# Math needed for undergrad Statistical Mechanics/Thermal Physics [duplicate]

A professor recommended me to take a course on Statistical Physics as preparation for agent-based computing in social sciences.

Now I have no experience in physics beyond basic highschool, and mathematics I have taken several discrete math courses (for computer science) and no calculus yet. I have had basic differentiation/trigonometry/integration in high school as well.

What math/physics do i need to be able to understand undergrad stat mechanics?

(btw. I am already planning to take classical mechanics, because that's what the university states as prerequisite)

• Possible duplicates: physics.stackexchange.com/q/234/2451 and links therein. – Qmechanic Nov 28 '13 at 18:24
• Well, it depends how far you want to go, but there is no way you can achieve a deep understanding of stat. mech. without having at least a reasonable understanding of probability theory... – Yvan Velenik Nov 28 '13 at 20:13

Depending on what your undergraduate class focuses on you will need some mathematical background in the following:

1. Basic probability theory: Some idea of permutations, probability distributions, mean and variance etc. Depending on how statistical the class gets you might need more.

2. Partial Differentiation: For the thermal physics side of things, a solid understanding of partial derivatives is key. Even though this is usually taught in a multivariable calculus class, you can easily pick this up if you understand basic derivatives, but don't underestimate its usefulness.

3. Basic Series Expansions: Approximations are everything, if you can't find an exact answer, a good approximation is the next best thing. Be able to expand simple polynomials and trigonometric functions. Stirling's Approximation is also used quite often.

For the physics side of things:

1. Basic Kinematics: Understanding of introductory physics ideas about force, momentum and energy. Basic systems like harmonic oscillators.

2. Quantization: Again depending on how in depth the class is, but it can be good to have an idea about quantization in physics. eg: de Broglie relations

This is not meant to be exhaustive, but a list of things that I remember being useful. Some basic chemistry might also be useful, but probably not necessary. I would strongly recommend talking to the professor teaching it to get a good idea of what to expect.