 | "e", The Story of a Number by Eli Maor
Buy used from: £2.89 The first good mathematics book that I read though inferior to Maor's "To Infinity and Beyond". e itself is an excellent book.
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 | Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise by Manfred R. Schroeder
Buy used from: £11.99 Challenging book covering many fascinating ideas, and lots of excellent illustrations, (in no way glossy).
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 | Chaos: Making a New Science by James Gleick
Buy new: £6.47 / Used from: £0.55 Too esoteric to be a popular science book IMO. This is excellent as a history of chaos theory, but scientifically too rushed for readers to gain an appropriate understanding of many concepts.
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 | Mathematics for the Million: How to Master the Magic of Numbers by Lancelot Hogben
Buy used from: £4.93 Perhaps may not fulfil it's goal of teaching maths from scratch nowadays though offers some nice historical mathematical figures such as those geometry ones of Ancient Egypt.
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 | To Infinity and Beyond: A Cultural History of the Infinite (Princeton Paperbacks) by Eli Maor
Buy new: £11.88 / Used from: £6.87 This has proven to be the most excellent popular maths book that I have seen. Particularly notable is the explanation of Cantor's levels of infinity.
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 | Godel, Escher, Bach: An Eternal Golden Braid (20th anniversary edition with a new preface by the author) by Douglas R Hofstadter
Buy new: £13.27 / Used from: £10.25 I agree with the reviews so far, (p250ish), apart from the negative one concerning the quality of this edition: the book is in a good font size/layout/is huge. V.Good value for money.
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 | Taking Chances: Winning with Probability by John Haigh
Buy used from: £2.99 I would recommend this for an interesting look at the applications of the theory of large numbers to games; becomes boring after circa a hundred pages.
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 | The Thirteen Books of The Elements: Volume 1: Books 1 and 2 by Euclid
Buy new: £9.02 / Used from: £5.99 Not the 1414 pages I was expecting; it is actually 432 pages including index etc. Some very nice sections on Greek maths/Euclid's life etc, and lots of nice Greek extracts.
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 | Impossibility: Limits of Science and the Science of Limits by John D. Barrow
Buy new: £6.97 / Used from: £0.91 Myriad open minded, original musings from Barrow. This is a good starting point for his popular science output.
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 | The World within the World (Oxford paperbacks) by John D. Barrow
Buy used from: £0.88 Quite a lot more challenging than Impossibility, attempts a conceptual explanation of relativity among it's very numerous inclusions.
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 | The Book of Nothing by John D. Barrow
Buy new: £6.97 / Used from: £0.15 I bought this about 2 days before writing this list. Barrow is an addictive polymath.
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 | A Brief History of Time: From the Big Bang to Black Holes by Stephen Hawking
Buy new: £5.74 / Used from: £0.48 Has pages of predictable reviews, anoying, which often seem second-hand. I didn't like this in general. Text is too big, (like a childs fiction book), diagrams often tougher than equations ommitted.
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 | About Time: Einstein's Unfinished Revolution (Penguin Science) by Paul Davies
Buy new: £6.48 / Used from: £0.36 This was the first biographical book that I had read on Einstein. The discussions on Einstein's time are satisfying.
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 | The Origin of Life (Penguin Science) by Paul Davies
Buy new: £6.47 / Used from: £4.29 The best book that I have ever read on astrobiology.
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 | Trigonometric Delights by Eli Maor
Buy new: £12.52 / Used from: £9.73 This does not live up to Maor previous two similar books - 'Infinity' and 'e' - as the mathematical proofs of geometrical results are inately boring, as found in Euclid. Good historical approach.
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 | How to Prove It: A Structured Approach by Daniel J. Velleman
Buy used from: £8.00 This is one of the best maths textbooks that I own and is a good introduction to set notation and logic, and of course, to proof.
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 | Elementary Number Theory (Springer Undergraduate Mathematics) (Springer Undergraduate Mathematics Series) by Gareth A. Jones
Buy new: £17.50 / Used from: £14.48 This was written by my tutor at University and that doesn't mean that I am biased in praising this excellent number theory text. One of the best maths books that I have.
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 | Calculus: A Complete Course by Robert A. Adams
Buy used from: £37.50 I have seen this fifth edition and I wouldn't recommend it above the forth, the latter being much thicker and probably more comprehensive.
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 | The Elegant Universe: Superstrings, Hidden Dimensions and the Quest for the Ultimate Theory by Brian Greene
Buy new: £6.72 / Used from: £2.76 This is perhaps the best introductory book that includes quantum theory, relativity, and superstrings. I would like to look for a more mathematical text on these subjects now.
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 | The Constants of Nature by John D. Barrow
Buy new: £6.97 / Used from: £0.31 This is poor in contrast to Impossibility or The Book Of Nothing, (it borrows plenty of figures from the latter), and is not hugely inspired. I did however enjoy the section on Eddington.
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 | Elementary Linear Algebra by Stanley I. Grossman
Buy used from: £13.34 I have two books called "Elementary Linear Algebra", and it was because the other was insufficient that I bought this excellent text, (there is not picture unfortunately).
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 | Elementary Differential Equations and Boundary Value Problems by William E. Boyce
Buy used from: £19.67 I would stress that I have the sixth edition of this book, but I doubt if the seventh is worse, (though such things aren't unheard-of). The sixth edition is ideal for a differential equations course.
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| Information and the Internal Structure of the Universe: An Exploration into Information Physics by Tom Stonier
Buy used from: £22.20 I was lucky to find this book in an Oxfam shop and it was exactly the kind of thing that I was looking for that addresses information theory and entropy. The philosophy is probably questionable.
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 | Groups and Symmetry (Undergraduate Texts in Mathematics) by Mark A. Armstrong
Buy used from: £144.73 This is a very concise and palatable book for a first group theory course.
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 | Probability and Statistics (Pie) by Morris H. DeGroot
I wouldn't recommend this unless you are doing a third year course or higher; everything is done in conditional probabilities - it is like a differential equations book only using partial derivatives.
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