• 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.

Contents

Chaos

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.

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

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.

Recommended here.

Recommended here.

History of Mathematics

Recommended here.

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.

Recommended here.

Biographies

An excellent account of one of the 20th Century's most prolific mathematicians.

Yet another biographical book, but well worth the read! Not that much maths in it, but looks interesting. MrMathsGenius.

Book about Ramanujan, yet again more biographical, but still worth a look.

Mathematical Physics

Recommended here.

A book about string theory, but most of the book is about relativity and quantum mechanics etc, says Speleo.

Sequel to the above. Focuses more on new research. Both books are very interesting.

Mathematical Philosophy

Recommended here.

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.

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

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

Recommended here and here.

Strongly recommended here.

Recommended here.

Recommended here.

Recommended here.

About the Riemann hypothesis and other various topics in number theory. Recommended, says Speleo. And here, here, here and here.

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

Recommended here.

Recommended here.

Definitely not very heavy, but nonetheless, an interesting/relaxing read about imaginary numbers and a vast array of other topics:

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

Recommended here and here.

  • 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

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