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April 1st, 2016, 05:46 PM   #1
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math for undergraduate physics

I'm more of a physics person, but i am also interested in the mathematics. Currently, I am in 11th grade and have finish Calc I to III and and an introduction to Linear Algebra course. What i am interested in is a good solid review of Geometry, trigonometry, algebra, and less importantly (to me at least) combinatorics/probability. Suggest any textbooks that are good for these foundational topics. I do not mind studying topics that arent directly related to trig.

Note: I have a dire need for knowledge of hyperbolic trig functions, as they show up a bit in special relativity.

Also, if anyone is familiar with the AoPS series, what are the prerequisites for volume 1?
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April 2nd, 2016, 01:02 AM   #2
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Many university books on mathematics for physics start with an introductory chapter summarising what you should already know and you will find much of your list in this chapter in these books, which then rapidly step up a gear or three as they progess through the subject.

You really seem to be asking for a 'crossover' textbook which expands that summary chapter.

A book that does this well is

The Chemistry Maths Book

Steiner

Oxford University Press

You can carry forward for at least two years into any physical science course.
This book boasts a particularly clear section on the hyperbolic trig functions you asked about.

A couple modern books of interest that you can carry forward beyond a first degree are

Mathematical Techniques

Jordan and Smith

Oxford University Press


Mathematical Methods for the Physical Sciences

Riley

Cambridge University Press.

Beyond this list you are moving into the realms of specialist single topic books,
of which there are many in maths for physics, some of them quite weighty to say the least.

One topic you will need is a good intro to is group theory, which is vital to modern theoretical physics. Steiner does provide a start.
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April 3rd, 2016, 07:47 AM   #3
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I will check out all those books. Note that my textbook request was more along the lines of "how do i consolidate foundations" instead of what math do i learn for physics. I don't really mind learning how to do proofs and/or geometry that won't come into play in physics very frequently. I guess you could say that I'm asking for textbooks to prepare for math olympiad, since that is the type of rigor and the collection of topics that i am interested in.
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April 3rd, 2016, 08:03 AM   #4
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Math Focus: Linear algebra, linear statistical models
For combinatorics, probably pick up a discrete maths book. They're usually aimed at computer science students and I don't know how useful they are for physics, but you should be able to find the basics of combinatorics and and graph theory there.

For probability, any formal, rigorous introduction to probability and statistics will do - just look in your local library and see what they've got. I don't know how much probability you know, but if you only know the bare basics (i.e. up to Bayes' theorem) then you should start from random variables - PDFs, PMFs, CDFs, MGFs, formal definitions of expected value/mean, variance, skewedness and kurtosis, special distributions like binomial, negative binomial, geometric, hypergeometric, Poisson, exponential, beta, gamma, chi-square, and of course normal. Then look at joint distributions (which you should be able to handle since you did Calc III). (After that, you might also want to pick up some statistics - confidence intervals and hypothesis testing with the Z-, t- F- and chi-square distributions, and correlation and regression.) I haven't done any probably beyond that yet, so I don't know what else you'll need...

Last edited by 123qwerty; April 3rd, 2016 at 08:07 AM.
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