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Good book to read

by phrygian
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phrygian
#1
Jun22-08, 06:20 PM
P: 80
I just graduated high school having taken AP calculus and am heading off to college this fall. I really enjoy math and have a great interest in it and am wondering if anyone can reccommend me any good books on math to read this summer. I will be taking math classes at college so obviously I am not trying to learn everything in math but more looking for an overview of the world of mathematics if that makes sense.
Thanks
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Werg22
#2
Jun22-08, 07:34 PM
P: 1,520
I recommend Foundations and Fundamental Concepts of Mathematics by Howard Eves.
Werg22
#3
Jun23-08, 01:01 AM
P: 1,520
There is also Concepts of Modern Mathematics by Ian Stewart and What is Mathematics? by Courant - Robbins - Stewart. My personal favorite is the first recommendation, though.

Shaun Culver
#4
Jun23-08, 03:46 PM
Shaun Culver's Avatar
P: 69
Good book to read

Mathematics: Its Content, Methods and Meaning - AD Aleksandrov, AN Kolmogorov, MA Lavrent'ev
mal4mac
#5
Aug20-08, 03:31 AM
P: 1,054
"Mathematics: a very short introduction" by fields medallist Timothy Gowers FRS, Rouse Ball Professor of Mathematics at Cambridge University (i.e. the biggest of big cheeses in UK Maths -- Roger Penrose held the identical chair at Oxford). The book is especially appropriate for an 18 year old about to go off to University. Website:

http://www.dpmms.cam.ac.uk/~wtg10/

It's the best short overview I've encountered, though Ian Stewart is good as well.

From a totally different angle (psychological) try The Number Sense: How the Mind Creates Mathematics by Stanislas Dehaene. It's full of fun examples, like how they got Dobbin to count, chimps doing arithmetic, and babies spotting disappearing puppets...
qspeechc
#6
Aug21-08, 03:54 PM
P: 792
"A Pure Course in Mathematics" by Hardy.
"How to Prove It" Velleman (sp?)

Not really overviews, but I would think very useful indeed.
mal4mac
#7
Aug21-08, 04:41 PM
P: 1,054
Gower's "further reading" section is superb. He recommends books to readers with different kinds of interest -- history, applicability, formality, philosophy -- and for areas he doesn't cover, e.g., probability, women in mathematics. I like his subtle "maybe not for further reading" recommendations:

"Russell and Whitehead's famous Principia Mathematica (Cambridge University Press, 2nd edn., 1973) is not exactly light reading, but if you found some of my proofs of elementary facts long-winded, then for comparison you should look up their proof that 1 + 1 = 2."


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