Stanford University

Sample Course Plans

Students majoring in mathematics have a wide range of eventual interests: some go into academia, a finance, cryptography, the tech industry, and more.

The sample course plans below are examples of course selections a Math major can take depending on their interests. These sample plans are simply possibilities; there are many choices a Math major can make based on their interests.

Note: Math 56 (Proofs and Modern Mathematics, 3 units) can be used as part of any of the sample plans provided below in place of any of the listed Math department courses or electives.

One of the following (10 units):

Math 19, Math 20, Math 21 or 

AP Calculus

One of the following sequences (15 units):

Math 51, Math 52, Math 53 or 

Math 61CM, Math 62CM, Math 63CM, or 

Math 61DM, Math 62DM, Math 63DM


Math Courses:

Math 104: Applied Matrix Theory or Math 113: Linear Algebra and Matrix Theory (3 units)

Math 106: Functions of a Complex Variable or Math 116: Complex Analysis (3 units)

Math 107: Graph Theory (3 units)

Math 108: Introduction to Combinatorics and its Applications (3 units)

Math 109: Applied Group Theory or Math 120: Groups and Rings (3 units)

Math 110: Applied Number Theory and Field Theory (3 units)

Math 115: Functions of a Real Variable or Math 171: Fundamental Concepts of Analysis (3 units)

Math 144: Introduction to Geometry and Topology ​​​​​​​(3 units)

Math 173: Theory of Partial Differential Equations ​​​​​​​(3 units)

Math 175: Elementary Functional Analysis ​​​​​​​(3 units)

Math 151: Introduction to Probability Theory or Stats 116: Theory of Probability ​​​​​​​(3-4 units)


Elective courses from Computer Science, Economics, Engineering, Physics, and Statistics (6 units).


TOTAL UNITS: 64-65

One of the following (10 units):

Math 19, Math 20, Math 21 or AP Calculus

One of the following sequences (15 units):

Math 51, Math 52, Math 53 or 

Math 61DM, Math 62DM, Math 63DM


Eight of the following courses:

Math 107: Graph Theory (3 units)

Math 109: Applied Group Theory (3 units)

Math 113: Linear Algebra and Matrix Theory (3 units)

Math 120: Groups and Rings (3 units)

Math 121: Galois Theory (3 units)

Math 145: Algebraic Geometry (3 units)

Math 151: Introduction to Probability Theory or Stats 116: Theory of Probability (3-4 units)

Math 154: Algebraic Number Theory (3 units)

Math 159: Discrete Probabilistic Methods (3 units)


Elective courses from Computer Science and Statistics (15 units).


TOTAL UNITS: 64-65

One of the following (10 units):

Math 19, Math 20, Math 21 or 

AP Calculus

One of the following sequences (15 units):

Math 51, Math 52, Math 53 or 

Math 61CM, Math 62CM, Math 63CM, or 

Math 61DM, Math 62DM, Math 63DM


Math Courses:

Math 113: Linear Algebra and Matrix Theory (3 units)

Math 143: Differential Geometry (3 units)

Math 144: Introduction to Geometry and Topology (3 units)

Math 147: Differential Topology or Math 148: Algebraic Topology (3 units)

Math 151: Introduction to Probability Theory (3 units)

Math 171: Fundamental Concepts of Analysis (3 units)

Math 172: Lebesgue Integration and Fourier Analysis or Math 205A: Real Analysis (3 units)

Math 175: Elementary Functional Analysis or Math 205B: Real Analysis (3 units)

CS 148: Introduction to Computer Graphics and Imaging (3-4 units)

CS 250L: Continuous Mathematical Methods with an Emphasis on Machine Learning (3 units)

CME 302: Numerical Linear Algebra* (3 units)

*Sufficient to have taken Math 113; know basic coding.

