9
votes
4answers
369 views

In what ways has physics spurred the invention of new mathematical tools?

I came across this comment: Mathematical rigor is not a criterion that physicists have for evaluating their theories. From a mathematical perspective, the non-rigorous theories are far more ...
1
vote
2answers
67 views

Books that integrate physical reasoning with mathematical reasoning? mathematicians?

As the title says, can anyone help me to find any book that shows how physical reasoning using concepts from classical/quantum mechanics and physics in general can enlighten us about mathematical ...
-1
votes
2answers
110 views

List of Advanced Math Text Books with answers

Can anybody please recommend a list of Advanced Mathematics Books for physics that can be used for self study. Most importantly they must have answers for odd or even problems. I have a big list of ...
69
votes
10answers
9k views

Why can't you add apples and oranges, but you can multiply and divide them?

What is the algebraic difference between arithmetic operations, that prevents entities with different units from being summed or subtracted, but allows them to be multiplied or divided? This looks ...
0
votes
0answers
45 views

Invalid use of the analytic continuation of the Riemann zeta function?

Watching this video on You Tube I got the impression that some sciences (in this case physics) use the analytic continuation of the Riemann zeta function without justification. Maybe this is just my ...
0
votes
2answers
29 views

what are some typical systems of equations generating from practical problems?

I want to know some typical forms of system of equations generating from practical problems in engineering/economics/physics,etc. Some examples or research articles would be good. Specifically, I am ...
0
votes
2answers
25 views

Helmholtz decomposition - motivation

Our lecturer presented us the Helmholtz decomposition of smooth vector fields. He added a proof, but he didn't provide any single motivation - e.g. where Helmholtz used the decomposition or for which ...
0
votes
0answers
43 views

Mathematics Necessary for General Relativity and Quantum Physics.

I am a self-learner in Mathematics. I was wondering, given some background in calculus and a tiny bit of topology and group theory, what series of documents I would have to learn to be able to ...
5
votes
1answer
126 views

Physical Meaning of Symplectic Vector Fields

The mathematics of symplectic (as well as Hamiltonian) vector fields is something that has been quite clear to me for some time, but recently I have been thinking much more about what certain ...
1
vote
0answers
108 views

Applications of identity theorem to physics

Holomorphic functions have the property that they can be uniquely analytically continued to (almost) the entire complex plane. So, just by knowing how the function behaves at a teenie-weenie open disc ...
8
votes
4answers
365 views

What are applications of number theory in physics?

I was reading Goro Shimura's The Map of My Life. He wrote the following quote in the book. It made me come up with the title question. In particular, is there any application of the theory of modular ...
3
votes
2answers
278 views

Examples of applications of Linear differential equations to physics.

I wonder which other real life applications do exist for linear differential equations, besides harmonic oscillators and pendulums. I'm looking for examples to include in a document that talks about ...
1
vote
3answers
269 views

Thermodynamics for math majors

I'm about to wrap a course in partial differential equations. We've discussed the heat/wave equations and introductory Fourier Analysis. I'd like to do some reading into the field of thermodynamics. ...
7
votes
6answers
957 views

What is this physicist saying?

I do not want to poison this forum with politics. But I want to understand, precisely, what is meant by the bolded statement. It is made by a physicist who used to work at Harvard regarding the ...
10
votes
2answers
2k views

Is it better to learn math before physics?

It seems that a persons ability to understand physics at a high level is limited primarily by their understanding of math. It also seems to be more efficient to learn the underlying math for a ...
1
vote
2answers
189 views

Diadics and tensors. The motivation for diadics. Nonionic form. Reddy's “Continuum Mechanics.”

I'm taking a course in continuum mechanics. Our book is Continuum Mechanics by Reddy, a Cambridge edition. In the second chapter he introduces tensors and defines them to be polyadics. He is ...
2
votes
0answers
545 views

Publication date for Michael Spivak - Physics for Mathematicians II?

I bought the book "Physics for Mathematicians I" by Michael Spivak (http://www.amazon.com/Physics-Mathematicians-Mechanics-Michael-Spivak/dp/0914098322), have worked through quite some chapters and ...
17
votes
5answers
748 views

What Mathematics questions can be better solved with concepts from Physics?

Over the years, I've seen several questions in mathematics that can be solved using concepts borrowed from Physics. Having seen these question, I'm interested to find out what other mathematics ...
6
votes
3answers
375 views

Learning about the universe or special/general relativity

I have done a standard course in differential geometry/Riemannian geometry. Am I now able to understand the concepts people talk about when they say things like "spacetime is curved" and when I see ...
1
vote
1answer
326 views

What is the relationship between variance and energy

I was speaking with someone today who told me that variance, in the sense of probability theory, is equivalent mathematically to energy in physics. Can anyone elaborate on this relationship?
4
votes
1answer
109 views

Is $\Delta^2V$ one of the nature's favourite patterns?

I was reading Sawyer's Prelude to Mathematics, he says that there's one suposed nature's favourite pattern which is: $$\Delta^2V$$ He also says that this pattern is found in a dozen areas: conection ...
14
votes
7answers
2k views

Using mathematics in theoretical physics

I'm a non-mathematician who is self-studying mathematics. Although I'm very interested in mathematics, my main purpose is to apply math in theoretical physics. The problem is that when I read a ...
4
votes
2answers
577 views

What math is used in the theory of quantum computing?

I'd like to know what rung of the math ladder one need be on to grasp how a quantum computer computes. I realize this might not be a simple answer, so I'm just looking for an idea of the broad topics ...
11
votes
4answers
898 views

Pure maths vs applied

Is there any point in an aspiring theoretical physicist doing pure math topics such as analysis? (Assuming that he would not be doing them out of pure interest.)
2
votes
1answer
182 views

Embrace applied mathematics [closed]

Does anyone have any suggestions as to what is a good topic for a short talk on theoretical physics to a bunch of Math and Physics undergrads that might make them "embrace" theoretical physics? ...
3
votes
0answers
180 views

Designing a mathematical physics class

Surprisingly, the university (a major tech school) I attended does not offer a mathematical physics class. Consequently, I often get asked by my physics friends what are some good math classes to take ...
13
votes
3answers
954 views

Quantum mechanics for mathematicians

I'm looking for books about quantum mechanics (or related fields) that are written for mathematicians or are more mathematically inclined. Of course, the field is very big so I'm in particular ...
49
votes
10answers
5k views

Is learning (theoretical) physics useful/important for a mathematician?

I'm starting to read The Princeton Companion to Mathematics, at the beginning it says: A proper appreciation of pure mathematics requires some knowledge of applied mathematics and theoretical ...
14
votes
6answers
2k views

Books to learn physics, being a math major

What books would you recommend to learn physics, being a a Math major, from classical mechanics, electricity, etc. to modern physics?
81
votes
19answers
3k views

Good Physical Demonstrations of Abstract Mathematics

I like to use physical demonstrations when teaching mathematics (putting physics in the service of mathematics, for once, instead of the other way around), and it'd be great to get some more ideas to ...