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April 1st, 2016, 05:46 PM  #1 
Newbie Joined: Apr 2016 From: california Posts: 2 Thanks: 0  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? 
April 2nd, 2016, 01:02 AM  #2 
Senior Member Joined: Jun 2015 From: England Posts: 829 Thanks: 244 
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. 
April 3rd, 2016, 07:47 AM  #3 
Newbie Joined: Apr 2016 From: california Posts: 2 Thanks: 0 
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.

April 3rd, 2016, 08:03 AM  #4 
Senior Member Joined: Dec 2012 From: Hong Kong Posts: 853 Thanks: 311 Math Focus: Stochastic processes, statistical inference, data mining, computational linguistics 
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, chisquare, 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 chisquare 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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