Reading material for highschool mathematics

Question

my name is gaurav. I'm presently self-employed aged 32. During my school days i was unable to study maths & physics in a manner that cleared my basic concepts. When i got hold of the way,it was late, i got admission in an engineering college but my yearning for understanding & lack of basic foundation proved counterproductive. I had to drop out of college due to some situation.

I always feel that if i understand concepts in high school maths & physics, it will help me in providing a better understanding of whatever i do. I need help from people who can suggest me books for high school maths & physics ( viz.arithmatic, euclidean geometry, algebra,calculus, permutations & combinations, probability, number theory,complex no.s,vectors,logarithms,inequalities,induction, mechanics, electricity.magnetism from a high school perspective). My intention at this moment is to study high school level, take it to MO level( even if i can"t appear in MO's)

I'ld like to re-start my studies along with my work.

Answer 1

For permutations and combinations, and a start at probability, at a high school level, I like Ivan Niven's The Mathematics of Choice: how to count without counting, in one of the great MAA series.

Answer 2

I like "Mathematics for the Million" by Lancelot Hogben, available for \$14 new or \$6 used here: http://www.amazon.com/Mathematics-Million-Master-Magic-Numbers/dp/039331071X/

Answer 3

Gaurav, the books in the NML are great, but they're also mostly on the difficult side. And they don't really teach you basic algebra, which seems to be one of the topics you've listed, as they assume you've already learned it in school. I also agree with the series by Gelfand that was mentioned, but it too, I think, is meant as a sort of complement to a more systematic course in algebra.

I would recommend Serge Lang's Basic Mathematics for an overall foundation in math at the high school level. If you find that a bit tough, I also like the books E-Z Algebra and E-Z Trigonometry by Douglas Downing.

You mentioned arithmetic. I don't know if you really need to work on your arithmetic, but if you do, the best choice is probably to get a textbook intended for people who plan to teach in elementary school. The one by Sybilla Beckmann, Mathematics for Elementary School Teachers, is supposed to be good. Old editions seem to be cheap on Abebooks. Make sure not to waste time on things you're comfortable with.

Once you've learned enough high school algebra and trigonometry, come back and ask again for recommendations of calculus books, as the recommendations will depend on your level of ability in high school math.

For physics, I'm convinced that the best textbook at the high school level (that is, for people who haven't yet learned calculus) is PSSC Physics, which is over 50 years old. There are a bunch of films that go with that too, many of which are on Youtube. (Search for the classic "Frames of Reference" on Google Video.) All the books that have been mentioned so far assume you already know calculus.

Once you've learned calculus, the Berkeley Physics Course or the series by Serway (an older edition) might be a good choice. The Feynman Lectures are notoriously difficult for beginners to learn from.