Major: Bachelor of Science
MajorOverview
The undergraduate program in Mathematics aims to provide students with a broad understanding of mathematics encompassing logical reasoning, generalization, abstraction, and formal proof. Courses in the program teach students to create, analyze, and interpret mathematical models and to communicate sound arguments based on mathematical reasoning and careful data analysis. The mathematics degree prepares students for careers in the tech and finance industries, graduate programs in quantitative fields, computational sciences, and the corporate sector.
Requirements
Core Program Requirements
Math Course Requirement
MATH 56 may count toward the eight courses.
STATS 116 (No longer offered), STATS118 opens in a new tab or STATS200 opens in a new tab(at most one among STATS 118 and STATS 200, but not both, and neither if STATS 116 is being used), PHIL 151, & PHIL 152 count as 100-level Math courses. No other classes outside the Math department can count in this way. There are no exceptions to this for any reason.
The following course do not count toward the Math Course Requirement:
MATH 190, MATH 193, MATH193X opens in a new tab, MATH197 opens in a new tab, MATH198 opens in a new tab, and MATH199 opens in a new tab (MATH 190, MATH193X and MATH199 can count towards the Elective Course Requirement, see below.)
Up to 10 units of Single Variable Calculus can be used as part of the Math Course Requirement.
If you have not earned 10 units of single-variable calculus credit but have Math course credit that affirms your mastery of single-variable calculus, please email mathstudentservices@stanford.edu and specify what that course credit is (it must entail substantial use of both derivatives and integrals). Examples include Math 51 + either Math 52 or Math 53, Math 61CM, or Math 61DM + 63DM. To fulfill the Math Major, you will need to make up whatever portion of such 10 units you don’t have on your transcript, but can do so with approved electives.
Only Math 50/60CM/60DM series and first-year calculus can be double-counted toward any other major or minor (Note: The completion of 15 units from the multivariable math sequences is recommended but not a requirement, and at most 15 of such units can be used towards the major).
Electives
Required Electives
Four elective courses are required for the Math major.
Math Department courses numbered Math 101 and above can be used as electives except for MATH193 opens in a new tab, MATH197 opens in a new tab, and MATH198 opens in a new tab
MATH190 opens in a new tab, MATH193X opens in a new tab and MATH199 opens in a new tab may only be counted toward electives, not toward the 57 Core units above.
In addition, there are approved out-of-department electives that can be used as electives (See list below).
Non-MATH Elective Options
AA 216
Projection-Based Model Order Reduction
APPPHYS 229
Statistical Mechanics of Learning and Computation
APPPHYS 237
Quantitative Evolutionary Dynamics and Genomics
BIO 141
Introduction to Statistics for Biology
BIO 165
Quantitative Approaches in Modern Biology
BIO 188
Systems Biology: Principles of Cell Signaling
BIOE 101
Systems Biology
CHEM 151
Inorganic Chemistry I
CHEM 153
The Chemistry of Extended Solids
CHEM 171
Linking the Molecular to the Macroscopic: Foundations of Physical Chemistry
CHEM 173
Physical Chemistry II
CHEM 175
Physical Chemistry III
CLASSICS 136
The Greek Invention of Mathematics
CME 108
Introduction to Scientific Computing with Machine Learning Applications
CS 103
Mathematical Foundations of Computing
CS 123
A Hands-On Introduction to Building AI-Enabled Robots
CS 109
Introduction to Probability for Computer Scientists
CS 129
Applied Machine Learning
CS 148
Introduction to Computer Graphics and Imaging
