Explore Math World: Best Books for Recent HS Grad Heading to College

[phrygian]

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 recommend 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

 

[Werg22]

I recommend Foundations and Fundamental Concepts of Mathematics by Howard Eves.

 

[Werg22]

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]

Mathematics: Its Content, Methods and Meaning - AD Aleksandrov, AN Kolmogorov, MA Lavrent'ev

 

[mal4mac]

"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]

"A Pure Course in Mathematics" by Hardy.
"How to Prove It" Velleman (sp?)

Not really overviews, but I would think very useful indeed.

 

[mal4mac]

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."