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I'm hoping to self-study Geometry, Algebra, Calculus, Vector Calculus, Linear Algebra, Probability and Statistics, and other intermediate maths. I've found the best way for me to learn is to work on problems. Unfortunately, many math textbooks don't provide all the answers so that I can check my work.

Does anyone have any suggestions for materials that do provide all answers to problems so that I can feel comfortable that I am solving the problems correctly?

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@mixedmath: for future reference, you should flag it for moderator attention in addition to leaving a comment. –  Willie Wong Aug 11 '11 at 20:06
    
@Willie Sure thing - and I think in the past there was maybe a CW-type flag, or something? I suppose I'll use the other function. Thanks Willie. –  mixedmath Aug 11 '11 at 20:09
    
@mixedmath: honestly, I don't remember. You can just say that the question needs moderator attention, with the "other" option selected, and type "should be CW". The SE2 interface is in large enough flux that I have trouble keeping track of all the changes. –  Willie Wong Aug 11 '11 at 20:11
    
Interesting no one's mentioned khanacademy yet. –  anon Aug 11 '11 at 20:15

5 Answers 5

up vote 7 down vote accepted

Schaums outlines. And forums like this one.

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Schaum's outlines. Worked problems, plus additional problems for the reader to do. –  GEdgar Aug 11 '11 at 15:11

The Springer Undergraduate Mathematics Series consists of textbooks with a lot of worked out exercises, designed for self study. Have e.g. a look at

  • T. S. Blyth, Edmund F. Robertson: "Basic Linear Algebra"

  • John M. Howie: "Real Analysis"

  • Paul C. Matthews: "Vector Calculus"

etc.

(Disclaimer: I'm not associated with Springer or one of the authors.)

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My answer may be a little off-topic.

Well, you got the problem as I did when I was a high school student. Even when I was a freshmen, I would like to find the "materials that do provide all answers to problems so that I can feel comfortable that I am solving the problems correctly" exactly as you do now. However, my experience tells me that it may be harmful to do so.

On the one hand, it is very possible to lead to one's laziness if he/she has the complete solution books. After all, one seldom wants to go through a "hard time" for problem solving, which I think is quite instructive and necessary, when one has the solutions by hand.

On the other hand, there is no solution at all when you do research problem or solve the problem in your real life. What you need to do then is tell the correctness of your own solutions yourself instead of referring to a solution manual. In the spirit of Polya, one should be able to check his/her own answer himself/herself. And it is a very good chance to practice this skill when you do elementary exercises.

Actually, almost every textbook contains answers to some special "exercises". Think about the theorems and examples in the book. You can regard them as exercises and check your solutions by reading the book. Finally, you can convince yourself that you don't need "all answers" to check your solution. Why? Think about the arithmetics you learned. Do you still need a solution manual to check?

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Check out http://projecteuler.net/ and other problemsolving websites.

What worked and works in my case, playing with problemsolving from programming contests. I know it's math forum, but designing algorithms on your own develops discrete-math, combinatorial, algebra and many other skills greatly, and make them sitting well in your head - as you've used it, by your own.

If not problem sets from programming contests, than, maybe check out some math contests. There are books and websites related to them, full of puzzles.

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For calculus: http://www.lightandmatter.com/calc/ Nearly all the problems have answers given in the back of the book. (Disclaimer: I'm the author. The book is free, however.)

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