Books for oxbridge, IC, UCL and Warwick type-maths?

Hi anyone got any name of those "bible-like" maths books that seem to be godly for courses in maths at the above universities, with particular reference to oxbridge?

Reply 1

ssmoose

Here are some first year notes from Imperial:
http://www.maths.mq.edu.au/~wchen/ln.html

Reply 2

Spenceman_

Most of the one's considered relatively godly aren't actually textbooks. Some people seem to think that everyone should have read Fermat's Last Theorem by Simon Singh, for example...or some of Ian Stewart's popular books. I particularly enjoyed The Man Who Loved Only Numbers, which is a biography of Paul Erdos...author's name escapes me. If you search around the cambridge maths faculty's site you ought to be able to find their reading list without too much trouble. It has both popular books and readable textbooks.

Reply 3

AlphaNumeric

Hobson, Riley and Bench is the 1st year's bible for Cambridge. Covers most vector calculus, differential equations, algebra & geometry and probability material. Doesn't cover everything, but that should keep you busy :p:

Reply 4

The Orientalist

AlphaNumeric

"Mathematical Methods for Physics and Engineering" by Hobson, Riley and Bench. Is it that one you're talking about? Mmm, doesn't sound like pure maths lol.

Reply 5

AlphaNumeric

The hint is in the title :wink:

What you're not realising perhaps is that 'pure maths A Level' is mostly applied maths. It has no rigour (almost complete lack of proofs) and you use the methods you learn to be applied in mechanics A Level. This is extended in uni. 'Differential Equations' is considered an applied course, the first year exams have 4 papers, one applied topic, one pure topic per paper and the DE course is in a paper with group theory, definitely a pure course (well, until you start doing Part III and then it's in all the quantum field theory courses! Much to my dismay :frown:

). You then use differential equations and vector calculus (which is pretty much n variable differential equations) to do things like fluid mechanics and electromagnetism (both 2nd year courses) and their more complicated descendents.

You'll get a whole new definition of 'pure maths' when you get to uni. As a hint, here's the Analysis notes from 10 years ago at Cambridge, with proofs. And some A Level students might have thought they knew how integration was proved (well, one form of integration anyway :wink:

). The notes are obviously a decade old (given the title page) but most of that is still on the syllabus.

Reply 6

Wrangler

If I remember correctly, Riley, Hobson and Bence contains a few chapters on the pure side of things. I'm a little sketchy, but I think there's introductions to:

Real Analysis
Complex Analysis
Groups
Linear Algebra
Representation Theory

To name a few. It's worth bearing in mind, that while Physicists/Engineers won't spend their days delving through the deepest dregs of analysis, algebra, combinatorics etc, doesn't mean they don't need to know any. So don't be put off by a book that's catered for a large audience - it'll be a while before you really need to look at any specialist texts.

:smile:

Reply 7

The Orientalist

AlphaNumeric

The hint is in the title :wink:

). The notes are obviously a decade old (given the title page) but most of that is still on the syllabus.

Thanks for all this info, the link you gave me is quite interesting, definitely what I expected to be uni "pure maths" :wink:

. I don't know how A-levels maths works but in France, we already start to do some rigorous proofs in our last year making transition between high school and uni much easier, which is pretty cool. :smile:

EDIT: We recently did some proofs of section 1 of your link hehe, it's good stuff.

Reply 8

The Orientalist

Wrangler

To name a few. It's worth bearing in mind, that while Physicists/Engineers won't spend their days delving through the deepest dregs of analysis, algebra, combinatorics etc, doesn't mean they don't need to know any. So don't be put off by a book that's catered for a large audience - it'll be a while before you really need to look at any specialist texts. :smile:

Thanks, will be doing some reading this summer :wink:

Reply 9

PennyRoyalTea

Spenceman_

. I particularly enjoyed The Man Who Loved Only Numbers, which is a biography of Paul Erdos...author's name escapes me. .

Paul Hoffman..great book.. :smile:

Reply 10

silent ninja

Anyone read What Is Mathematics?: An Elementary Approach to Ideas and Methods

http://www.amazon.co.uk/exec/obidos/tg/detail/-/0195105192/ref=wl_it_dp/203-7260196-0574353?%5Fencoding=UTF8&coliid=I6GTSVKP5HZAZ&v=glance&colid=X6UYA9RRVC5H

not going to uni for another year yet. imperial recommend this to get a feel for uni maths. anyone read it? used it?

Reply 11

username22878

Started reading it, read about half of it in preparation for an interview. It's interesting but not really light reading material. Mostly takes A Level material and extends it.

Reply 12

Shickles

having looked at the contents of "Mathematical Methods for Physics and Engineering" on amazon, i feel quite excited now about going to university to do real maths!

"Concise Introduction to Pure Mathematics" by Liebeck has also been recommended to me, i haven't had a look but it's apparently very good. it's even better if you're going to Imperial to do maths, because Prof Liebeck is a lecturer there!