  This is a growing list of personal recommendations. Do you agree? Please note that none are available direct from MathsNet. Try your normal educational suppliers. To order online, you can shop around. Use the links below or the ordering links given on this page, which are to either the Internet BookShop, Amazon.co.uk, Amazon.com or barnesandnoble.com. Find the cheapest price. |
recommended by MathsNet |
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 Books
You can tell a good book by its cover | School texts |
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| Mathematics Any recommendations about mathematics books have to include Martin Gardner, who, inspired no doubt by Lewis Carroll, in turn has the knack of finding and "collecting" other excellent writers about mathematics. Collecting in the sense that their books will include a commendation on the cover from him or else a foreword or else are edited by him. So, they include David Wells, Keith Devlin, Rudy Rucker, Boris Kordemsky, H.E.Dudeney, Sam Loyd.Martin Gardner wrote the column "Mathematical Games" for Scientific American for many years (Paul Erdös' biographer was his editor for a while) and then passed on the baton to Douglas Hofstadter who scrambled it into "Metamagical Themas", before handing over to Ian Stewart. Also writing a column for Scientific American, though more on the... Mathematics & Computers ... computer side, was A.K.Dewdney, who has written extensively about fractals, as have Clifford Pickover, James Gleick, Peitgen & Richter, Mandelbrot of course, and the creators of the definitive fractal generating program Fractint .More mathematically less computerly, logo has some good books, notably by Papert, Abelson and diSessa, but if... Computers ... computers are still the issue, then find out about the Internet, HTML and JavaScript. |
| Douglas Hofstadter College Professor of Cognitive Science and Computer Science; Adjunct Professor of History and Philosophy of Science, Philosophy, Comparative Literature, and Psychology Ph.D. in physics, University of Oregon, 1975; Pulitzer Prize (General Nonfiction category), 1980, American Book Award (Science Hardback category), 1980, for Gödel, Escher, Bach: an Eternal Golden Braid; Guggenheim Fellow, 1980-81. Visit his homepage |
 Gödel, Escher, BachPenguin. A classic book about mathematics (Gödel), art (Escher) and music (Bach), written in the spirit of Lewis Carroll. A work of art in itself. Everything is a symbol, and symbols can combine to form patterns. Patterns are beautiful and revelatory of larger truths. These are the central ideas in the thinking of Kurt Gödel, M.C. Escher, and Johann Sebastian Bach, perhaps the three greatest minds of the past quarter-millennium. In a stunning work of humanism, Hofstadter ties together the work of mathematician Gödel, graphic artist Escher, and composer Bach. Buy at 
  MetaMagical
ThemasPenguin. This sentence is the first one here that tries to summarise the book's contents. This, the second sentence, continues in the same vein. Questing for the essence of mind and pattern, an interlocking collection of literary, scientific and artistic studies. The title is an anagram of "Mathematical Games". What about this: "This sentence contains exactly threee erors." Buy at
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M.C.Escher
A Dutch graphic artist, most recognized for spatial illusions, impossible buildings, repeating geometric patterns (tessellations), and his incredible techniques in woodcutting and lithography. M.C. Escher was born June 1898 and died March 1972. He was studied and greatly appreciated by respected mathematicians, scientists and crystallographers yet he had no formal training in math or science. He was a humble man who considered himself neither an artist or mathematician. Intricate repeating patterns, mathematically complex structures, spatial perspectives all require a "second look". In Escher's work what you see the first time is most certainly not all there is to see. Visit the World of Escher. Or the Escher Centential Congress In Rome, June 1998 |
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Master Prints Copies of his prints, including many deceptive mathematically based optical illusions (the impossible waterfall, the endless staircase, the Mott The Hoople LP cover!) and illustrations of self-referential concepts (two hands drawing each other). Buy at
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| Martin
Gardner Martin Gardner (1914 - ) was the Mathematical Games columnist for Scientific American. He originated the column in 1956, and his columns appeared until his retirement from the magazine in 1986. He graduated Phi Beta Kappa from the University of Chicago in 1936. Prior to his Navy service in World War II, he was a reporter on the Tulsa Tribune and a staff writer with the University of Chicago Press Relations Department. After the war, he became a freelance writer. His more-than-60 books have served generations of scholars, the merely curious, and serious researchers into esoteric branches of mathematics and "hard" sciences such as physics -- all of whom are astonished to learn that Mr. Gardner has no formal academic status in any of those disciplines. Now ''retired," Martin Gardner turns out ''only two or three" books a year, and shows no signs of decelerating. For a detailed index to 11 of his books see this Gardner index. |
 The Ambidextrous
Universe Penguin. "Is God left-handed?" Martin Gardner takes an entertaining look at one of man's most puzzling questions: Is the universe symmetrical? This book is a popular survey of mirror symmetry (left vs. right) and asymmetry, and the significant roles they play in such diverse fields as mathematics, physics, art, music, poetry, and more! Buy at
Mathematical Puzzles and Diversions Penguin. Buy at
 The Annotated
Alice by Martin Gardner (and Lewis Carroll), Penguin. Summarises the mathematics disguised within the Alice books. The only single-volume edition of Carroll's masterpieces, Alice in Wonderland and Alice Through the Looking Glass, contains the complete text of both works and annotations that highlight the games, references, and parodies in the works. Buy at
