Capstone

All undergraduates, including transfer students, need to complete the capstone requirement.

Mathematics Capstone Requirements

Note: Fulfilled capstone courses for the non-thesis options count toward the 57 units of Math Courses.

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: 

Honor Thesis Option

Earn at least 6 credits from the following:

  • Math 197 - Senior Honors Thesis

    Completion of the honors program.

Capstone Project Option
  • Math 195 - Senior Exploration and Synthesis
  • This capstone course offers senior mathematics majors the opportunity to synthesize and apply their mathematical knowledge through collaborative, project-based learning. Students will be assigned to small groups to explore topics ranging from real-world applications to open-ended problems in mathematics. Through a combination of guided research, skill-building workshops, and peer collaboration, students will develop both professional and academic skill sets, supporting their transition into industry roles or graduate study in quantitative fields.
  • There are two offerings of Math 195, in Fall and Winter quarters of an academic year. Enrollment in any of the two offerings requires filling out an intent form by the beginning of June prior to the academic year. The link to the intent form will be shared in an email at the end of May. The applications will be reviewed in the Summer and you will receive an email indicating the quarter in which you should enroll. A permission number to enroll in the assigned quarter will be provided.
Undergraduate Course Option

Complete at least 1 of the following Courses:

  • 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
  • MATH 195 - Senior Exploration and Synthesis
  • PHIL 152 - Computability and Logic
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
  • MATH230A - Theory of Probability I

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

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