Pure and Applied | Graduate School | Applied Math | Physics | Finance | Cryptography | Data Science | Subplan in CS Theory/Discrete Mathematics
Getting Started:
Students majoring in mathematics have a wide range of eventual interests: some go into academia (in a variety of fields), and many pursue careers in finance, cryptography, the tech industry, and so on. The sample course plans below illustrate course selections that one can make as a Math major depending on one’s eventual aims, and are merely one possibility for each of the areas of interest listed; there are many other choices that a Math major can make within each area of interest (such as for the balance of courses between those in the Math department and math-related electives in other departments).
For details on the additional requirements for an Honors degree in Math, please see the Honors page. Since most Math courses are proof-based, early in the major we recommend (for those without proof-writing experience) taking one of the courses which introduce proof-writing: Math 104, Math 110, Math 113, or Math 115 (at least one of which is in each sample plan below).
The course plans below do not explicitly mention single-variable calculus or the 10 units associated with AP credit, but they assume the student has acquired those 10 units (so the total unit count in all sample course plans below includes these 10 units).
Here are the course options which we recommend to begin the major:
Course |
Course Title |
Units |
AP Credit (5 on BC) or Math 19, 20, 21 | Calculus | 10 |
One of the following sequences: | 15 | |
Math 51, 52, 53 | Multivariable Calculus and Linear Algebra | |
Math 61CM, 62CM, 63CM | Modern Mathematics: Continuous Methods (a proof-oriented sequence) | |
Math 61DM, 62DM, 63DM | Modern Mathematics: Discrete Methods (a proof-oriented sequence) |
For students with both Pure and Applied interests:
Course |
Course Title |
Units |
One of the following sequences: | Math 51, 52, 53
or Math 61CM, 62CM, 63CM or Math 61DM, 62DM, 63DM |
15 |
Math 104 or Math 113 | Applied Matrix Theory or Linear Algebra and Matrix Theory | 3 |
Math 106 | Functions of a Complex Variable | 3 |
Math 109 | Applied Group Theory | 3 |
Math 110 | Applied Number Theory and Field Theory | 3 |
Math 115 | Functions of a Real Variable | 3 |
Eight of the following courses, including at least three Math courses: | 24 | |
Math 107 | Graph Theory | |
Math 108 | Introduction to Combinatorics and Its Applications | |
Math 143 | Differential Geometry | |
Math 146 | Analysis on Manifolds | |
Math 147 | Differential Topology | |
Math 148 | Algebraic Topology | |
Math 152 | Elementary Theory of Numbers | |
Math 161 | Set Theory | |
Math 171 | Fundamental Concepts of Analysis | |
Math 173 | Theory of Partial Differential Equations | |
CME 108 | Introduction to Scientific Computing | |
Econ 50 | Economic Analysis I | |
Physics 41 | Mechanics | |
Physics 43 | Electricity and Magnetism | |
Physics 45 | Light and Heat | |
Stats 116 or Math 151 | Theory of Probability or Introduction to Probability Theory | |
Total Units | 64 |
For students with strong theoretical interest and considering Graduate School in Math:
Course |
Course Title |
Units |
One of the following sequences: | Math 51, 52, 53
or Math 61CM, 62CM, 63CM or Math 61DM, 62DM, 63DM |
15 |
Math 101 | Math Discovery Lab | 3 |
Math 113 | Linear Algebra and Matrix Theory | 3 |
Math 116 | Complex Analysis | 3 |
Math 120 | Groups and Rings | 3 |
Math 147 | Differential Topology | 3 |
Math 171 | Fundamental Concepts of Analysis | 3 |
Seven additional Math courses numbered 121 or higher (the logic courses Phil 151 and Phil 152 are considered to be such courses) | 21 | |
Total Units | 64 |
Those contemplating graduate school in Mathematics are recommended to take least 2 or 3 graduate-level math courses, such as Math 205A or Math 205B (on real analysis), Math 210A or Math 210B (on modern algebra), or Math 215A or Math 215B (on algebraic and differential topology). Such students should also consider entering the Honors program (hence writing a senior thesis).