Mathematics Magic and Mystery Dover. Why do card tricks work? Or mind-reading tricks? Cards, dice, coins, topological tricks, geometrical vanishing tricks, pure numbers, Moebius strips... and no sleight of hand required. Includes the "divining a number" trick where he asks someone to choose a number between 1 and 10, then gets them to do some mental arithmetic and finally, after asking for NO information from them, tells them what number had been chosen! Buy at
Anything else by Martin Gardner too. |
| Lewis Carroll Charles Dodgson was a mathematics lecturer and author of mathematics books who is better known by the pseudonym Lewis Carroll. Dodgson is known especially for Alice's adventures in wonderland (1865) and Through the looking glass (1872), children's books that are also distinguished as satire and as examples of verbal wit. He invented his pen name by anglicizing the translation of his first two names into the Latin 'Carolus Lodovicus'. The son of a clergyman Dodgson, from 1846 to 1850, attended Rugby School and graduated from Christ Church College Oxford in 1854, coming first in the Finals. Dodgson remained there, lecturing on mathematics and writing treatises and guides for students until 1881. ...excerpts from his biography. |
Alice in Wonderlandand Alice Through the Looking
Glass by
Lewis Carroll. |
Does God play
Dice
The Magical
Maze|
Henry Ernest Dudeney
Born 10 April 1857 in Mayfield,
Sussex, England Died 24 April 1930 in Lewes, Sussex, England. He learnt to play
chess at a young age and became interested in chess problems. From the age of
nine he was composing problems and puzzles which he published in a local paper.
Although he only had a basic education, he had a particular interest in
mathematics and studied mathematics and its history. He began to write articles
for magazines and joined a group of authors which included Arthur Conan Doyle.
He was doing well publishing mathematical puzzles under the pseudonym 'Sphinx'.
Read this biography. |
Amusements in Mathematics Dover. A collection of teasers, first published in 1917. For example"... the twelve ways that eight queens can be placed on a chessboard without attacking one another..." . Buy at
 536 Curious Problems and
PuzzlesBarnes & Noble Books. This book is a compilation of some of Dudeney's most challenging conundrums culled from two printed collections, MODERN PUZZLES and PUZZLES AND CURIOUS PROBLEMS and runs the gamut from arithmetical, algebraic, and geometrical problems to game and domino puzzles, combinatorial and topological problems, and match puzzles. The answer section includes editorial footnotes, which in some instances point out how a solution has been improved or a problem extended by later experts. . Buy at |
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Sam Loyd Sam Loyd (born 31 Jan 1841 in Philadelphia, Pennsylvania , USA, died 10 April 1911 in New York, USA) was America's greatest puzzle expert and invented thousands of ingenious and tremendously popular puzzles. After his death, Loyd's son published the Cyclopedia of Puzzles, a huge collection of Loyd's puzzles which had appeared in various newspapers and magazines over the previous fifty years. Try his 15 puzzle or some other classic puzzles |
Mathematical Puzzles of Sam Loyd Dover. A collection of classic puzzles and teasers. Buy at
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The Moscow
Puzzles| Paul Erdös Erdös wrote a huge number of significant papers about mathematics. See the Erdös Number Project for more. |
 The Man Who Loved Only NumbersFourth Estate. A biography by Paul Hoffman. The story of Paul Erdös, the most prolific and eccentric mathematician of our times, who lived for more than six decades out of two tattered suitaces, and gave his love to numbers and the search for mathematical proof. He published almost 1500 scholarly papers before his death in 1996, and he probably thought more about math problems than anyone in history. Like a traveling salesman offering his thoughts as wares, Erdös would show up on the doorstep of one mathematician or another and announce, "My brain is open." After working through a problem, he'd move on to the next place, the next solution. Buy at
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Rudy Rucker Visit his homepage |
 Infinity and the
MindPrinceton University Press. The Science and Philosophy of the Infinite. Rudy Rucker leads an excursion to that stretch of the universe he calls the "Mindscape," where he explores infinity in all its forms: potential and actual, mathematical and physical, theological and mundane. Here Rucker acquaints us with Godel's rotating universe, in which it is theoretically possible to travel into the past, and explains an interpretation of quantum mechanics in which billions of parallel worlds are produced every microsecond. It is in the realm of infinity, he maintains, that mathematics, science, and logic merge with the fantastic. Using cartoons, puzzles, and quotations to enliven his text, Rucker guides us through such topics as the paradoxes of set theory, the possibilities of physical infinities, and the results of Godel's incompleteness theorems. Buy at
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| Cundy & Rollett |
Mathematical Models Tarquin Publications. How to make a wide variety of models, including Archimedean and Stellated polyhedra. Buy at
Anything published by Tarquin Books. |
The Penguin
Dictionary of Curious and Interesting numbers
The Penguin
Dictionary of Curious and Interesting Geometry
You Are A
Mathematician
Mind-storms,
Harvester Press. All about logo - how it was invented and how it works. A
visionary book that began the computer revolution in schools. The bible of
thousands of teachers who have sought creative ways to use computers in
schools, this book tells the story of the invention of LOGO, the first
child-friendly computer programming language.
