Exercises on mathematical physics

[PhysiSmo]

Hi everyone, I'm looking for textbooks that contain exercises on various aspects of mathematical physics (everything a theoretical physicist needs actually, i.e. from linear algebra and tensor analysis to differential geometry and topology etc.) at a graduate level.

I am aware, of course, that there cannot exist a single textbook to do job. However, I' m pretty interesting in hearing others' suggestions and opinions for these subjects!

 

[will.c]

Arfken & Weber has exercises.

 

[oswaler]

I would recommend beginning with a thorough understanding of the fundamentals of mathematical physics, such as calculus, linear algebra, and differential equations. From there, textbooks such as "Mathematical Methods in the Physical Sciences" by Mary L. Boas and "Mathematical Methods for Physicists" by George B. Arfken and Hans J. Weber can provide a solid foundation in the mathematical concepts needed for theoretical physics.

For exercises specifically on linear algebra, I would suggest "Linear Algebra Done Right" by Sheldon Axler or "Introduction to Linear Algebra" by Gilbert Strang. For tensor analysis, "Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers" by Hung Nguyen-Schäfer and Jane Schäfer-Korting is a good resource.

In terms of more advanced topics like differential geometry and topology, "Differential Geometry, Lie Groups, and Symmetric Spaces" by Sigurdur Helgason and "Topology, Geometry and Gauge Fields: Foundations" by Gregory Naber are both highly recommended.

Ultimately, the best approach may be to use a combination of textbooks and online resources, such as lecture notes and problem sets from universities, to cover all the necessary topics and provide a variety of exercises at a graduate level. It's also important to practice and apply these mathematical concepts to real-world problems in physics to truly solidify your understanding.