
Ask HN: Good books on mathematics for somebody who's only taken high school math? - unalone
I was just reading Lockhart's Lament again (http://www.maa.org/devlin/LockhartsLament.pdf, if you haven't read and reread it yet), and I got a tremendous urge to really start getting into math. Problem is, I don't know where to begin with it. So I figured I'd ask: what books out there discuss math in the same way Lockhart does? I don't want a drab textbook: I want something that makes math as fascinating as it was in middle school, when I actually had fun learning about this stuff. Something that really is ecstatic about math.&#60;p&#62;I remember having a book about Fibonacci that was like that, but it was a pretty small book. Just as an aside.&#60;p&#62;And, if you don't have a good math book (though that's what I'm looking for), are there any books you've read that inspire that same sort of ecstasy in you? Personally, I've found myself inspired both by Bill Bryson's A Short History of Nearly Everything, along with Malcolm Gladwell's The Tipping Point. (Even though the latter wasn't exactly a scientific book like it purports itself to be, I was still fascinated by the concept it discussed.) Anything else?
======
mechanical_fish
A snapshot of my bookshelf's "math" section, which really hasn't changed much
since I was in high school and hadn't taken calculus:

W.W. Sawyer, _What is Calculus About?_ and _Mathematician's Delight_

Courant and Robbins, _What is Mathematics?_

Hogben, _Mathematics for the Million_

Steinhaus, _Mathematical Snapshots_

Ivars Peterson, _The Mathematical Tourist_

Davis and Hersh, _The Mathematical Experience_

Polya, _How to Solve It_

Huff, _How to Lie With Statistics_

McGervey, _Probabilities in Everyday Life_

Raymond Smullyan: _The Lady or the Tiger_ , _Alice in Puzzle-Land_ , others

Anything by Martin Gardner. I happen to have picked up _Mathematical Magic
Show_ and _Mathematical Circus_ , but I'm sure there are many other
collections.

I also recommend cryptography stuff. David Kahn's _The Codebreakers_ is not
really a math book, but it is awesome and it stars mathematicians, as does
Simon Singh's _The Code Book_. You could read Schneier's _Applied
Cryptography_.

This is HN, so I would be remiss if I didn't point out that you can learn a
lot of fun _and_ useful math by reading SICP, Knuth, or any good algorithms
book.

If anybody out there knows a good, spirited statistics book addressed to
someone who knows calculus, tell me. I keep planning to go through
_Fundamentals of Applied Probability Theory_ but I never get around to it; see
"Related Resources" here:

[http://ocw.mit.edu/OcwWeb/Electrical-Engineering-and-
Compute...](http://ocw.mit.edu/OcwWeb/Electrical-Engineering-and-Computer-
Science/6-041Spring-2006/CourseHome/index.htm)

Having said all of that: I have a Ph.D. in physics/EE, so I've _got_ to tell
you, if you haven't tried calculus you haven't lived. ;) I'm not sure how to
go about learning calculus in a _fun_ way for a _mathematician_ \-- I took
fairly standard first- and second-year college courses in calculus and physics
and learned it that way. The folks on Amazon seem kind of enthusiastic about
Spivak:

[http://www.amazon.com/Calculus-Michael-
Spivak/dp/0914098918/...](http://www.amazon.com/Calculus-Michael-
Spivak/dp/0914098918/ref=pd_cp_b_1?pf_rd_p=413864201&pf_rd_s=center-41&pf_rd_t=201&pf_rd_i=0471000051&pf_rd_m=ATVPDKIKX0DER&pf_rd_r=0WF0SV95HM895E3YYW28)

~~~
unalone
I took calculus my junior year, but again: I don't trust my high school
experience to tell me whether or not I like something.

Thanks a ton for the names. I'll check out the library later this afternoon!

------
newton
Check out Mind Tools by Rudy Rucker. He is a math professor and novelist, and
this book is a tour of advanced math concepts. Super fun and interesting.
[http://www.amazon.com/Mind-Tools-Levels-Mathematical-
Reality...](http://www.amazon.com/Mind-Tools-Levels-Mathematical-
Reality/dp/0395468108)

------
newton
If you like to be instructed by trippy 1970s cartoon characters, Prof. E.
McSquared's Calculus Primer is good. [http://www.amazon.com/Prof-McSquareds-
Calculus-Primer-Interg...](http://www.amazon.com/Prof-McSquareds-Calculus-
Primer-Intergalactic/dp/0971462402)

~~~
tjr
Totally awesome.