Chaos | Benoit B. Mandelbrot Benoit Mandelbrot was largely responsible for the present interest in Fractal Geometry. He showed how Fractals can occur in many different places in both Mathematics and elsewhere in Nature. Born in Poland in 1924. His family emigrated to France in 1936. Benoit attended the Lyce Rolin in Paris, then studied at Lyon, then at the California Institute of Technology in the USA. In 1945 his uncle introduced him to Julia's important 1918 paper as a masterpiece and a potential source of interesting problems, but Mandelbrot did not like it. Instead he chose his own very different course which, however, brought him back to Julia's paper in 1977 after a path through many different sciences which some characterise as highly individualistic or nomadic. ...an excerpt from his biography. |
 Fractal Geometry of Nature W H Freeman & Co. The immortal classic. Imagine an equilateral triangle. Now, imagine smaller equilateral triangles perched in the center of each side of the original triangle--you have a Star of David. Now, place still smaller equilateral triangles in the center of each of the star's 12 sides. Repeat this process infinitely and you have a Koch snowflake, a mind-bending geometric figure with an infinitely large perimeter, yet with a finite area. This is an example of the kind of mathematical puzzles that this book addresses. The Fractal Geometry of Nature is a mathematics text. But buried in the deltas and lambdas and integrals, even a layperson can pick out and appreciate Mandelbrot's point: that somewhere in mathematics, there is an explanation for nature. It is not a coincidence that fractal math is so good at generating images of cliffs and shorelines and capillary beds. Buy at
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| Fractint | Fractal Creations Tim Wegner, Bert Tyler, Waite Group Press. All about fractals, including software (Fractint) and hundreds of high resolution images on CD. See their web-site Buy at |
The Beauty of Fractals 
The Magic
Machine 
200% of Nothing |
Clifford A.
Pickover "My primary interest is finding new ways to continually expand creativity by melding art, science, mathematics and other seemingly-disparate areas of human endeavor. I seek not only to expand the mind, but to shatter it." Cliff Pickover, besides writing popular books about science, computers and computer art, conducts research in the fields of computer graphics and scientific visualization, edits scientific journals, and creates puzzles for Discover magazine. See Clifford A. Pickover's Home Page . |
Computers, Pattern, Chaos, and
Beauty Alan Sutton. Graphics from an unseen world. Buy at
Anything by Clifford A. Pickover. Computers and the Imagination, Alan Sutton. Visual adventures beyond the edge. "In this book, I examine the manifold ways in which computers transform how we both perceive and understand the world around us. Computers and the Imagination includes a range of topics from artificial spider webs, to pain-inducing patterns, to computer-generated poetry. Along the way, I use the computer to gain new insights into the very origins of human creativity. The book includes: computer graphics, strange problems, and startling applications of computer science to art, music, poetry, science, and technology." Buy at |
| The Internet |
The schools' guide to the INTERNET
Peter McBride, Heinemann. Put the Net to work searching, downloading, publishing, emailling. Buy at |
HTML: The Definitive
Guide 
Mastering
JavaScript | And finally | ||
| "The first sign of senility is that a man forgets his theorems, the second sign is that he forgets to zip up, the third sign is that he forgets to zip down." - Stanislaw Ulam |
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