# Capstone

All undergraduates matriculating as first-year students in academic year **2021-22** or later and graduating in academic year **2024-25** or later must complete a capstone requirement in their major. Transfer students who enter in academic year **2022-23** or academic year **2023-24** and plan to graduate in academic year **2024-2025** or later will also be required to complete a capstone.

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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:

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Honor Thesis Option

**Earn at least 6 credits from the following:**

Math 197 - Senior Honors Thesis

Completion of the honors program.

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Undergraduate Course Option

**Complete at least 1 of the following Courses:**

- MATH101 - Math Discovery Lab
- MATH110 - Number Theory for Cryptography
- MATH116 - Complex Analysis
- MATH121 - Galois Theory
- MATH122 - Modules and Group Representations
- MATH136 - Stochastic Processes
- MATH144 - Introduction to Topology and Geometry
- MATH145 - Algebraic Geometry
- MATH147 - Differential Topology
- MATH154 - Algebraic Number Theory
- MATH155 - Analytic Number Theory
- MATH158 - Probability and Stochastic Differential Equations for Applications
- MATH159 - Discrete Probabilistic Methods
- MATH161 - Set Theory
- MATH172 - Lebesgue Integration and Fourier Analysis
- MATH173 - Theory of Partial Differential Equations
- MATH175 - Elementary Functional Analysis
- PHIL151 - Metalogic

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Graduate Course Option

**Complete at least 1 of the following Courses:**

- MATH205A - Real Analysis
- MATH205B - Real Analysis
- MATH210A - Modern Algebra I
- MATH210B - Modern Algebra II
- MATH210C - Lie Theory
- MATH215A - Algebraic Topology
- MATH215B - Differential Topology
- MATH215C - Differential Geometry
- MATH216A - Introduction to Algebraic Geometry
- MATH216B - Introduction to Algebraic Geometry
- MATH216C - Introduction to Algebraic Geometry
- MATH230A - Theory of Probability I
- MATH230B - Theory of Probability II
- MATH230C - Theory of Probability III

*if you have any questions regarding the Mathematics department capstone requirements please email: *mathstudentservices [at] stanford.edu (mathstudentservices[at]stanford[dot]edu)