A mathematician starting to study physics

[Dark666]

Hi everyone, let me introduce myself. I'm studying my M. Sc. in mathematics and I'm very interested in singularities.

I have read some books and articles and it's very common hear about singularities in physics, actually one professor of my institute told me that some results of the fibration theorem of Milnor are used in the string theory.

Well the point is that I want to start to learn physics in order to study the singularities in both fields, math and physics, but I haven't found any good book in order to start.

Any one could recommend me some good books in order to start ?? I know that it's going to take some time the learn enough physics but I don't have any hurry.

By the way all my knowledge of physics it's like the first course of classical mecanics of the first semester of the career, it's almost nothing :S.

Thanks.

 

[homeomorphic]

First course in classical mechanics means introductory physics, right?

Best place to learn physics in the ENTIRE universe (for mathematicians):

John Baez's website.

Here are some general book recommendations.

http://math.ucr.edu/home/baez/books.html

I'm not sure if I like all of those books. Jackson sounds pretty awful for E and M from what I've heard. I looked up some things in it once, too. But, overall, his taste in books is pretty good. But, his own material is better than the books he recommends:

For quantum mechanics, I particularly recommend Sudbery's book, which is listed there (although the book is aimed at mathematicians, it's not completely rigorous, but it's good).

http://math.ucr.edu/home/baez/QG.html

This is Baez's quantum gravity seminar. At the bottom of the page, you will also find links to lecture notes and classical mechanics and quantum mechanics.

Oh, and I should mention that differential topology was used by Penrose to prove the existence of singularities within the event horizon of a black hole. He wrote a book about it. Techniques of differential topology in relativity.

 

[Hobin]

If I may give you some general advice, don't buy books. Yet.

Take a good look at the forums first. Browse around, and see what you like. By doing this, you can find out about the different subjects of study in physics. Seeing as you're - by your own words - new to physics, this would give you an overview of the field itself as well. As an added bonus, everything you can read on the forums is free. When you've done this, you will find it much easier to find books on the subjects you're interested in, without wasting a lot of money.

 

[yenchin]

I had math background [both B.Sc. and M.Sc.], but I am now a PhD student in physics, so I understand the daunting task you are facing to try to understand physics...

Anyway it depends on how much do you want to learn about physics. If you are only interested in singularities, you probably don't need to learn *all* of physics from scratch. You can start looking at general relativity (as long as you have differential geometry under your belt, it should not be too difficult). I recommend "https://www.amazon.com/dp/0125267401/?tag=pfamazon01-20".

Also look at "https://www.amazon.com/dp/0521336120/?tag=pfamazon01-20" by Naber.

Your library should have these books, so there is no need to buy them yet, until you decided that you really like them ;-)

In addition, this might be useful: http://arxiv.org/abs/math/0603190".

 

[Matrix0]

Hello there! It's great to hear that you are interested in studying singularities in both mathematics and physics. I can assure you that this is a fascinating and challenging area of research.

I would recommend starting with some introductory books on theoretical physics, such as "Introduction to Classical Mechanics" by David Morin or "Introduction to Quantum Mechanics" by David Griffiths. These books will provide you with a solid foundation in the basic principles and concepts of physics.

Once you have a good understanding of the fundamentals, you can then move on to more advanced texts that specifically focus on singularities, such as "Singularities and Topology of Hypersurfaces" by V.I. Arnold or "Singularities of Differentiable Maps" by V. I. Arnold and S. M. Gusein-Zade.

It's important to keep in mind that studying physics takes time and patience, so don't be discouraged if it seems challenging at first. With your background in mathematics, you already have a strong foundation for understanding the mathematical concepts involved in physics. Just keep an open mind and be willing to learn new things.

Best of luck on your journey into the world of physics and singularities!