Math with Physics
A major in Physics can work with a major or minor in Mathematics to various degrees, depending on the physics track.
Overlap by track
Professional Option
Much of the overlap between the Physics - Professional Option major (and most of the other options included below) lies in the calculus courses:
- Calculus I: Math 151
- Calculus II: Math 152
- Calculus III/Multivariable Calculus: Math 251 or Math 291
- Calculus IV/Ordinary Differential Equations: Math 244 or 252 or Math 292
- “Calculus V” (unofficial)/Partial Differential Equations: Math 421 or Math 423
Calculus I-IV counts towards the core calculus requirements of a math major, while the PDE course will count towards a math major elective; all five courses count towards the math minor. Note that Math 252 has an Introduction to Linear Algebra (Math 250) prerequisite, a course that does not count towards physics requirements; however, a physics student may find the course helpful. Note that Math 244 does not satisfy math major core calculus requirements by default, but it may be possible to make it count; consult the Math Advisor about this if 244 is the ODE course you have or plan on completing.
Applied Option
The Applied Option has Calculus I-IV requirements. In addition, the six credit natural science elective requirement for the Applied Option can be satisfied by two Mathematics courses.
General Option
In addition to the Calculus I+II requirements for the General Option, the 18 credit natural science elective requirement for the General Option can be satisfied by up to six Mathematics courses.
Planetary Physics Option/Astrophysics
The amount of overlap with the Astrophysics option is similar to the overlap the Professional Option has. There is no requirement for a PDE course (421/423); however, the computing class requirement for Astrophysics can also satisfy the corresponding requirement for the Math major, so in total five courses can be shared between the two majors, as is the case with the Professional Option.
Other suggestions for math with physics
From here on the audience will be primarily assumed to be students who are likely to take advanced physics courses and are interested in mathematical physics.
Options for Calculus Courses
A Physics student may take either Math 244 or 252 or Math 292 and either Math 421 or Math 423 where it is required for their major. Depending on the amount of interest you have in the theory, you may prefer to take Math 252 or Math 292 and Math 423 over their engineering-audience counterparts. There is significantly more focus on the theory in these courses (especially in Math 292 over the alternatives), and if you are primarily interested in mathematics these courses are what you should take to fulfill the requirements.
This difference is particularly clear between Math 421 and Math 423, where the latter is sometimes a proof-based course with an expectation of mathematical maturity. Regardless, if you are interested in physics theory it is helpful to have a grasp of the notions and vocabulary of PDE when it will appear in your physics courses (Phys 382, 385, 386, 361, 417).
Linear Algebra
If you are at all interested in physics theory, knowing linear algebra will be required at some point. For Physics 417 (Intermediate Quantum Mechanics), the linear algebra background required is similar to that of Math 350 (Linear Algebra). You should take this course to satisfy your math major algebra course requirement.
The prerequisites for Math 350 include Math 250 (Introductory Linear Algebra) and Math 300 (Intro to Math Reasoning), which is the general prerequisite for most proof-based courses and required for the mathematics major.
Probability
Math 477 (Mathematical Theory of Probability) is another course with content relevant to some physics theory. Arguably, probability is more helpful early on compared to linear algebra, especially if you do not have much previous exposure to probability. The prerequisite is Math 251 (Multivariable Calculus), which allows you to take it before/during Phys 351 (Thermal Physics). The follow-up course Math 478 (Intro to Stochastic Processes) may also be of interest.
Math Courses and Their Related Physics Courses
Provided is a table of popular fields of Physics with their associated undergraduate classes (graduate courses omitted). In all cases, the authors recommend that the relevant math classes are taken currently or before the physics class. Any classes in bold denote classes typical of a professional physics/astrophysics major. To avoid frequent repetition, the Math column is cumulative—classes above the current cell are included, so the list compounds as you read down the column. We also avoid discussing lab classes, but the Professional track requires three upper-level labs (Phys 326, 327, 388/9) and the Astrophysics track requires two upper-level experiential classes (Phys 345-6) in addition to the classical labs.
| Field of Physics | Relevant Math Classes | Relevant Physics Classes |
|---|---|---|
| Classical Mechanics | 250, 251/291, 244/252/292 Intro Lin Alg, Calc 3, ODEs |
123-4, 271, 381-2 Analytical 1a-b, Honors Phys 1, Mechanics 1-2 (with relevant labs) |
| Electromagnetism | 421/423 PDEs (note that 421/423 are only essential for Phys 385-6.) |
227, 272, 385-6 Analytical 2a, Honors Phys 2, EM 1-2 (with relevant labs) |
| Quantum Mechanics | 350, 403, 477 Lin Alg, Intro Complex (soft suggestion), Probability Theory |
228, 273, 361, 417 Analytical 2b, Honors Phys 3, QM & Atomic Physics, Intermediate QM |
| Stat Mech/Thermal | Math 478 Intro Stochastics (soft suggestion) |
351 Thermal Physics |
| Condensed Matter | 406, 421, 464 Solid State, Intro QC, Math Physics |
|
| Particle Physics | 418 Nuclei and Particles |
|
| Astrophysics | Math 432 Diff Geo |
341-2, 441/2/3/4 Principle of Astro 1-2, Stars, High Energy Astro, Galaxies, Cosmo |