Math 226/CME 306: Numerical Solution of Partial Differential Equations (3 units)

Math 228/CME308/MS&E 324: Stochastic Methods in Engineering (3 units)

EE 261: The Fourier Transform and its Applications (3 units)


TOTAL UNITS: 67-68


Courses that are less essential to Computer Graphics/Numerical Methods but are useful:

Math 107: Graph Theory (3 units)

Math 106: Functions of a Complex Variable or Math 116: Complex Analysis (3 units)

Math 120: Groups and Rings (3 units)

Math 220/CME 303: Partial Differential Equations of Applied Mathematics (3 units)

Physics 61: Mechanics and Special Relativity (4 units)

Physics 110: Advanced Mechanics (3-4 units)

One of the following (10 units):

Math 19, Math 20, Math 21 or 

AP Calculus

One of the following sequences (15 units):

Math 51, Math 52, Math 53 or 

Math 61CM, Math 62CM, Math 63CM, or 

Math 61DM, Math 62DM, Math 63DM


Math Courses:

Math 104: Applied Matrix Theory (3 units)

Math 107: Graph Theory (3 units)

Math 108: Introduction to Combinatorics and its Applications (3 units)

Math 114/CME 108: Introduction to Scientific Computing (3 units)

Math 115: Functions of a Real Variable (3 units)

Math 136: Stochastic Processes

Math 151: Introduction to Probability Theory or Stats 116: Theory of Probability (3-4 units)

Math 159: Discrete Probabilistic Methods (3 units)


Elective courses from Computer Science and Statistics (15 units).


TOTAL UNITS: 64-65

One of the following (10 units):

Math 19, Math 20, Math 21 or 

AP Calculus

One of the following sequences (15 units):

Math 51, Math 52, Math 53 or 

Math 61CM, Math 62CM, Math 63CM, or 

Math 61DM, Math 62DM, Math 63DM


Math Courses:

Math 104: Applied Matrix Theory or Math 113: Linear Algebra and Matrix Theory (3 units)

Math 108: Introduction to Combinatorics and its Applications (3 units)

Math 151: Introduction to Probability Theory or Stats 116: Theory of Probability (3-4 units

Math 114/CME 108: Introduction to Scientific Computing (3 units)

Math 115: Functions of a Real Variable (3 units)

Math 131P: Partial Differential Equations (3 units)

Math 136: Stochastic Processes or Math 158: Basic Probability and Stochastic Processes with Engineering Applications (3 units)

Math 159: Discrete Probabilistic Methods (3 units)

Math 171: Fundamental Concepts of Analysis (3 units)

Math 173: Theory of Partial Differential Equations (3 units)


Elective Courses:

Bio 113: Fundamentals of Molecular Evolution (4 units)

Bio 172:  Ecological Dynamics: Theory and Applications (4 units)

Bio 183: Theoretical Population Genetics (3 units)

CS 161: Design and Analysis of Algorithms (3-5 units)

Stats 155: Statistical Methods in Computational Genetics (3 units)


TOTAL UNITS: 64

One of the following (10 units):

Math 19, Math 20, Math 21 or 

AP Calculus

One of the following sequences (15 units):

Math 51, Math 52, Math 53 or 

Math 61CM, Math 62CM, Math 63CM


Math Courses:

Math 104: Applied Matrix Theory (3 units)

Math 115: Functions of a Real Variable (3 units)

Math 136: Stochastic Processes (3 units)

Math 151: Introduction to Probability Theory or Stats 116: Theory of Probability (3-4 units)

Math 131P: Partial Differential Equations (3 units)

MS&E 245A: Investment Science* (3-4 units)

*Provides a first introduction to financial math. Sufficient background for this course is provided by Math 104, Math 136, and Stats 116.


Seven of the following courses:

Math 171: Fundamental Concepts of Analysis (3 units)

Math 173: Theory of Partial Differential Equations (3 units)

Math 175: Elementary Functional Analysis (3 units)

Math 230A/Stats 310A: Theory of Probability (3 units)

Math 236: Introduction to Stochastic Differential Equations (3 units)

Math 237: Default and Systemic Rish (3 units)

Math 238/Stats 250: Mathematical Finance (3 units)

MS&E 245B: Advanced Investment Science* (3 units)

*Gives additional undergraduate-level instruction in financial math. Math 131P is helpful background.


