Math prereq for Theoretical & Solid-State Physics

[neuralnode]

Hi all,

I'm interested in theoretical & solid-state physics, but not planning to start an academic path (because of my age, job, other plans etc.). Nonetheless, I'd like to get as much university-grade knowledge as possible. I'd appreciate some suggestions as to the math branches/topics I'll need to study, and examples of the best (in your opinion) textbooks on those subjects. I have a basic understanding of calculus and have read mainly pop-sci books on physics, so my list of required reading would really need to start from fundamentals. Still, I'm quite fast at grasping concepts and math, as long as they're served in the right way (i.e. without omissions or frequent references to "assumed" knowledge). Again, I'm asking primarily about math, which I'm the most behind with.

(BTW: Is the math required in theoretical physics sufficient to study solid-state concepts?)

Thanks in advance.

 

[Dr. Courtney]

Hi all,

I'm interested in theoretical & solid-state physics, but not planning to start an academic path (because of my age, job, other plans etc.). Nonetheless, I'd like to get as much university-grade knowledge as possible. I'd appreciate some suggestions as to the math branches/topics I'll need to study, and examples of the best (in your opinion) textbooks on those subjects. I have a basic understanding of calculus and have read mainly pop-sci books on physics, so my list of required reading would really need to start from fundamentals. Still, I'm quite fast at grasping concepts and math, as long as they're served in the right way (i.e. without omissions or frequent references to "assumed" knowledge). Again, I'm asking primarily about math, which I'm the most behind with.

(BTW: Is the math required in theoretical physics sufficient to study solid-state concepts?)

Thanks in advance.

Any area of study in physics requires:

Calc I, II, and III
Differential Equations
Linear Algebra

Also recommended:

partial differential equations
complex analysis
numerical analysis

 

[Mene]

As a scientist in the field of physics, I would recommend that you focus on strengthening your understanding of calculus, linear algebra, and differential equations. These are essential mathematical tools for theoretical and solid-state physics. In particular, you should have a strong grasp of vector calculus, as it is used extensively in both fields.

For textbooks, I would suggest "Mathematical Methods in the Physical Sciences" by Mary L. Boas as a comprehensive guide to the mathematical techniques used in physics. Another useful resource is "Mathematical Methods for Physics and Engineering" by K.F. Riley, M.P. Hobson, and S.J. Bence. Both of these books are widely used in university courses and cover the necessary topics in a clear and thorough manner.

In terms of solid-state physics, a strong understanding of quantum mechanics is also crucial. I would recommend "Introduction to Quantum Mechanics" by David J. Griffiths as a good starting point. As for your question about whether the math required in theoretical physics is sufficient for studying solid-state concepts, the answer is yes. The mathematical tools used in theoretical physics are also applicable to solid-state physics, as they both involve the study of fundamental physical laws and their mathematical representation.

I wish you all the best in your pursuit of university-grade knowledge in theoretical and solid-state physics. With dedication and hard work, I have no doubt that you will be able to grasp the necessary math concepts and excel in your studies.