Need help for studying math needed for physics

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Joined: Sat Jun 21, 2014 7:32 am

Need help for studying math needed for physics

Post by as_vinoth » Sat Jun 21, 2014 9:15 am

I am interested in physics.To learn physics, math is the tool. When I started studying a branch in maths they found to be interconnected among themselves. So, while studying a topic(advanced level) in a branch it depends on other branch which I was planned to study later :( . I am experiencing same problem when i studied the prerequesities i experienced the same problem :cry: . So please help me from where to start learning the maths needed for physics(from basic concepts till string theory).I need a sorted list of math branches(basic to advanced) needed for studying physics if possible some book titles.

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Re: Need help for studying math needed for physics

Post by TakeruK » Sat Jun 21, 2014 2:30 pm

In my opinion, you can't just study one branch of math all the way to the advanced level and then move on to the next branch! I think you need to learn a little of each branch at a time.

Here are the names of the math courses I took in college as part of my physics degree and some books I used. These courses are very similar across most undergraduate physics programs in North America / the world so I think it's a good representation of the math you need to learn some physics. However, I did not focus on theoretical physics in the end (I am an astronomer/planetary scientist) so I skipped all of the upper level math courses, perhaps someone else can help you with those. I only covered enough math to learn undergraduate physics, not graduate level physics.

0. High school math -- stuff like logs, trigonometry, exponents, completing the square, etc.

First year math courses
1. Single variable calculus: For me, this was two courses covering differential calculus for 3 months then integrals for 3 months. We used Stewart Early Transcendentals (5th edition, it's now on the 7th edition). Reviews online says this book is terrible to learn from for a beginner student, but it sounds like you've moved beyond that. I don't know for sure--I didn't self-learn Calculus, I went to lectures and did the problems in the book. I found the book's text to be pretty useful as reference after learning it in class first, but I don't know if it would be good if you had to learn from only the book.

Second year math courses
2. Linear algebra: This was another 3 month I highly recommend Lay ( ... 0321780728) -- I used the 3rd edition, it's on the 4th edition now.
3. Ordinary Differential Equations: Also a 3 month course for me. We learned how to solve first order and second order differential equations. We used Boyce and DiPrima ... 0470458313 (I hated the 9th edition though, but now it's on the 10th edition which may be better). I think it's important to know how to solve various forms of differential equations, especially separation of variables.
4. Multivariable Calculus Part 1: A 3 month course where we used Stewart again, focussing on the beginning part of its chapters on multivariable calculus. We covered things like expressing vectors in 3D, basic vector operations, dot product, cross product, equations for lines and planes, some geometry, partial derivatives, directional derivatives, Lagrange multipliers, double and triple integrals over various types of regions. A lot of repeat of Single Variable Calculus, but in 2- and 3-dimensions.
(In second year, the optional math courses were a proofs class and a real analysis class, both of which I did not take)

Third year math courses
5. Multivariable Calculus Part 2: Another 3 months finishing up Stewart's multivariable chapters. I think this was one of the more useful courses for physics. We learned curl, divergence, Green's theorem and all of those other vector rules that you find in the cover/appendices of E&M textbooks. Useful stuff!
6. Partial differential equations: 3 months. Another really useful class. It's the same idea as Ordinary Differential Equations except for partial derivatives. Very relevant to almost everything in physics! There was a numerical component to this as we learned how to solve them with a computer as well as analytically.
7. Intro to Complex analysis: 3 months. We used ... x+analysis
I did not enjoy this class because despite the name ("applications for engineering & science"), it was taught very much like a pure math class instead. I think the beginning chapters that introduce you to complex numbers is important for some physics (namely optics, E&M, waves) and the residue theorem at the end is somewhat useful. Other than that, I have never worked in the complex plane, but that's probably just because my field does not do this. I even took a graduate level E&M course to fill a requirement and it was the only time we ever mentioned anything from this course. Even so, the prof did not assume knowledge of residue theorem and it would have been possible for me to never take this course and still learn college level physics just fine.
8. Probability and Stats: 3 months. We followed ... ross+stats (again, we used a different version).

Fourth Year Math courses
--I didn't take any. One optional recommendation was a mathematical methods class for physicists where we would learn how to solve a lot of math problems numerically, using MATLAB. It sounds like a good class, I just didn't have room but I took a numerical applications of linear algebra class instead. It covered no more new theory compared to the second year linear algebra class, but we really learned a lot about applications and how to do things like compute a least squares fit or a cubic spline numerically using MATLAB and matrices. We also did a fast Fourier transform (FFT) by hand, so that we understood better what was going on.

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Re: Need help for studying math needed for physics

Post by timjackson86 » Mon Aug 25, 2014 12:43 pm

If you are a math students then it's help you in learning physics, even math students can learn physics fast as compare to biology students.

So I suggest you to learn both subjects which is also used in most of the competitions as well other exams.

Here I also suggest for physics and math help.


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Re: Need help for studying math needed for physics

Post by bfollinprm » Mon Aug 25, 2014 5:26 pm

You ask for a programme of study from 'basic concepts to string theory'. First, a warning that I think trying to learn like this isn't the smartest way to go about it; you should learn enough maths to udnerstand undergraduate physics, take that, and see if you enjoy yourself enough to continue onward to the more 'advanced' topics.

But your wish is my command. Here's a set of tiered requisites for a career in mathematical physics, assuming you've completed the high school curriculum. Given focused and committed study, I'd expect, starting from scratch, this programme to take 1-2 years--more if you have other stuff to do.
  • 1. First Tier:
    a. Elementary calculus. Something like Spivak provides the requisite rigour you'll need later.

    2. Second Tier:
    a. Linear Algebra: Lay, plus an introductory book on quantum mechanics (Griffiths is my recommendation).
    b. Ordinary Differential Equations: You need to get as far as Green's functions for linear nonhomogeneous differential equations. I never took a course in this (learned it on my own through application), so I don't have a recommendation. Spivak might be enough; I haven't looked at that book since college.
    c. Fourier Analysis: this one, maybe? Again, I learned this on my own through application.

    3. Third Tier:
    a. Lagrangian Mechanics and Classical Field Theory: Goldstein
    b. Advanced Quantum Mechanics: Messiah
    c. Harmonic Analysis: Whittaker and Watson
    d. Group Theory: Herstein

    4. Fourth Tier:
    a. Quantum Field Theory: Peskin and Schroeder
    b. Lie Groups, representation theory, and differential geometry: This one looks good.
    c. General Relativity: first Carroll, then Hawking and Ellis
At that point you're probably ready to pick up some texts on string theory. Which ones will depend on your interests at this point, so I'll stop there.

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Re: Need help for studying math needed for physics

Post by Catria » Mon Aug 25, 2014 7:47 pm

Since string theory is topology-heavy, I recommend:

Topology: Munkres

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