# Joint Major in Mathematics and Physics

The fields of physics and mathematics have been closely intertwined, with significant influences on each other, for hundreds of years. Numerous courses and research programs at Harvey Mudd draw heavily on both disciplines. The Joint Major in Mathematics and Physics highlights the intersections between physics and mathematics while preparing a student with solid foundations in both fields. Graduates of this program should be well positioned for further study in physics or mathematics, or for immediate employment.

The major is cooperatively administered by the Mathematics and Physics departments, and students have faculty advisors in both departments. Students complete courses from the mathematics and physics major sequences, as well as a required course in computational techniques relevant to the field. Each student must complete a capstone (thesis or clinic), which may be chosen from either department’s offerings.

## Course Requirements

### Mathematics Courses (18.5 units)

- Mathematics 55: Discrete Mathematics (3)
- Mathematics 70: Intermediate Linear Algebra (1.5)
- Mathematics 80: Intermediate Differential Equations (1.5)
- Mathematics 131: Mathematical Analysis I (3)
- Mathematics 115: Fourier Series and Boundary Value Problems (3)

*or*Mathematics 180: Introduction to Partial Differential Equations (3) - Mathematics 157: Intermediate Probability (2)
- Mathematics 171: Abstract Algebra I (3)
- Mathematics 198: Undergraduate Mathematics Forum (1)
- Mathematics 199: Math Colloquium (0.5)

### Physics Courses (19 units)

- Physics 52: Quantum Physics (3)
- Physics 54: Modern Physics Laboratory (1)
- Physics 111: Theoretical Mechanics (3)
- Physics 116: Quantum Mechanics (3)
- Physics 117: Statistical Mechanics and Thermodynamics (3)
- Physics 134: Optics Laboratory (2)
- Physics 151: Electromagnetic Fields (3)

*or*Physics 154: Fields and Waves (3)

*or*Physics 156: Foundations of Field Theory (3) - Physics 195/Physics 196 Physics Colloquium (two semesters) (1)

### Joint Course Requirements (8 or 9 units)

#### Computational or Analytical Methods

One of

- Mathematics 164: Scientific Computing (3)
- Mathematics 165: Numerical Analysis (3)
- Physics 170: Computational Methods in Physics (2)

#### Capstone Research

Two semesters of capstone research experience in physics or mathematics, taken as *one* of the following four options:

- Mathematics Clinic
- Two semesters of Mathematics 197
- Physics Clinic
- Physics 193 and Physics 194
- Mathematics Thesis
- Two semesters of Mathematics 193
- Physics Thesis Research
- Three units each of Physics 191 and Physics 192

Students completing a thesis follow the practices and guidelines of the thesis advisor’s department.

## Electives

Suggested math and physics electives of interest (not part of the major):

- Mathematics 136: Complex Variables and Integral Transforms (students who take Mathematics 180: Introduction to Partial Differential Equations instead of Mathematics 115: Fourier Series and Boundary Value Problems are encouraged to take this class)
- Mathematics 142: Differential Geometry
- Mathematics 181: Dynamical Systems
- Physics 161: Topics in Quantum Theory

## Study Abroad Considerations

The following applies only to students who will be studying abroad for a semester in their junior or senior year:

- Sophomores may enroll in Mathematics 198: Undergraduate Mathematics Forum.
- Mathematics Colloquium requirement will not be waived.
- At most one semester of Physics Colloquium may be waived.