CS 154
Introduction to the Theory of Computation
CS 157
Computational Logic
CS 161
Design and Analysis of Algorithms
CS 166
Advanced Data Structures
CS 168
The Modern Algorithmic Toolbox
CS 205L
Continuous Mathematical Methods with an Emphasis on Machine Learning
CS 221
Artificial Intelligence: Principles and Techniques
CS 224N
Natural Language Processing with Deep Learning
CS 224R
Deep Reinforcement Learning
CS 228
Probabilistic Graphical Models: Principles and Techniques
CS 229
Machine Learning
CS 229M
Machine Learning Theory
CS 230
Deep Learning
CS 233
Geometric and Topological Data Analysis
CS 234
Reinforcement Learning
CS 235
Computational Methods for Biomedical Image Analysis and Interpretation
CS 250
Algebraic Error Correcting Codes
CS 251
Cryptocurrencies and blockchain technologies
CS 254
Computational Complexity
CS 255
Introduction to Cryptography
CS 256
Algorithmic Fairness
CS 259Q
Quantum Computing
CS 261
Combinatorial Optimization
CS 265
Randomized Algorithms and Probabilistic Analysis
CS 354
Topics in Intractability: Unfulfilled Algorithmic Fantasies
CS 355
Advanced Topics in Cryptography
ECON 50
Economic Analysis I
ECON 51
Economic Analysis II
ECON 52
Economic Analysis III
ECON 102A
Introduction to Statistical Methods (Postcalculus) for Social Scientists
ECON 102B
Applied Econometrics
ECON 102C
Advanced Topics in Econometrics
ECON 111
Money and Banking
ECON 136
Market Design
ECON 137
Decision Modeling and Information
ECON 140
(FIN I) Introduction to Corporate Finance
ECON 141
Investments in Financial Markets
ECON 160
Game Theory and Economic Applications
ECON 167G
Game Theory and Social Behavior
ECON 180
Accelerated Game Theory
ECON 202
Microeconomics I
ECON 203
Microeconomics II
ECON 204
Microeconomics III
ECON 284
Simplicity and Complexity in Economic Theory
EE 363
Linear Dynamical Systems
EE 387
Algebraic Error Correcting Codes
ENGR 14
Intro to Solid Mechanics
ENGR 15
Dynamics
ENGR 60
Engineering Economics and Sustainability
ENGR 62
Introduction to Optimization
ENGR 76
Information Science and Engineering
ESS 246A
Atmosphere, Ocean, and Climate Dynamics: The Atmospheric Circulation
MS&E 111
Introduction to Optimization
MS&E 111DS
Introduction to Optimization: Data Science
MS&E 111X
Introduction to Optimization (Accelerated)
MS&E 112
Graph and Combinatorial Optimization
MS&E 120
Introduction to Probability
MS&E 121
Introduction to Stochastic Modeling
MS&E 135
Networks
MS&E 145
Introduction to Finance and Investment
MS&E 211
Introduction to Optimization
MS&E 211X
Introduction to Optimization (Accelerated)
MS&E 220
Probabilistic Analysis
MS&E 221
Stochastic Modeling
MS&E 223
Stochastic Simulation and Monte Carlo Methods
MS&E 226
Fundamentals of Data Science: Prediction, Inference, Causality
MS&E 232
Introduction to Game Theory
MS&E 232H
Introduction to Game Theory (Accelerated)
MS&E 244
Statistical Arbitrage
MS&E 245A
Investment Science
MS&E 245B
Advanced Investment Science
MS&E 310
Linear Programming
MS&E 338
Aligning Superintelligence
MUSIC 320
Introduction to Audio Signal Processing
MUSIC 423
Graduate Research in Music Technology
PHIL 151
Metalogic
PHIL 152
Computability and Logic
PHIL 162
Philosophy of Mathematics
PHYSICS 14N
Quantum Information: Visions and Emerging Technologies
PHYSICS 41
Mechanics
PHYSICS 43
Electricity and Magnetism
PHYSICS 45
Light and Heat
PHYSICS 61
Mechanics and Special Relativity
PHYSICS 71
Quantum and Thermal Physics
PHYSICS 81
Electricity and Magnetism Using Special Relativity and Vector Calculus
PHYSICS 100
Introduction to Observational Astrophysics
PHYSICS 104
Introduction to Electronic Techniques for Physics Research Instrumentation
PHYSICS 108
Advanced Physics Laboratory: Project
PHYSICS 110
Advanced Mechanics
PHYSICS 111
