In addition to all the other good suggestions, the following are recommended (have not seen these mentioned so far);

- Concepts of Modern Mathematics - https://www.amazon.com/Concepts-Modern-Mathematics-Dover-Boo...

- Methods of Mathematics Applied to Calculus, Probability, and Statistics - https://www.amazon.com/Methods-Mathematics-Calculus-Probabil... (all books by Richard Hamming are recommended)

- Calculus: An Intuitive and Physical Approach - https://www.amazon.com/Calculus-Intuitive-Physical-Approach-...

For a Textbook reference, the following are quite good;

- Mathematical Techniques: An Introduction for the Engineering, Physical, and Mathematical Sciences - https://www.amazon.com/Mathematical-Techniques-Introduction-... (easy to read and succinct)

- Mathematics for Physicists: Introductory Concepts and Methods - https://www.amazon.com/Mathematics-Physicists-Introductory-C...

For General reading (all these authors other books are also worth checking out);

- Mathematics, Queen and Servant of Science - https://www.amazon.com/Mathematics-Queen-Servant-Science-Tem...

- Mathematics and the Physical World - https://www.amazon.com/Mathematics-Physical-World-Dover-Book...

- Mathematician's Delight - https://www.amazon.com/Mathematicians-Delight-Dover-Books-Ma...

I suggest the following approach;

Start with some school textbooks for grades 8-12 i.e. Secondary Education. This is more for a refresher course in the absolute basics.

The above can be supplemented with the following books to develop intuition;

1) Who is Fourier - https://www.amazon.com/Who-Fourier-Mathematical-Adventure-2n...

2) Functions and Graphs - https://www.amazon.com/Functions-Graphs-Dover-Books-Mathemat...

After this is when you enter undergraduate studies and you have to fight the dragon of "Modern Maths" which is more abstract and conceptual. In addition to standard textbooks; i suggest the following;

1) Concepts of Modern Mathematics - https://www.amazon.com/Concepts-Modern-Mathematics-Dover-Boo...

2) Mathematics: Its Content, Methods and Meaning - https://www.amazon.com/Concepts-Modern-Mathematics-Dover-Boo...

3) Mathematical Techniques (i am linking this so you can see the reviews but get the latest edition) - https://www.amazon.com/Mathematical-Techniques-Dominic-Jorda...

Finally, if you would like to learn about all the new-fangled mathematics your best bets are;

a) The Princeton Companion to Mathematics - https://www.amazon.com/Princeton-Companion-Mathematics-Timot...

b) The Princeton Companion to Applied Mathematics - https://www.amazon.com/Princeton-Companion-Applied-Mathemati...

One important piece of advice that i have is to become comfortable with the Symbols, Notation and Formalism used in Mathematics. Most students are intimidated by the Formalism (which is nothing more than a precise form of shorthand to express abstract concepts) and give up on studying Mathematics altogether. This is a shame since it is merely the Form and not the Function of Mathematics.

The last time people asked, I collected the responses so I could do the same thing as you. Note that I'm wanting to learn it in a way where I can do proofs. So, I have general-purpose books and stuff for that. I just ordered the three books I've seen pop up the most. Although 2 are in the mail, Concepts of Modern Mathematics by Stewart just got here yesterday. It had an awesome opening that made me wish the math I was taught in school was done like this back when I went. Makes newer stuff make a lot more sense, too. I included a link to Dover that has a Google Preview button on it where you can read full, first chapter for free to see if it's what you like. Other two are more about exploring and proving things which may or may not interest you. I added them in case anyone is reading your question to learn that stuff.

Concepts of Modern Mathematics by Stewart

https://www.amazon.com/Concepts-Modern-Mathematics-Dover-Boo...

Dover Version with Google Preview Button

http://store.doverpublications.com/0486284247.html

Introduction to Mathematical Reasoning: Numbers, Sets, and Functions

https://www.amazon.com/Introduction-Mathematical-Reasoning-N...

How to Prove It by Velleman

https://www.amazon.com/How-Prove-Structured-Approach-2nd/dp/...

There is plenty of math that does not lie on the academic beaten path (i.e. arithmetic -> algebra -> calculus --> etc.) I would recommend trying to figure out what area of math you are most interested in first, that way you will be enthusiastic about learning it. Once you have the mathematical momentum from that you will probably be able to learn whatever math you need to. A couple of books that helped me to find a direction were Mathematical Ideas[1] and Concepts of Modern Mathematics[2], which cover many different areas with just enough depth to give you a feel for each. If you are wanting to learn math solely for CS I would also recommend something like Schaum's Outline of Discrete Mathematics[3].

[1]http://www.amazon.com/Mathematical-Ideas-Edition-Charles-Mil...

