Books about maths

[the tree]

I'm looking for a non-textbook about maths wich suits pre-university level (that's not to say I don't want anything challenging).

 

I would quite like to learn about something entirely new to me, such as chaos theory or cryptogoraphy.

 

What can you recomend?

[matt grime]

Tom Korner's The Pleasure of Counting springs to mind. Gleick's was the coffee table book for Chaos when I was applying to university.

 

The former book has exercises I believe and makes you think, and the latter is a handwavy load of crap about nothing (as you come to appreciate if you ever actually come to do mathematics).

 

Do you mean that you don't want something with exercises? You won't actually learn any maths from the Gleick type of book.

[the tree]

I meant that I don't just want a collection of instructions and exercises like in the text books wich only seem concerned with getting me to pass an exam.

 

I searched for the Tom Korner book on Amazon but it didn't have it, any others?

[matt grime]

fortunately amazon isn't the only seller of books in the world:

 

http://www.cambridge.org:80/uk/catalogue/catalogue.asp?isbn=0521568234

 

admittedly i did get the title slightly wrong.

 

to rephrase my question: do you want something that is mathematically rigorous or just a handwavy and inaccurate load of waffle? or general ethos of mathematics, perhaps, like Hardy's Apology, or Polya's How to Prove It (perhaps it's how to solve it), then there's Tim Gowers's VSI book.

[the tree]

Yes, I do want something mathmatically rigorous, thanks for your help, I'll consider buying that book.

[shmoe]

I read Gleick when I was in high school. At the time I thought it was great. In retrospect "handwavy load of crap about nothing" is more accurate though possibly a tad harsh. The danger is that you may walk away from the book with the impression of 'chaos' that annoys the heck out of matt. These kinds of math-free popsci books are mostly good for the tidbits of folklore inside, you won't learn much (or any) actual math from them.

 

Two books I really enjoyed in high school were by Paulos, "Innumeracy" and "a mathematician reads the newspaper". You probably won't learn any math from them either, but they are pretty amusing and I think good books for the 'average' person to read.

 

Derbyshire's "Prime Obsession" is a decent treatment of the Riemann Hypothesis (for the laymen). It has some great history in it and I think the math content should be at a good level for a high school student (hard to tell) though it necessarily has plenty of handwaving.

 

Hardy's Apology is sad but enlightening. No math here, but a good read. Get a later edition with the lengthy foreward by Snow.

 

I haven't seen the book by Korner before, it looks interesting.

[matt grime]

The chaos thing....

 

here's what 'chaos' is:

 

the study of dynamical systems that display sensitive dependence on initial conditions and topological transitivity. The former of these might get a mention in the likes of Gleick (which I too read before going to university and thought was 'amazing'). It is about homoclinic and heteroclinic orbits, and the like, solving annoying PDE's, all kinds of things.

 

Summing it up as "butterfly effect" is completely unhelpful and mathematically inaccurate: even without any chaotic behaviour a butterfly flapping its wings in CHina can cause a hurricane in Guatemala, but that is not chaos just amplification of causes. Jeff Goldblum rambling on about nature always finding a way is not chaos theory. Drawing Mandelbrot sets and reading Arthur C Clarke is not learning about chaos theory.

 

Sadly, I know, discussing mathematics can be dry and dull, but it is possible, as Korner, Gowers, Hardy, Baez, Devlin, and a multitude of others have shown to avoid this trap. Chaos theory books have a hint of 'jumping on the bandwagon' about them that makes me sick.

 

To a certain degree white lies when explaining maths are necessary, even to other mathematicians, yet the white lies in books about chaos theory have become gospel truth.

[deltanova]

Everything and More David Foster Wallace, its a look at infinity, popular science, should be able to pick it up at you local bookshop. highly reccomended

[doG]

I enjoy my copy of the "Handbook of Mathematics" by Bronshtein and Semendyayev. It's strictly a reference with no exercises and covers the needs of just about any scientist or engineer.

[Trurl]

I like Schaum's Outlines when doing a self study. But I think the best choice for you is at this link

 

Click Here

 

these books are involved and not a traditional textbook. You will learn a lot.

[the tree]

The Tom Korner arrived this weekend and so far it's great. Thanks for the recomendation Matt, it looks like it'll prove useful when I have something important I'd rather not be doing as well.