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Recommended Mathematics Reading
Now, I know mathematicians don't like reading but if you want to take a degree in Maths, it might be nice to have a book to talk about in your interview. And the physicists have got a list, so we ought to have one too. Here's the collated recommendations from various threads on the site. I give multiple recommendations for the same book to give a feel for popularity.
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Chaos
- Does God Play Dice by Ian Stewart
Recommended here and here. An introduction to chaotic dynamics. Doesn't contain that many actual sums, but lots of pretty pictures, and a good overview of the role of chaos. Quite a popularist style.
- Chaos by James Gleick
Quite Physicsy, but a good read, yet again quite biographical, some have said that it gets hard work to read quite soon after opening! MrMathsGenius. NB: I've seen this dissed a couple of times on the threads that provide the source for this page. Mr Dactyl
Cryptography
- The Codebook by Simon Singh
Recommended here. Interesting exploration into the different types of codes and CYPHERS used throughout history. Is a very good GENERAL MATHS BOOK, covering elements of basic number theory, physics (potential of photon money!), statistics (frequency Analysis) and computing. I found it interesting but view it more as an encyclopedia for reference rather than a comprehensive account. Says MrMathsGenius.
- The Mathematics of Ciphers by S.C. Coutinho
Recommended here.
- In Code by Sara Flannery
Recommended here.
History of Mathematics
- A History of Mathematics by Carl B. Boyer
Recommended here.
- Infinity: The Quest to Think the Unthinkable by Brian Clegg
Am currently reading this. This is definitely one of the better books on the subject. A chronological biography of the concept of infinity, from Greeks to present day. Says MrMathsGenius.
- E, the Story of a Number by Eli Maor
Recommended here.
Biographies
- The Man Who Loved Only Numbers by Paul Hoffman
An excellent account of one of the 20th Century's most prolific mathematicians.
- My Brain is Open: The Mathematical Journeys of Paul Erdos by Bruce Schecter
Yet another biographical book, but well worth the read! Not that much maths in it, but looks interesting. MrMathsGenius.
- The Man who knew Infinity by Robert Kanigel
Book about Ramanujan, yet again more biographical, but still worth a look.
Mathematical Physics
- A Brief History of Time by Stephen Hawking
Recommended here.
- The Elegant Universe by Brian Greene
A book about string theory, but most of the book is about relativity and quantum mechanics etc, says Speleo.
- The Fabric of the Cosmos by Brian Greene
Sequel to the above. Focuses more on new research. Both books are very interesting.
Mathematical Philosophy
- Introduction to Mathematical Philosophy by Bertrand Russell
Recommended here.
- A Mathematician's Apology by G. H. Hardy
Recommended here and here. Beginning to look decidedly old-fashioned, and Hardy makes some points which are clearly wrong about the role of mathematics in society. When he talks about the subject itself, he is powerful. This is a classic, and widely read. Try to find the version with introduction by CP Snow.
- Thinking About Mathematics by Stewart Shapiro
A good introduction to the philosophy of maths, presents an overview of the history and current positions in the field. Likely to be of less interest to those interested in straight maths, though.
Mathematical Problems
- Fermat's Last Theorem by Simon Singh
Recommended here, here, here, here, here, here, here, here, here, here, here and here. So basically, everyone reads this. You won't stand out at all. An enjoyable read all the same and "you must read this story" according to Cambridge's Faculty of Maths.
- The Millenium Problems by Keith Devlin
- Journey Through Genius: The Great Theorems of Mathematics by William Dunham
Strongly recommended here.
- The Equation That Couldn't Be Solved by Mario Livio
Recommended here.
- Kepler's Conjecture by George Szpiro
Recommended here.
- Poincaré's Prize by George Szpiro
Recommended here.
- The Music of the Primes by Marcus du Sautoy
About the Riemann hypothesis and other various topics in number theory. Recommended, says Speleo. And here, here, here and here.
- Four Colors Suffice by Robin Wilson
Recommended here.
Logic
- Godel, Escher, Bach by Douglas Hofstadter
A book about formal logic, Godel's Incompleteness theorems, and about 400 tedious pages on neuroscience and music. It's very interesting in parts, the dialogues especially are wonderful, but about half the book has nothing to do with maths and is tedious beyond belief, says Speleo. And here and here.
Readable Textbooks
- Concepts in Modern Mathematics by Ian Stewart
Recommended here.
- Geometry for Dummies by Mark Ryan
Recommended here.
- Concise Introduction to Pure Mathematics by Martin Liebeck
Definitely not very heavy, but nonetheless, an interesting/relaxing read about imaginary numbers and a vast array of other topics:
- Mathematical Methods for Science Students by G Stephenson
A very clear and readable text useful for introducing some university level concepts to the top end of the A level cohort. The book starts off easy and gradually progresses onto some very interesting mathematics such as multivariable calculus and a study of the gamma function.
Other
- The Emperor's New Mind by Roger Penrose
Recommended here.
- The Mathematical Universe by William Dunham
Recommended here.
- The Wonders of Numbers by Clifford Pickover
Recommended here.
- From Here to Infinity by Ian Stewart
Recommended here.
- The Art of the Infinite: Our Lost Language of Numbers by Robert Kaplan
Recommended here.
- What is Mathematics? by Richard Courant, Herbert Robbins and Ian Stewart
- Flatterland by Ian Stewart
Fantastic take on a 19th century book about different geometries, starts by explaining 4d by exploring the way our 3d world would look to a 2d or 1d person! Recommended here.
- The Number Devil: A Mathematical Adventure by Hans Magnus Enzensberger
Recommended here. An entertaining book, and certainly one for younger people looking for some interesting, yet accessible, mathematics.
- Art of the Infinite by Kaplan
More mainstream, targeted at expanding mathematical awareness. Certainly a good read for those who have perhaps gained Mathmophobia! MrMathsGenius. And here.
- Imagining Numbers: Particularly the Square Root of Minus Fifteen by Barry Mazur
Good(ish). Mazur takes the scenic route to complex numbers, via a deep exploration of their history and a brief tour of the science of the imagination. No challenging maths, but a readable book. Recommended here.
- A Very Short Introduction to Mathematics by Timothy Gowers
Tiny, incredibly dense book written by a Fields Medallist. Provides a great jumping off point for further independent reading around maths, and a glimpse of the character of 'real maths'. User:Mr Dactyl
Other Reading Lists
- Oxford is here.
- Cambridge is here.
- Balliol '04 here.