[2]http://www.amazon.com/Concepts-Modern-Mathematics-Dover-Book...

[3]http://www.amazon.com/Schaums-Outline-Discrete-Mathematics-R...

I would recommend 'Concepts of Modern Mathematics' [1], by Ian Stewart. It has some very nice illustrations and humor, and reminds me of 'Learn You A Haskell For Great Good' (though I believe CoMM came out before LYaH). It's a wonderful preview of a variety of topics, and is intended to introduce someone with a poor math background to some of the different fields of math.

From the Amazon description:

In this charming volume, a noted English mathematician uses humor and anecdote to illuminate the concepts underlying "new math": groups, sets, subsets, topology, Boolean algebra, and other subjects. No advanced mathematical background is needed to follow thought-provoking discussions of such topics as functions, symmetry, axiomatics, counting, topology, hyperspace, linear algebra, and more. 200 illustrations.

---

[1]: http://www.amazon.com/Concepts-Modern-Mathematics-Dover-Book...

these nine videos are fantastic http://www.dimensions-math.org/Dim_tour_E.htm

here's a whirlwind tour http://www.amazon.com/Concepts-Modern-Mathematics-Ian-Stewar...

To get better intuition without a math degree I'd recommend: Concepts of Modern Mathematics which only requires elementary algebra, but will give you great intro treatments of everything from groups to number theory.

http://www.amazon.com/Concepts-Modern-Mathematics-Ian-Stewar...

My son (an occasional Hacker News participant) was in a similar position a few years ago. I'll list here a variety of books that should be helpful, some of which were recommended to him by summer program instructors, and others of which were recommended to me by parents of other children with similar activity backgrounds.

For access to a lot of mathematical concepts at a reasonable reading level, not at all expensive, I recommend Concepts of Modern Mathematics by Ian Stewart.

http://www.amazon.com/Concepts-Modern-Mathematics-Ian-Stewar...

Ian Stewart is a mathematician who loves to write popular writings on mathematics, and you can hardly go wrong with anything he has written.

From Zero to Infinity: What Makes Numbers Interesting by Constance Reid

http://www.amazon.com/Zero-Infinity-Makes-Numbers-Interestin...

is very accessible and covers a number of interesting topics.

The Art of Problem Solving by Richard Rusczyk and Sandor Lehoczky

http://www.artofproblemsolving.com/Store/viewitem.php?item=p...

http://www.artofproblemsolving.com/Store/viewitem.php?item=p...

is a straight-up contest preparation book, in two volumes, that your son may find interesting. Volume 2 is for high school level contests.

For an interesting (in places laugh-out-loud funny) book about the place of mathematics in modern life and how mathematicians think about mathematics, I recommend The Pleasures of Counting by T. W. Körner.

http://www.amazon.com/Pleasures-Counting-T-246-rner/dp/05215...

This one is more challenging as to reading level and as to mathematical level than the recommendations above, but well worth having around the house.

That thread recommends many very few good books, but probably mostly books too hard at first for the participant who has posted this new thread.

I'll recommend a couple of books from that thread:

http://www.springer.com/physics/book/978-0-306-45036-5

http://www.amazon.com/Mathematics-Short-Introduction-Timothy...

I agree with the recommendation of An Introduction to Mathematical Reasoning in this thread.

Another participant has already recommended my favorite for background reading, Concepts of Modern Mathematics by Ian Stewart.

http://www.amazon.com/Concepts-Modern-Mathematics-Ian-Stewar...

Get that right away.

Sawyer's A Mathematician's Delight is surely also good (I've read other books by Sawyer).

http://www.amazon.co.uk/gp/product/0486462404/

Read those for background as you get my favorite overviews of mathematics: Basic Mathematics by Serge Lang and Numbers and Geometry by Joseph Stillwell.

http://www.amazon.com/Basic-Mathematics-Serge-Lang/dp/038796...

(Basic Mathematics is mostly high school level math, with a minimum of fuss and bother, and good exercises.)

http://www.amazon.com/Numbers-Geometry-John-Stillwell/dp/038...

(Numbers and Geometry is mostly undergraduate level math, with very good explanations and excellent exercises.)

Some favorites about mathematics:

Concepts of Modern Mathematics by Ian Stewart

http://www.amazon.com/Concepts-Modern-Mathematics-Ian-Stewar...

Numbers and Geometry by John Stillwell.

http://www.amazon.com/Numbers-Geometry-John-Stillwell/dp/038...

The Pleasures of Counting by T. W. Körner

http://www.amazon.com/Pleasures-Counting-T-W-K%C3%B6rner/dp/...

Mathematics: A Very Short Introduction by Timothy Gowers

http://www.amazon.com/Mathematics-Short-Introduction-Timothy...