For students interested in Applied Math:
Course |
Course Title |
Units |
One of the following sequences: | Math 51, 52, 53
or Math 61DM, 62DM, 63DM |
15 |
Math 104 | Applied Matrix Theory | 3 |
Math 106 | Functions of a Complex Variable | 3 |
Math 107 | Graph Theory | 3 |
Math 108 | Introduction to Combinatorics and Its Applications | 3 |
Math 109 | Applied Group Theory | 3 |
Math 110 | Applied Number Theory and Field Theory | 3 |
Math 115 | Functions of a Real Variable | 3 |
Math 171 | Fundamental Concepts of Analysis | 3 |
Math 173 | Theory of Partial Differential Equations | 3 |
Stats 116 or Math 151 | Theory of Probability or Introduction to Probability Theory | 3 |
Three elective courses from among Computer Science, Economics, Engineering, Physics, and Statistics | 9 | |
Total Units | 64 |
For students interested in Physics:
Course |
Course Title |
Units |
One of the following sequences: | Math 51, 52, 53
or Math 61CM, 62CM, 63CM |
15 |
Eight of the following courses: | 24 | |
Math 106 | Functions of a Complex Variable | |
Math 113 | Linear Algebra and Matrix Theory | |
Math 114/CME 108 | Introduction to Scientific Computing | |
Math 115 | Functions of a Real Variable | |
Math 118 | Mathematics of Computation | |
Math 120 | Groups and Rings | |
Math 122 | Modules and Group Representations | |
Math 131P | Partial Differential Equations | |
Math 137 | Mathematical Methods of Classical Mechanics | |
Math 146 | Analysis on Manifolds | |
Math 175 | Elementary Functional Analysis | |
Math 220/CME 303 | Partial Differential Equations of Applied Mathematics | |
Five elective courses from among Physics, Engineering, and Statistics | 15 | |
Total Units | 64 |
For students interested in Finance:
Course |
Course Title |
Units |
One of the following sequences: | Math 51, 52, 53
or Math 61CM, 62CM, 63CM |
15 |
Math 104 | Applied Matrix Theory | 3 |
Math 115 | Functions of a Real Variable | 3 |
Math 136 | Stochastic Processes | 3 |
Math 151 or Stats 116 | Introduction to Probability Theory or Theory of Probability | 3 |
Math 131P | Partial Differential Equations | 3 |
MS&E 245A (a pre-approved elective) provides a first introduction to financial math; sufficient background for this course is provided by Math 104, Stats 116, and Math 136. | Investment Science | 3-4 |
Seven of the following courses: | 21 | |
Math 171 | Fundamental Concepts of Analysis | |
Math 173 | Theory of Partial Differential Equations | |
Math 175 | Elementary Functional Analysis | |
Math 230A/Stats 310A | Theory of Probability | |
Math 236 | Introduction to Stochastic Differential Equations | |
Math 237 | Default and Systemic Risk | |
Math 238/Stats 250 | Mathematical Finance | |
MS&E 245B (a pre-approved 3-unit elective and sequel to MS&E 245A) gives additional undergraduate-level instruction in financial math; Math 131P is helpful background (beyond MS&E 245A). | Advanced Investment Science | |
Total Units | 64-65 |
Math 180, Introduction to Financial Mathematics, is no longer offered.
For students interested in Cryptography:
Course |
Course Title |
Units |
One of the following sequences: | Math 51, 52, 53
or Math 61DM, 62DM, 63DM |
15 |
Eight of the following courses: | 24 | |
Math 107 | Graph Theory | |
Math 109 | Applied Group Theory | |
Math 113 | Linear Algebra and Matrix Theory | |
Math 120 | Groups and Rings | |
Math 121 | Galois Theory | |
Math 145 | Algebraic Geometry | |
Math 151 or Stats 116 | Introduction to Probability Theory or Theory of Probability | |
Math 152 | Elementary Theory of Numbers | |
Math 154 | Algebraic Number Theory | |
Math 159 | Discrete Probabilistic Methods | |
Five elective courses from among Computer Science and Statistics | 15 | |
Total Units | 64 |
For students interested in Data Science:
Course |
Course Title |
Units |
One of the following sequences: | Math 51, 52, 53
or Math 61DM, 62DM, 63DM |
15 |
Math 104 | Applied Matrix Theory | 3 |
Math 107 | Graph Theory | 3 |
Math 108 | Introduction to Combinatorics and Its Applications | 3 |
Math 109 | Applied Group Theory | 3 |
Math 114/CME 108 | Introduction to Scientific Computing | 3 |
Math 115 | Functions of a Real Variable | 3 |
Math 151 or Stats 116 | Introduction to Probability Theory or Theory of Probability | 3 |
Math 159 | Discrete Probabilistic Methods | 3 |
Five elective courses from among Computer Science and Statistics | 15 | |
Total Units | 64 |