Partial Differential Equations of Mathematical Physics
PHYSICS 112
Mathematical Methods for Physics
PHYSICS 113
Computational Physics
PHYSICS 120
Electromagnetism
PHYSICS 121
Electrodynamics
PHYSICS 130
Quantum Mechanics I
PHYSICS 131
Quantum Mechanics II
PHYSICS 134
Advanced Topics in Quantum Mechanics
PHYSICS 160
Introduction to Stellar and Galactic Astrophysics
PHYSICS 161
Introduction to Cosmology and Extragalactic Astrophysics
PHYSICS 170
Thermodynamics, Kinetic Theory, and Statistical Mechanics I
PHYSICS 171
Thermodynamics, Kinetic Theory, and Statistical Mechanics II
PHYSICS 172
Solid State Physics
PHYSICS 210
Advanced Mechanics
PHYSICS 212
Statistical Mechanics
PHYSICS 216
Back of the Envelope Physics
PHYSICS 220
Classical Electrodynamics
PHYSICS 230
Graduate Quantum Mechanics I
PHYSICS 231
Graduate Quantum Mechanics II
PHYSICS 234
Advanced Topics in Quantum Mechanics
PHYSICS 240
Introduction to the Physics of Energy
PHYSICS 241
Introduction to Nuclear Energy
PHYSICS 252
Introduction to Particle Physics I
PHYSICS 260
Introduction to Stellar and Galactic Astrophysics
PHYSICS 261
Introduction to Cosmology and Extragalactic Astrophysics
PHYSICS 262
General Relativity
PHYSICS 266
Statistical Methods in Experimental Physics
PHYSICS 269
Neutrinos in Astrophysics and Cosmology
PHYSICS 331
Quantum Field Theory II
POLISCI 356A
Formal Theory I
POLISCI 356B
Formal Theory II
STATS 110
Introduction to Statistics for Engineering and the Sciences
STATS 117
Introduction to Probability Theory
STATS 118
Probability Theory for Statistical Inference
STATS 141
Introduction to Statistics for Biology
STATS 191
Introduction to Applied Statistics
STATS 200
Introduction to Theoretical Statistics
STATS 202
Statistical Learning and Data Science
STATS 203
Regression Models and Analysis of Variance
STATS 205
Introduction to Nonparametric Statistics
STATS 206
Applied Multivariate Analysis
STATS 207
Time Series Analysis
STATS 217
Introduction to Stochastic Processes I
STATS 218
Introduction to Stochastic Processes II
STATS 229
Machine Learning
STATS 270
Bayesian Statistics
STATS 271
Applied Bayesian Statistics
STATS 305A
Applied Statistics I
STATS 315B
Modern Applied Statistics: Learning II
STATS 318
Modern Markov Chains
MUSIC 423: Limit of three units.
PHIL 151 & PHIL 152: This may count toward either the Math Course Requirement or Elective Course Requirement, but not both.
PHYSICS 41 and 61 are mandatory S/NC grading, so at most, one may be counted as a Math elective.
STATS 116 (No longer offered) and STATS 118 or STATS 200 (at most one, but not both, and neither if STATS 116 is being used) may count toward the Math Course Requirement or Elective Course Requirement, but not both.
Writing in the Major (WIM)
Writing in the Major (WIM)
All majors, including transfer students, need to complete the WIM requirement.
The two course options for fulfilling WIM, Math 190 and Math 195, are each offered twice per year in Fall and in Winter. Enrollment in each of these courses is limited to officially approved Math majors, and is done via an application process that begins near the end of the preceding Spring (all Math majors who have not fulfilled WIM will be contacted about applying in late Spring).
Math 190 is a 3-unit class with background prerequisites in proof-based math (such as Math 113 or 115 with a grade of at least B) and does not entail learning new mathematics, so it does not count as one of the eight 100-level classes toward the Math major but does count as an elective. It can be taken in the second year or later.
Math 195 is a 4-unit class limited to senior Math majors only, and also fulfills the capstone requirement. This course entails learning new mathematics, and as such it does count as one of the eight 100-level classes toward the Math major.
