Improving my mathematical foundation for physics

[WWCY]

Hi all,

I am making a decision regarding the mathematics courses I should take before graduating so that I can leave Uni with a "decent enough" mathematical foundation.

Some courses I had in mind were Linear Algebra, Group Theory, and Probability & Statistics, however I have little knowledge about these courses, much less their significance to physics. Could anyone kindly elaborate on how important these fields of mathematics are to varying fields of physics?

Also, are there other mathematics courses I should be looking out for?

Many thanks in advance.

P.S. The LA I have in mind is the one people in Math read. The LA I have read is "catered" to physics students, and I have found its content woefully inadequate.

 

[FactChecker]

The subjects of differential equations, Fourier series, and complex analysis come to mind. I don't know if full courses are needed in these or the ones you have mentioned. I would recommend those over full courses of group theory (abstract algebra) and statistics. But definitely get some probability and statistics. If there are some overview mathematics for physicists courses, you should take those and work from there.

PS. When you don't put your educational background in your profile for people to view, you need to completely describe it in these posts.

 

[WWCY]

Thank you for your response.

The subjects of differential equations, Fourier series, and complex analysis come to mind. I don't know if full courses are needed in these or the ones you have mentioned. I would recommend those over full courses of group theory (abstract algebra) and statistics. But definitely get some probability and statistics. If there are some overview mathematics for physicists courses, you should take those and work from there.

PS. When you don't put your educational background in your profile for people to view, you need to completely describe it in these posts.

I have read the subjects mentioned above in my mathematics courses, except that they have been "watered down" for physics students. I have found this to be a big limiting factor especially in Linear Algebra when it comes to studying QM. Perhaps I should look to read the pure maths versions of Linear Algebra instead of the courses I initially mentioned? It seems to me that Linear Algebra is a pretty useful tool in many fields of physics, and not having a good grasp of it is just asking for trouble.

For what its worth, the course descriptions to the courses are in the link here: http://www1.spms.ntu.edu.sg/~maths/Undergraduates/MASUndergradModules.html

Linear Algebra (physics version): MH2800
Linear Algebra I (maths version): MH1200
Linear Algebra II (maths version): MH1201

PS. I will look to update my educational profile as soon as I can, thanks for the tip.

 

[FactChecker]

I agree that linear algebra is a must-have. I'm sorry that I did not say that.

 

[ZapperZ]

Thank you for your response.
I have read the subjects mentioned above in my mathematics courses, except that they have been "watered down" for physics students. I have found this to be a big limiting factor especially in Linear Algebra when it comes to studying QM. Perhaps I should look to read the pure maths versions of Linear Algebra instead of the courses I initially mentioned? It seems to me that Linear Algebra is a pretty useful tool in many fields of physics, and not having a good grasp of it is just asking for trouble.

For what its worth, the course descriptions to the courses are in the link here: http://www1.spms.ntu.edu.sg/~maths/Undergraduates/MASUndergradModules.html

Linear Algebra (physics version): MH2800
Linear Algebra I (maths version): MH1200
Linear Algebra II (maths version): MH1201

PS. I will look to update my educational profile as soon as I can, thanks for the tip.

How about pick up one of the mathematical physics text that have been recommended all over this forum, look at the various math topics that are covered, and use that as a starting guide on the type of mathematics that you might need?

Example: Mary Boas "Mathematical Methods in the Physical Sciences". If you do a search on this, you'll see plenty of recommendations. Beyond that, there's always Arfken's mathematical physics text.

Zz.

 

[FactChecker]

Symmetry and Noether's theorem are important in physics. So abstract algebra may also be important for you.

 

[MidgetDwarf]

There is a nice Linear Algebra book. Very easy to read and informative, without sacrificing rigor. Sterling Berberian writes very clear math books.
https://www.amazon.com/dp/0486780554/?tag=pfamazon01-20
You can buy the hardcover first edition for about $4 more.
This is more along the lines of a pure math book. Theorems and Proofs. Everything is explained well. It feels like cheating. Can be used for both a first and second exposure to Linear Algebra. Once you finish this book, you can move onto more advance books.

I gained a good understanding of Linear Algebra from this book, and I used what I learned here to do well in courses in E&M and QM.

 

[MidgetDwarf]

For probability, I would not recommend a full course, especially if it very theoretical in nature.

I would get an old copy of Degroot: Introduction to Probability and Statistics. Good for exercises. Some explanations are rather vague.

I used this book, and it is one of my favorite math books. Joseph K. Blitzstein, is a Harvard professor.
https://www.amazon.com/dp/1466575573/?tag=pfamazon01-20

The information here, would probably be used in statistical mechanics course. I can see ideas from probability being put to good use in a modeling course/project and experiments... I would just read books, for the sake of learning fun math.