skip to main content
Search
Contact
Site Map
Instagram
Facebook
Bluesky
Youtube
About
About Us
Welcome
Awards
History
Simons Building
Directions
Employment
Contact Us
People
All People
Faculty
Instructors
Postdocs
Researchers
Graduate Students
Staff
Visitors & Affiliates
Research
Research
Pure
Applied
Graduate Research
Undergraduate Research
High School Programs
Academics
Academics
Academic Services
Undergraduate Program
Graduate Program
Prospective Undergrads
Class Schedule
Online Classes
Services
Services
Orientation
Visitor Policies
Proposal Submissions
Internal
Computer Help
Room Reservations
Reimbursements
Community
Community
Math Community
Women in Math
Sponsors
Giving
Visiting Committee
News & Events
News Overview
News Archive
Math Calendar
Seminars
Conferences
Integral
x
Search
About
About Us
Welcome
Awards
History
Brief History
Facts
Past Faculty
Photos
In Memoriam
Simons Building
About
Slideshow
Construction Photos
Completed Photos
Directions
Employment
Contact Us
People
All People
Faculty
Faculty
Professors
Associate Professors
Assistant Professors
Emeriti Professors
Visiting Professors
Instructors
Postdocs
Researchers
Graduate Students
Staff
Visitors & Affiliates
Research
Research
Pure
Pure
Algebra & Algebraic Geometry
Algebraic Topology
Analysis & PDEs
Geometry & Topology
Mathematical Logic & Foundations
Number Theory
Probability & Statistics
Representation Theory
Applied
Applied
Combinatorics
Computational Biology
Physical Applied Mathematics
Computational Science & Numerical Analysis
Theoretical Computer Science
Mathematics of Data
Graduate Research
Graduate Research
Thesis Defenses
Undergraduate Research
Undergraduate Research
SPUR
SPUR
Admission to SPUR
Past Projects
Lecture Series
Rogers Prize
DRP
UROP
UROP+
UROP+
Papers
MSRP
High School Programs
High School Programs
PRIMES
PRIMES
Why Choose PRIMES
Areas of Research
MIT PRIMES
MIT PRIMES
How to Apply
PRIMES-USA
PRIMES-USA
Apply
CrowdMath
PRIMES Circle
PRIMES Circle
Students Say
Circle Mentors
Papers
Apply
Yulia's Dream
Yulia's Dream
2025 Conference
2024 Conference
2023 Conference
Research Papers
Media Reports
√MathROOTS
PRIMES STEP
PRIMES-Switzerland
Reading List
Annual Conference
Annual Conference
2024
2023
2022
2021
2020
2019
2018
2017
2016
2015
2014
2013
2012
2011
Research Papers
Honors and Awards
Response to COVID
Advisory Board
Program Staff
Mentors
Named Mentorships
Alumni
Testimonials
Testimonials
Parents
Devadas Interview
MathROCs Q&A
Sponsorship
How to Apply
Other Programs
FAQ
Contact
RSI
RSI
Past Projects
Lecture Series
Academics
Academics
Academic Services
Academic Services
Forms and Requests
Learning Center
Student Jobs
Undergraduate Program
Undergraduate Program
Math Major
Math Major
Course 18
Course 18
General
Applied
Pure
Course 18C
CI-M
Advising
Math Minor
First Year Subjects
First Year Subjects
Calculus
Advanced Placement
Transfer Credit
Transfer Credit
Pre-approved Summer Subjects
Advanced Standing
Subject Goals
Subjects Overview
Subjects Overview
18.0x
18.1x
18.2x & 18.3x
18.4x
18.5x
18.6x
18.7x
18.8x
18.9x
Roadmaps
Opportunities
Opportunities
International Study and Internships
MCM Competition
Putnam Competition
Summer Programs
Undergraduate Math Association
USWIM
CoMM
Careers
Careers
Preparing for Non-Academic Jobs
Preparing for Grad School
Graduate Program
Graduate Program
Admission
Admission
FAQ
Financial Support
Financial Support
Payroll/Visa Details
Funding Sources
Fellowships
Summer Support
Summer Support
Mentorships
Summer Teaching
Travel Support
Timeline
Timeline
Orientation
Coursework
Plan of Study
Qualifying Exams
External Thesis Advisor Info
Teacher Training
Thesis Proposal
Graduation Deadlines
Thesis Defense
After Graduate School
Prospective Undergrads
Class Schedule
Online Classes
Services
Services
Orientation
Visitor Policies
Visitor Policies
Visiting Students
Proposal Submissions
Proposal Submissions
Funding Opportunities
Internal
Internal Resources
Math Department Forms
Undergrad Office Resources
Data Administration
Internal Archives
Computer Help
Hours & Contact
Workstations
Audio Visual
Printing
New Users
New Users
Unix Tutorial
Policies
Remote Access
Remote Access
SSH, SFTP and SCP
Websites
Creating Websites
Web Accessibility
Course Websites
Math Account
Math Account
Math Email
Math Email
Math Webmail
Thunderbird
Outlook
Gmail
Pine
Mac Mail
Spam & Viruses
FAQ
FAQ
FAQ
General Questions
Using Linux
Laptops
Athena
Mailing Lists
Room Reservations
Reimbursements
Community
Community
Math Community
Women in Math
Sponsors
Giving
Giving
Donor Profiles
Visiting Committee
News & Events
News Overview
News Archive
Math Calendar
Seminars
Seminars
Simons Lectures
Conferences
Integral
Instagram
Facebook
Bluesky
Youtube
Course Websites
Course 18.721 is not offered this semester (Spring 2026).
18.721 - All Semester Websites:
18.721 -- Spring 2016 (Artin)
18.721 -- Spring 2020 (Artin)
18.721 -- Fall 2021 (Costa, Schiavone, van Bommel)
18.721 -- Spring 2024 (Yang)