TOTAL UNITS: 64-66

One of the following (10 units):

Math 19, Math 20, Math 21 or 

AP Calculus

One of the following sequences (15 units):

Math 51, Math 52, Math 53 or 

Math 61CM, Math 62CM, Math 63CM, or 

Math 61DM, Math 62DM, Math 63DM


Math Courses:

Math 113: Linear Algebra and Matrix Theory (3 units)

Math 116: Complex Analysis (3 units)

Math 120: Groups and Rings (3 units)

Math 144: Introduction to Geometry and Topology (3 units)

Math 147: Differential Topology (3 units)

Math 171: Fundamental Concepts of Analysis (3 units)


Seven additional Math courses numbered 121 or higher. Phil 151 and Phil 152 are accepted (21 units).


TOTAL UNITS: 64


Students contemplating graduate school in Mathematics are recommended to take least 2 or 3 graduate-level math courses, such as Math 205A or Math 205B (real analysis), Math 210A or Math 210B (modern algebra), or Math 215A or Math 215B (algebraic and differential topology).

Students can also consider applying for the Math honors program and writing a senior thesis.

One of the following (10 units):

Math 19, Math 20, Math 21 or 

AP Calculus

One of the following sequences (15 units):

Math 51, Math 52, Math 53 or 

Math 61CM, Math 62CM, Math 63CM


Eight of the following courses:

Math 106: Functions of a Complex Variable or Math 116: Complex Analysis (3 units)

Math 113: Linear Algebra and Matrix Theory (3 units)

Math 114/CME 108: Introduction to Scientific Computing (3 units)

Math 115: Functions of a Real Variable or Math 171: Fundamental Concepts of Analysis (3 units)

Math 120: Groups and Rings (3 units)

Math 122: Modules and Group Representations (3 units)

Math 131P: Partial Differential Equations or Math 173: Theory of Partial Differential Equations (3 units)

Math 143: Differential Geometry (3 units)

Math 144: Introduction to Geometry and Topology (3 units)

Math 151: Introduction to Probability Theory (3 units)

Math 171: Fundamental Concepts of Analysis (3 units)

Math 175: Elementary Functional Analysis (3 units)


Five elective courses from Physics, Engineering, and Statistics (15 units).


TOTAL UNITS: 64

One of the following (10 units):

Math 19, Math 20, Math 21 or 

AP Calculus

One of the following sequences (15 units):

Math 51, Math 52, Math 53 or 

Math 61CM, Math 62CM, Math 63CM, or 

Math 61DM, Math 62DM, Math 63DM


Math Courses:

Math 104: Applied Matrix Theory or Math 113: Linear Algebra and Matrix Theory (3 units)

Math 106: Functions of a Complex Variable or Math 116: Complex Analysis (3 units)

Math 109: Applied Group Theory or Math 120: Groups and Rings (3 units)

Math 110: Applied Number Theory and Field Theory or Math 121: Galois Theory (3 units)

Math 115: Functions of a Real Variable (3 units)


Eight of the following courses including at least three Math courses:

Math 107: Graph Theory (3 units)

Math 108: Introduction to Combinatorics and its Applications (3 units)

Math 143: Differential Geometry (3 units)

Math 144: Introduction to Geometry and Topology (3 units)

Math 147: Differential Topology (3 units) 

Math 148: Algebraic Topology (3 units)

Math 152: Elementary Theory of Numbers (3 units)

Math 161: Set Theory (3 units)

Math 171: Fundamental Concepts of Analysis (3 units)

Math 173: Theory of Partial Differential Equations (3 units)

Math 114/CME 108: Introduction to Scientific Computing (3 units)

Econ 50: Economic Analysis I (3 units)

Physics 41: Mechanics (3 units)

Physics 43: Electricity and Magnetism (3 units)

Phyiscs 45: Light and Heat (3 units)

Math 151: Introduction to Probability Theory or Stats 116: Theory of Probability (3-4 units)


TOTAL UNITS: 64-65