say, Basic Elements of the Geometry of n-Space and Their Application to the Advanced Theoretical Statistics: An Intuitive Approach, would better relate the contents of the book to a potential reader. But that, of course, would be too long a title for such a small book. More ...
To paraphrase the memorable speech given by Bilbo Baggins on the occasion of his eleventy-first birthday, I liked less than half of the book half as well as it deserves. Let me explain. More ...
... there is nothing in the world of mathematics that corresponds to an audience in a concert hall, where the passive listen to the active. Happily, mathematicians are all doers, not spectators. Doing is much more fun than merely watching or listening, and I celebrate this in the title of the book.
Unfortunately, the celebration does not seem to propagate into the body of the book leaving the title quite detached from the contents and the manner in which the book has been written. More ...
