Math courses for Theoretical Condensed Matter

In summary, the conversation discusses the mathematics courses that a physics and math major should take in order to do research in theoretical aspects of condensed matter. The suggested courses include abstract algebra, differential geometry, topology, linear algebra, transform methods, chaotic and non-linear behavior, and differential forms. The speaker has already taken courses in real and complex analysis, ODEs, PDEs, and metric spaces, and plans to take a course in computational methods. They also mention the potential usefulness of differential geometry in general relativity and the recommendation for physicists to learn differential forms. However, the overall consensus is that linear algebra and transform methods are the most important courses for condensed matter research, while the others may not be necessary.
  • #1
Silicon-Based
51
1
I'm a physics and math major, going into my 3rd year. Suppose I want to do research in theoretical aspects of condensed matter. What would be the mathematics I should be learning as an undergraduate? Here is a rundown of courses I'm considering taking next year:
  1. Abstract Algebra: it seems a little preposterous for a math major to not have taken a course in abstract algebra, and things like group theory seem to be very applicable in theoretical physics from what I have read.
  2. Differential Geometry: from what I've read, differential geometry is not used in condensed matter, except for a few fancy things like cell membranes.
  3. Topology: it looks like topology is used extensively, although it isn't clear to me if taking a upper-undergrad course in point-set topology will be of any use. It looks like it isn't until one learns algebraic topology that some of the concepts (homotopy, homology etc.) would become of any use, and even then I'm not sure if physicists would learn those at the same level of rigour as a mathematician would. If I wanted to focus on topological effects specifically, would it be advisable to take a graduate sequence in algebraic topology, or take an undergraduate course in point-set topology, or neither?
  4. Linear Algebra: I have the option to take a more advanced proofs-based linear algebra course which mostly covers topics I haven't encountered in the first course I took (canonical forms, adjoints, operators, spectral theorem). I liked linear algebra and have seen some people comment to take as many linear algebra courses as possible for condensed matter / theoretical physics.
  5. Transform Methods: there is also one course that covers a wide range of transform techniques in depth (Fast and Discrete Fourier, Laplace, Radon) and their applications, and I'm not sure how useful these would be.
  6. There is also a course on chaotic and non-linear behaviour offered and I would have thought it would be a great course to take for condensed matter as it also touches on collective behaviour.
  7. Differential forms: I know nothing about this one.
I have taken courses in real and complex analysis, ODEs, PDEs + some numerical analysis, and metric spaces already, and will be taking a course in computational methods.
 
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  • #3
Topology, maybe. Linear algebra, absolutely. Transform methods, absolutely. Chaos and non-linear, yes, the others, I weouldn't think they would be necessary.
 
  • #4
Differential forms would be something i recommend every physicist take (learn properly). However, I am biased.

From the list I'd say, Linear algebra >>>>>>>>>>> transform methods > differential forms >> rest

Differential forms can speed up a lot of computations when learned, but more linear algebra/transform methods will be way more useful than the rest.
 

Related to Math courses for Theoretical Condensed Matter

1. What is the purpose of taking a Math course for Theoretical Condensed Matter?

The purpose of taking a Math course for Theoretical Condensed Matter is to develop a strong foundation in mathematical concepts and techniques that are essential for understanding and analyzing complex phenomena in condensed matter physics. These courses cover topics such as linear algebra, differential equations, complex analysis, and group theory, which are used to describe and model the behavior of condensed matter systems.

2. What are the prerequisites for enrolling in a Math course for Theoretical Condensed Matter?

The prerequisites for enrolling in a Math course for Theoretical Condensed Matter typically include a strong background in calculus, linear algebra, and differential equations. Some courses may also require knowledge of multivariable calculus, complex analysis, and group theory. It is important to check with the specific course or program to determine the exact prerequisites.

3. How will a Math course for Theoretical Condensed Matter benefit my research or career?

A Math course for Theoretical Condensed Matter will provide you with the necessary tools and techniques to analyze and solve complex problems in condensed matter physics. This will be beneficial for your research as it will allow you to better understand and interpret experimental data, develop new theoretical models, and make predictions about the behavior of condensed matter systems. It will also be beneficial for your career as it will make you a more competitive candidate for research positions in academia or industry.

4. Are there any specific topics covered in a Math course for Theoretical Condensed Matter?

Yes, there are specific topics that are typically covered in a Math course for Theoretical Condensed Matter. These may include linear algebra, differential equations, Fourier analysis, complex analysis, group theory, and tensor analysis. Some courses may also cover more specialized topics such as topology, functional analysis, and numerical methods. The exact topics covered may vary depending on the course or program.

5. Are there any online resources available for studying Math for Theoretical Condensed Matter?

Yes, there are many online resources available for studying Math for Theoretical Condensed Matter. These may include lecture notes, textbooks, video lectures, and practice problems. Some universities also offer online courses or open access materials for studying Math for Theoretical Condensed Matter. It is important to carefully evaluate the credibility and accuracy of these resources before using them for studying.

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