The Student Room Group

Maths Reading Recommendations

Hey everyone. I'm hoping that you can provide me with some recommendations of good maths books to read. I'm going to apply for a maths degree at Cambridge later this year and failing that, a joint degree in maths and economics at LSE.

Before I go through the application process for a maths degree, I want to develop my understanding of maths, plus find out more about what parts of maths I like and don't like. A-level maths isn't really enough to really get a feel for what maths is all about and I'd therefore like to read around the subject.

I'm especially interested in maths that links with physics, particularly stuff to do with relativity, black holes, space, quantum mechanics etc. Also, I'd like to read up on maths that links with economics (obviously!).

I'm aware of the oxford, lse and cambridge reading lists and while I've referred to them and am going to buy some of the books mentioned in them, I'd like to hear your opinions of good books and not just rely on pre-prepared lists if you know what I mean :smile:

I have a budget of about £60 right now to spend on books for maths, so if there are lots of suggestions I'll obviously have to cut a few out for now, but will obviously keep them in mind for later on.

Thanks to anyone who can help!
Reply 1
Here are some of the books I read relating to maths from about halfway through year 11 up to the end of lower sixth. I mentioned all but the last on my personal statement:

Goedel, Escher, Bach, Douglas Hofstadter
A book about formal logic, Goedel'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.

The Music of the Primes, Marcus du Sautoy
About the Riemann hypothesis and other various topics in number theory. Recommended.

The Elegant Universe, Brian Greene
A book about string theory, but most of the book is about relativity and quantum mechanics etc.

The Fabric of the Cosmos, Brian Greene
Sequel to the above. Focuses more on new research. Both books are very interesting.
Reply 2
Try reading about the millennium problems. There's a good book out there by Keith Devlin which gives an introduction to them. The problems pretty much encompass all the major areas of mathematics. Fairly interesting, but also pretty hard to understand in places.
Reply 3
I would recommend 'The Pleasures of Counting' and 'What is Mathematics?' from the Cambridge reading list, both contain a considerable amount of maths compared to other 'pop' maths books.

'What is Mathematics' is especially interesting as it covers topics you'll study at a level but also extends them and explains why you do certain things which don't get explained during the course. It also however touches on a lot of mathematics you won't have come across before (a significant portion of the book focuses on geometry and topology which are hardly mentioned at all in the a level syllabus).
Reply 4
I'd just like to point out that you don't have to be able to reel off a massive list of books you've read in order to get into Oxbridge for Maths!!!
Reply 5
Thanks everyone so far for your suggestions! Very much appreciated! :smile:

sebbie
I'd just like to point out that you don't have to be able to reel off a massive list of books you've read in order to get into Oxbridge for Maths!!!


Oooh no I know that, my main reason for wanting to read these books is purely out of interest and to see if maths is really what I want to do. I mean what better way to find out than to read outside the a-level course and see more of what it's about! :smile:
Reply 6
Where's the Cambridge reading list? I can't find it anywhere.
Reply 8
There's a pdf version?! Uchh would've saved me a lot of heartache. I could only find the postscript version which meant downloading some dos program, which wasnt easy to find. =/
Another vote for the pleasures of counting.
Reply 10
Thanks everyone! I think you've given me a fair list of books and it should keep me going for a while now. I'll probably get them tomorrow. Thanks again! :smile:
Reply 11
I read:

Godel, Escher, Bach
The Music of the Primes
The Man Who Loved Only Numbers
Fermat's Last Theorem
A Mathematician's Apology

Does God Play Dice?
Phi: The Extraordinary Number of Nature, Art and Beauty

I'd recommend the titles in bold, particularly for stimulating your interest in the subject which was also my main objective.
Reply 12
I stumbled upon this recently.

http://www.dpmms.cam.ac.uk/~twk/Naive.pdf

It's a draft of T.W. Korner's new book Naive Decision, from the introduction, the maths is more sophisticated than in his previous book. It definetly looks interesting.
Reply 13
I read Fermats Last Theorm, if u dnt read that it wd be foolish. An insight on number theory which would be valuble to oxbridge interviews; mine was all on number theory and without reading this book i would of struggled. U say u like maths with an application so with this u could say u have discovered maths as a pure form on its own etc. Peace out
Smyth11
I read Fermats Last Theorm, if u dnt read that it wd be foolish. An insight on number theory which would be valuble to oxbridge interviews; mine was all on number theory and without reading this book i would of struggled.


Maybe they talked to you about number theory because you had read Fermat's Last Theorem, so they asked you about stuff you mentioned in your PS? I dont agree that you would be foolish to not read it, but it does no harm.
Just make sure youd be happy talking about any books you mention in a PS.

Gordon
Reply 15
I read:
"5 Golden Rules" - a book that covers 5 important-ish theorems and their proofs, from Game Theory to Geometry.
"What is Mathematics?" - a general book the goes into enough depth to be satisfying.

Having read those, a few topics interested me enough to read further.

"A Topological Aperitif" - A really wonderful, short book with great illustrations, assumes little, a nice introduction into Topology.

"Elementary Number Theory" - Quite good - lots of worked examples meant I felt confident about using techniques that I'd learnt from the book.

"Principles of Mathematical Analysis" - Pretty terse at points, but I found it interesting. My interviewers were impressed by this choice also, commenting that it was a first year undergrad text, and continued to quiz me about it, just to check that I wasn't lying!

But don't read for the sake of a personal statement - read because you are genuinely interested! I also browsed through books like "Gamma" (a constant that was 'discovered' by Euler, but is somewhat less famous than 'e') and a few books about graph theory, which wasn't really my cup of tea - just read what takes your fancy. To be honest, I think that they don't care especially about how much reading you have done - they really just want to see if you can think logically, quickly, accurately, and perhaps laterally!!
Reply 16
Thanks for the further recommendations. I've already got a nice big pile of books to read. I've started reading "The Music of the Primes" and have really enjoyed it so far! It mentioned early on in the book about Gauss' Method for number sequences, and it was such a good feeling when the teacher first wrote the equation on the board a week later and I was able to think to myself, that's Gauss' Method for number sequences! Great stuff :biggrin:

Smyth11, thanks for that, I heard my physics teacher mention that he'd loaned a copy off my maths teacher and enjoyed it, so maybe I can convince my maths teacher to loan it to me as well! :p:

Don't worry henryt, I'm not really doing this for the sake of saying "I've read lots of books" to the interviewers, more to develop my 'mathematical personality', to get an idea of what I enjoy about maths and what I don't, what new concepts I can quickly grasp and those which I need to work harder on to understand, and of cours I can learn some new maths in general during the process! :smile:

Thought this topic had finished, nice to see a brief ressurection! :p:
Reply 17
GordonP
Maybe they talked to you about number theory because you had read Fermat's Last Theorem, so they asked you about stuff you mentioned in your PS? I dont agree that you would be foolish to not read it, but it does no harm.
Just make sure youd be happy talking about any books you mention in a PS.

Gordon


well i didnt put it in my personal statement genius! it was jus pot luck; and the fact that its a popular interview topic might of played apart aswell.

any other ingenius thoughts u would like to share? I'm sure everyone on here is jus dying to hear what u have to say.
Original post by ShaneP
I read:

Godel, Escher, Bach
The Music of the Primes
The Man Who Loved Only Numbers
Fermat's Last Theorem
A Mathematician's Apology

Does God Play Dice?
Phi: The Extraordinary Number of Nature, Art and Beauty

I'd recommend the titles in bold, particularly for stimulating your interest in the subject which was also my main objective.


Masterpiece. :smile:

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