I first encountered this book when I was about six years old, and my mother
was using it for a calculus class. I didn't understand the content by any
means, but I enjoyed the cartoon characters. Despite not understanding it, the
book helped instill in me a fondness for math.

------
emacdona
I read this little gem over the summer: Godel's Proof
([http://www.amazon.com/Godels-Proof-Ernest-
Nagel/dp/081475837...](http://www.amazon.com/Godels-Proof-Ernest-
Nagel/dp/0814758371/ref=pd_bbs_1?ie=UTF8&s=books&qid=1221043351&sr=8-1))

At 160 pages, it's the ideal size to carry with you everywhere you go. All
summer long, any time I had an extra half an hour, I would take it out and
read/re-read a chapter.

------
phllip
Steinhaus, Mathematical Snapshots Polya, Mathematics and Plausible Reasoning
Pappas, The Joy of Mathematics Gardner, The Colossal Book of Short Puzzles and
Problems Winkler, Mathematical Puzzles: A Connoisseur's Collection Andrews,
Number Theory (Dover Books on Advanced Mathematics)

\- The last book is not really that advanced, It can be understood by most
with an understanding through high school algebra II.

------
ibsulon
As an aside, does anyone know of a mathematical dictionary? I've been trying
to follow some books and I just get lost in the terminology -- as I scour the
net for the pieces I need, I can get the context, but that seems entirely
inefficient. Along the same lines, I'm having trouble making the leap from
understanding simple proofs to advanced ones.

Is there any hope, save for going back for a math degree? :)

~~~
kqr2
You should check out this online resource for mathematics:

<http://mathworld.wolfram.com/>

If you need a dead tree version, Harper Collins is coming out with a new
edition:

[http://www.amazon.com/Harper-Collins-Dictionary-
Mathematics-...](http://www.amazon.com/Harper-Collins-Dictionary-Mathematics-
Borowski/dp/1439508860/ref=sr_1_8?ie=UTF8&s=books&qid=1220994362&sr=8-8)

I have an older version and it's good for quickly looking up some of the
vocabulary, however, it won't give you a deep understanding.

~~~
ibsulon
I will definitely check out both. Thanks!

------
mhartl
Take a look at _Journey through Genius_ by William Dunham. I read it after
high school and ended up spending much of the summer with a straightedge and
compass making geometric constructions. It's not all geometry, though; there's
plenty of other good stuff, including some gems from Euler and Cantor's
incredible diagonal proof of the cardinality of the rationals.

------
dfarm
Based on what you wrote you would hate Courant and Robbins _What is
Mathematics?_ , too rigorous. I think you would enjoy _Mathematics from the
Birth of Numbers_ by Jan Gullberg and _Calculus Made Easy_ by Sylvanus
Thompson.

You might also find _Unknown Quantity_ interesting. I think Gullberg would be
my #1 req for you.

------
gojomo
On another thread, there was a recommendation for Roger Penrose's 'The Road to
Reality'. Haven't read it, but it purports to build from basic math through to
advanced concepts and physics, step by step.

------
abstractbill
One of my favorites:

[http://www.amazon.com/History-Mathematics-Carl-B-
Boyer/dp/04...](http://www.amazon.com/History-Mathematics-Carl-B-
Boyer/dp/0471543977)

------
janm
Concrete Mathematics by Graham, Kunth and Patashnik

<http://en.wikipedia.org/wiki/Concrete_Mathematics>

------
soho
Hmm. No math book suggestions but I recommend reading anything by Milan
Kundera.

------
mwerty
Men of mathematics (E T Bell) and A mathematician's apology (G H Hardy).

