Ask HN: Good books on mathematics for somebody who's only taken high school math?
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.<p>I remember having a book about Fibonacci that was like that, but it was a pretty small book. Just as an aside.<p>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?
13 comments
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...
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/...
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...
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/...
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!
Thanks a ton for the names. I'll check out the library later this afternoon!
/Great/ list. Thanks!
I just bought the Polya book a few days ago, and the majority of the rest are going on my wishlist.
I just bought the Polya book a few days ago, and the majority of the rest are going on my wishlist.
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...
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...
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.
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.
I read this little gem over the summer:
Godel's Proof (http://www.amazon.com/Godels-Proof-Ernest-Nagel/dp/081475837...)
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.
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.
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.
- The last book is not really that advanced, It can be understood by most with an understanding through high school algebra II.
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? :)
Is there any hope, save for going back for a math degree? :)
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-...
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.
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-...
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.
I will definitely check out both. Thanks!
Would comprehensive encyclopedias do instead of dictionaries? http://wikipedia.org/ and http://mathworld.wolfram.com/
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.
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.
You might also find Unknown Quantity interesting. I think Gullberg would be my #1 req for you.
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.
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/04...
Concrete Mathematics by Graham, Kunth and Patashnik
http://en.wikipedia.org/wiki/Concrete_Mathematics
http://en.wikipedia.org/wiki/Concrete_Mathematics
Hmm. No math book suggestions but I recommend reading anything by Milan Kundera.
Men of mathematics (E T Bell) and A mathematician's apology (G H Hardy).