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Mathematics
... at Amazon.co.uk


Any recommendations about mathematics books have to begin and end with Martin Gardner, who, inspired no doubt by Lewis Carroll, 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 by him or else are edited by him. So, they include David Wells, Keith Devlin, Rudy Rucker, Boris Kordemsky, Ivars Peterson, John Allen Paulos, H.E.Dudeney, Sam Loyd, Simon Singh.
Martin Gardner wrote the column "Mathematical Games" for Scientific American for many years (Paul Erdös' biographer was his editor for a while) before passing the baton on to Douglas Hofstadter, a promoter of Alan Turing's ideas, who scrambled the column into "Metamagical Themas", before in his turn handing over to Ian Stewart.
On the...

Mathematics & Science
... at Amazon.co.uk


... science side of mathematics, Richard Feynman, was winner of the Nobel Prize for Physics in 1965, and also a man who fell, often jumped, into adventure - as artist, safe-cracker, practical joker and storyteller. Amongst other things, James Gleick wrote his biography.
Also writing a column for Scientific American, though more on the...

Mathematics & Computers
... at Amazon.co.uk


... 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
... at Amazon.co.uk


... computers are still the issue, then find out about the Internet, HTML and JavaScript (but don't forget about Martin Gardner).






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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 Alice in Wonderland and Alice Through the Looking Glass

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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..." .
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536536 Curious Problems and Puzzles
Barnes & 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.


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.
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Richard Mankiewicz story of mathematicsThe Story of Mathematics
Cassell. Things might have been different in 3B if this handsome book had been a set text. Gorgeously illustrated, energetically written, full of smart and surprising quotations, it tells the exhilarating history of maths, from Pythagoras to Einstein, from algebra to fractals. But this is more than just a "biography". By interweaving maths and modern art, maths and medieval theology, even maths and Mayan calendrics, author Mankiewicz reveals the underlay of the mathematical tapestry, the sometimes unexpected junctures where mathematics has altered our world view.
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Boris Kordemsky moscow puzzlesThe Moscow Puzzles
Penguin. This book has been a classic in the former Soviet Union since it was first published in 1956, and it remains just as entertaining today. A master at making math fun for his high school students, Boris Kordemsky loaded this clever collection with a wide variety of math and logic related games and puzzles dealing with magic squares, tricky weights and measures, properties of numbers, mathematical tricks, and more. Number and math game fans are bound to find several new amusements here. Even many of the well-known classics from generations past take on new life with the fresh twists Kordemsky provides.
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Ivars Peterson
Read his Mathland archive.
jungles...The Jungles of Randomness: A Mathematical Safari
John Wiley & Sons. We use the word random as though we understood what it meant, but, of course, its superficial meaning only betrays our deep ignorance of what is really going on. Random is mostly used to label anything we can't predict, from the roll of a die to our spouse's next major purchase, but what's actually happening to cause the unanticipated results? Ivars Peterson makes this complexity simple in The Jungles of Randomness.
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Paul Erdös
Erdös wrote a huge number of significant papers about mathematics. See the Erdös Number Project for more.
the man who... The Man Who Loved Only Numbers
Fourth 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.
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also by Paul Hoffman...
Arcimedes Revenge
Penguin. A collection of articles on the highways and byways of mathematics. The book is written in the tradition of Martin Gardner and aims to be both entertaining and fascinating.
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Alan Turing
Alan Turing (1912 - 1954) was a British mathematician who made history: His breaking of the German U-boat Enigma cipher in World War II ensured Allied-American control of the Atlantic. Visit Andrew Hodges' website devoted to the ideas of Alan Turing. Visit also this java implimentation of the Enigma machine itself.
alan turing Alan Turing: the Enigma
Vintage. A biography by Andrew Hodges. Alan Turing was a brilliant Cambridge mathematician who has been described as the father of the modern computer. He masterminded the cracking of the German Enigma code and was caught up in the secrecy and bureaucracy of World War II and afterwards - continually frustrated in his desire to build a machine which could think, as those with power over him feared both his homosexuality and indiscretion. This is an account of his life, which ended by his own hand.
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John Allen Paulos
Innumeracy
Penguin. This is the book that made "innumeracy" a household word, at least in some households. Paulos admits that "at least part of the motivation for any book is anger, and this book is no exception. I'm distressed by a society which depends so completely on mathematics and science and yet seems to indifferent to the innumeracy and scientific illiteracy of so many of its citizens".
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A Mathematician reads the Newspaper
Penguin. In this book the author reveals the hidden mathematical angles in countless media stories. His real life perspective on the statistics we rely on and how they can mislead is for anyone interested in gaining a more accurate view of their world.
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Peter M. Higgins
maths for the curiousMathematics for the Curious
Oxford University Press. When do the hands of a clock coincide? How likely is it that two children in the same class will share a birthday? Should you play Roulette or the Lottery? How do we calculate the volume of a doughnut? Why does the android Data in "Star Trek" lose at poker? What is Fibonacci's Rabbit Problem? Many things in the world have a mathematical side to them, as revealed by the puzzles and questions in this book. It is written for anyone who is curious about mathematics and would like a simple account of what it can do. Peter Higgins provides clear explanations of the more mysterious features of childhood mathematics as well as novelties and connections to prove that mathematics can be enjoyable and surprising.
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Robert Kaplan
Notes on the text are at oup-usa
maths for the curiousThe Nothing That Is
Penguin. Unlike the so-called natural numbers like one, two, three and so on, the origins of zero are incredibly hard to pin down. Humans seem to have done quite well without nothing for tens of thousands of years: not even the Greeks, the master mathematicians of the Ancient World, had a symbol for zero. Or did they? Among the many delights of this book is the way Kaplan reveals the twists and turns in the story of the origin of the symbol for zero and his own suggested resolution of the mystery.
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art of the infiniteThe Art of the infinite
This accessible work aims to inspire the general reader with the wonder and beauty of mathematics - our first native language. To savour mathematics is to feel the same exhilaration that great music inspires - the wonder that something invented by humans is also timeless. The text starts from the basics, moving systematically to the frontiers of the topic. The authors draw on science, literature, history, biography and philosophy, clarifying the knowledge that patterns of mathematics are everywhere.
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Cundy & Rollett Mathematical Models
Tarquin Publications. How to make a wide variety of models, including Archimedean and Stellated polyhedra.
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Seymour Papert
Seymour Papert Ph.D. was arguably the first to recognize and articulate how computers could fundamentally revolutionize education. Visit his own site at www.papert.com
mindstormsMind-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.
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Abelson and diSessa Turtle Geometry
MIT Press. Described on its cover as being about "the computer as a medium for exploring mathematics"; it is an in depth look at the use of the logo language.
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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.
mandelbrot 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.
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fraxctals, graphics and mathematics educationFractal Geometry of Nature In 19 papers from a December 1997 conference at Yale University, teachers mostly of mathematics explain how they teach fractals, in order to help develop a set of common elements by which others may do the same without having to make it up all over each time.
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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.
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Peitgen & Richter beauty of fractalsThe Beauty of Fractals
Springer-Verlag. One of the essential reference books on fractals. The authors present an unusual attempt to publicize the field of Complex Dynamics, an exciting mathematical discipline of respectable tradition that recently sprang into new life under the impact of modern computer graphics. Where previous generations of scientists had to develop their own inner eye to perceive the abstract aesthetics of their work, the astonding pictures assembled here invite the reader to share in a new mathematical experience, to revel in the charm of fractal frontiers.
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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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