The laws of physics are written in the language of mathematics, so a solid footing in math will be fundamental to your education.
Majors are required to take four math courses – what is generally referred to as the calculus sequence:
- Math 131 – Calculus I
- Math 132 – Calculus II
- Math 233 – Calculus III
- Math 217 – Differential Equations
If you don’t like math, it’s okay; you’ll learn to appreciate (or accept) it during college. If you’re math-anxious, don’t worry there are plenty of resources on campus to help! Here’s an article: there’s no such thing as a math person.
Depending on your high school math background, you may be excused from some of the math requirements. However, make sure you know the contents of the course you’ll place out of; in undergrad physics courses, you’ll mainly focus on grinding through messy math and, in upper-level courses, developing mathematical and physical intuition — not writing formal proofs.
You’ll likely want to learn how to program if you want to go into a physics or tech-related job. If you know how to already, it’s possible to test out of Intro Computer Science – you do this at the beginning of each fall. Typically once you know one language it’s much easier to learn another: you can usually pick up new skills as you go along, especially in courses or if you work in a research lab.
If you want guided instruction in a specific computer program or language, parse through the math and engineering departments’ course offerings. Here are just a few examples of past courses and the languages taught:
- C – night or summer University College Math 123
- C++ – CSE 132, 332
- CAD – Mechanical Engineering 202
- Java – Computer Science 131, 132
- MATLAB – Physics 427 (Intro to Computational Physics), Math 449/450
- Python (often; check each semester) – Math 449/450
If you’re experienced in programming and up for a challenge giving a fast-paced introduction to many new languages in one semester, you may be interested in taking the graduate-level course Physics 584 – Computational Methods. Some majors choose to delve even deeper into computer science coursework, sometimes even getting a minor or second major in that field.
Beyond the Required Courses
If you want to stay in a science or tech field after graduation, you’re probably going to want more math or computer science background to be well-prepared. Some of the good 300-level courses that might give you a more solid foundation (there’s a lot of overlap between these) are:
- Math 308 – Math for the Physical Sciences
- Math 309 – Matrix Algebra
- ESE 318 – Engineering Math A
- ESE 319 – Engineering Math B
If you want to do research or jobs involving statistics or data processing (such as observational astrophysics or biological imaging), you might also try a course or two like:
- Math 3200 – Elementary to Intermediate Statistics
- Math 493 – Probability
- ESE 326 – Probability and Statistics for Engineering
- ESE 351 – Signals and Systems
- ESE 482 – Digital Signal Processing
- CSE 417 – Machine Learning
- Other upper-level math, electrical/systems engineering, and computer science electives
Future PhD students in Theoretical Physics
Theoretical physics refers anything where you’re not in a lab doing hands-on work or outside gathering data — rather, you’re developing theories about a specific area of physics using mathematics and computer modeling. You can be a theoretical biophysics, a theoretical astrophysicist, etc.
A closely related field, mathematical physics, is “the development of mathematical methods for applications to problems in physics.” It’s often considered a subfield of applied mathematics, but the flavor of what you end up doing (math-y physics or physics-y math) will depend on your research advisor and his/her area of study.
If you want to do theoretical or mathematical physics work, you’ll need a strong mathematical background. You need the fundamentals of a broad range of topics to understand physics, and when you start doing theoretical research (whether now or in grad school), you’ll go into depth into a few more specific to your field.
Many majors choose to get a complete second major in mathematics. However, you can also just pick and choose pure and applied math courses from various departments that suit your tastes, even if they don’t add up to a math major. What’s important for applying to graduate school is what you learn, not your degree title (yes, you’ll probably need a graduate degree to become a research scientist).
We’re quite partial to the physics department’s version of math courses; they usually strike a nice balance between giving an overview of a mathematical concept, learning how to solve problems using that concept, and building up intuition. You’ll find that upper-level Math Department courses are more focused on constructing rigorous arguments than solving problems and developing intuition. Likewise, you might find the engineers focus more on modeling and quantitative methods than the beautiful underlying mathematics of a problem. However, we still recommend that you look at other departments: they will expand your course choices greatly and can expose you to lots of new, exciting topics.
The following is just a list of many possibilities. Use it to generate ideas, but by no means feel stuck taking any of these courses right now. It’s crucial that you get a solid footing in math and physics in college so you have the skills and qualifications necessary to move on to the next stage of your life. However, it’s equally important to figure out what subjects most pique your interest, to explore what types of fields or careers might be a good fit, and to not get burned out.
(But if you’re the type of person who needs an extra intellectual challenge 24/7 to avoid burnout, by all means go full speed ahead. Nobody will stop you in this department.)
Also, it doesn’t really matter what department you take a course in; what matters is whether you learned the material or not. Read the course descriptions each semester to figure out which classes are the best fit for you.