Capstone
Mathematics Capstone Requirements
Mathematics majors have interests in many possible directions (e.g., applied math, algebra, geometry, probability, CS, finance, etc.). The capstone in Mathematics aims to ensure that each student takes part in some independent work or course experience in their area(s) of mathematical interest that exposes them to a culmination of the subject in these areas.
Such experiences can expose a student to an underlying and more abstract unity among disparate methods, a body of ideas displaying the intellectual beauty of the subject, or a compelling application of abstract mathematical concepts and techniques to a real-world context. Using these goals as a guide, the capstone in Mathematics can be fulfilled by carrying out (at least) one of the following three options:
Honors Thesis Capstone Option
Completion of the honors program.
MATH 197
Senior Honors Thesis
Undergraduate Course Option
MATH 117
Advanced Complex Analysis
MATH 122
Modules and Group Representations
MATH 147
Differential Topology
MATH 154
Algebraic Number Theory
MATH 155
Analytic Number Theory
MATH 158
Probability and Stochastic Differential Equations for Applications
MATH 173
Theory of Partial Differential Equations
PHIL 152
Computability and Logic
Graduate Course Option
MATH 205A
Real Analysis
MATH 205B
Real Analysis
MATH 210A
Modern Algebra I
MATH 210B
Modern Algebra II
MATH 210C
Lie Theory
MATH 215A
Algebraic Topology
MATH 215B
Differential Topology
MATH 215C
Differential Geometry
MATH 216A
Introduction to Algebraic Geometry
MATH 230A
Theory of Probability I
Capstone Project Option
MATH 195
Senior Exploration and Synthesis
Subplans
OptionalComputer Science Theory/Discrete Mathematics Subplan
Required Courses
Subplan students must include the following courses in their program of study (which can count toward the both the Math Course Requirement and the Elective Course Requirement).
All subplan courses must be taken for a Letter grade.
Combinatorics Course Requirement
Math Course Requirement
Computer Science Course Requirement
CS 168
The Modern Algorithmic Toolbox
CS 250
Algebraic Error Correcting Codes
CS 254
Computational Complexity
CS 254B
Computational Complexity II
CS 255
Introduction to Cryptography
CS 256
Algorithmic Fairness
CS 259Q
Quantum Computing
CS 261
Combinatorial Optimization
CS 263
Counting and Sampling
CS 265
Randomized Algorithms and Probabilistic Analysis
CS 269I
Incentives in Computer Science
Honors
OptionalHonors
Required Courses
Honors students must complete the core program requirements for all Math majors; see Core Program Requirements (above).
Honors students must have a minimum GPA of 3.3 across all Math courses to apply to the program.
It is strongly recommended that either the Math 60CM or Math 60DM sequences be taken during the student's freshman year. This is a recommendation, not a requirement.
Honors Course Requirements
MATH 193 does not count toward this requirement.
MATH 197 does not count toward this requirement.
MATH 198 does not count toward this requirement.
One 3-unit MATH 199 course may count toward this requirement with approval from the Director of Undergraduate Studies before the start of the course. Honors students must submit the request to the Student Services Officer two weeks before the beginning of the quarter for review. The criteria for approval include weekly homework graded by the instructor and topic coverage appropriate for Math honors.
Analysis Course Requirement
MATH 116
Complex Analysis
MATH 117
Advanced Complex Analysis
MATH 136
Stochastic Processes
MATH 151
Introduction to Probability Theory
MATH 155
Analytic Number Theory
MATH 172
Fourier Analysis
MATH 173
Theory of Partial Differential Equations
MATH 175
Elementary Functional Analysis
Graduate Level Course Recommended
MATH 205A, MATH 210A, MATH 215A, OR MATH230A opens in a new tab
Note: This is a recommendation. This is not required to complete Math honors.
Thesis Requirement. Completion of an honors thesis is required.
MATH 197
Senior Honors Thesis
MATH 197 must be taken over all three quarters for 2-3 units per quarter.
The 6 units of MATH 197 is in addition to the Math Course Requirement and Elective Course Requirement for the Math major.
A complete draft of the honors thesis is due by the end of week 7 in Spring quarter. A final draft is due by 5pm on the last day of classes in Spring quarter.

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