Math you should know
Here are some topics outside of the calculus sequence that you need to get familiar with during college. You can either learn them through the appropriate math courses offered in the math, physics, or electrical engineering departments, by self-study; through a core physics course that covers the appropriate topic.
- Vectors and tensors
- Matrix algebra
- Complex numbers
- Basics about special functions used in physics – Airy, Bessel, gamma, etc.
- Fourier transforms, Laplace transforms, etc.
- Basic probability and statistics
If you want to study mathematical physics, try to get exposed to most or all of the following areas before grad school. If you want to do theory but don’t know what type yet, it would be good to get a few of the following in your toolbox during undergrad. You can find appropriate courses in the math, physics, or electrical engineering departments; we list a few of the many options in parentheses.
- Calculus of several variables (Math 308/318, ESE 501)
- Complex analysis (Math 416, Phys 501, Math 5021)
- Partial differential equations (Math 415, Phys 501-502, ESE 501-502, ESE 517)
- Group theory and symmetries (Math 430, Phys 590.2)
- Approximation methods or computational methods (Phys 503-504, Phys 584)
And if you’re up for deeper study, you can choose from the breadth of fun pure mathematics topics too:
- Advanced statistics/data processing (Math 493, Math 5051, ESE 351, ESE 520, ESE 524, etc.)
- Differential geometry (Math 407)
- Topology (Math 4171-4181)
- Functional analysis (Math 4111-4121, Math 5051-5052)
- Algebraic geometry (Math 436)
Don’t worry if you can’t study everything – you’ll have plenty of time in graduate school. Besides, you’re a physicist, so enjoy learning about how the world works, and leave yourself time for exploration of other fields too.
If you already have a specific physics interest you know you want to pursue for grad school, you probably should listen to professors in that subfield, not us. For example, a general relativist will want to know differential geometry, whereas a quantum field theorist will be more interested in modern algebra (group theory and stuff, that is, not the same as the algebra you learn in middle school). But it also never hurts to branch out a bit just in case your interests change!
Mathematical Courses in the Physics Department
The only regularly offered math-for-physicists courses in our department are the graduate-level core courses. Technically, you can enroll in these as an undergrad, but you should speak with a professor to find out if you’re ready – graduate courses very rarely list prerequisites in their descriptions, and the professor isn’t going to slow down the course pace for you. Also, graduate students generally take only 9 credits per semester, so budget your time accordingly.
The core courses are taken by first- and second-year graduate students to review major topics like complex variables, partial differential equations, and special functions:
- Physics 501 – Theoretical Physics
- Physics 502 – Mathematical Methods of Physics II
Another core course covers interesting math, but historically it has not been as quickly paced and mostly attracts biosciences researchers, even from outside the department:
- Physics 509 – Nonlinear Dynamics
The department also offers special topics courses less frequently. Some mathematical ones have included:
- Physics 503 & 504 – Advanced Math Methods for Physicists and Engineers I & II
- Physics 584 – Computational Methods
- Physics 590.2 – Group Theory and Symmetries in Physics
Math Courses in Other Departments
Here’s just a partial listing of applied mathematics courses offered in departments other than Math and Physics. Feel free to choose from these too if they look interesting; don’t feel limited by silly department titles!
- Computer Science and Engineering (CSE) 240: Logic and Discrete Mathematics
- CSE 247: Data Structures and Algorithms
- CSE 347: Analysis of Algorithms
- CSE 515T: Bayesian Methods in Machine Learning
- CSE 541T: Advanced Algorithms
- CSE 542T: Advanced Data Structures and Algorithms
- CSE 543T: Algorithms for Nonlinear Optimization
- CSE 544T: Special Topics in Computer Science Theory
- CSE 546T: Computational Geometry
- CSE 554T: Topological Applications for Data Analysis and Machine Learning
- CSE 582T: Complexity Theory
- Economics 467: Game Theory
- Econ 493: Mathematical Economics
- Econ 511-513: Quantitative Methods in Economics and Econometrics
- Electrical/Systems Engineering (ESE) 318: Engineering Mathematics A
- ESE 319: Engineering Mathematics B
- ESE 326: Probability and Statistics for Engineering
- ESE 351: Signals and Systems
- ESE 415: Optimization
- ESE 425: Random Processes and Kalman Filtering
- ESE 427: Financial Mathematics
- ESE 501/502: Mathematics of Modern Engineering I & II
- ESE 516: Optimization in Function Space
- ESE 517: Partial Differential Equations
- ESE 520: Probability and Stochastic Processes
- ESE 524: Detection and Estimation Theory
- ESE 551/552: Linear Dynamic Systems I & II
- ESE 553/554: Nonlinear Dynamic Systems
- Finance 538: Stochastic Foundations for Finance
- Finance 539: Mathematical Finance
- QBA 120/121: Managerial Statistics