Math Subjects Overview
The MIT undergraduate mathematics curriculum is rich and varied, and no two students take the same path through it. There are at least three reasons for this: MIT mathematics majors have a wide variety of career goals; they have a wide range of backgrounds and preparations; and Mathematics itself, as represented by the research interests of the MIT faculty, is so broad that few undergraduates can absorb a truly representative fraction of it.
This makes choosing subjects complicated, but the absence of a universally accepted list of topics to cover means that students can explore without fear of missing crucial components. The degree options other than the General Mathematics option specify subjects which can be regarded as central to their fields.
Where to Begin
Some subjects have no formal prerequisites — they require only an interest in the mathematics. They are 18.01, 18.014, 18.510, 18.511, and 18.781.
A few more subjects open up as soon as you have credit for 18.01 — 18.05, 18.062J = 6.042J, and the IAP Lecture Series 18.095 — but most require at least 18.01 and 18.02. (All variants of 18.01 and 18.02 serve to fulfill prerequisites.)
18.03 is required by the Mathematics major. 18.03 has 18.01 as a prerequisite and has 18.02 as a corequisite: you can take 18.02 and 18.03 simultaneously.
There are a few subjects listing only 18.02 as a prerequisite:
18.06, 18.310, 18.440, 18.700, and 18.703.
Once you have completed 18.03, many additional undergraduate subjects open up, such as 18.04, 18.100, 18.311, 13.330.
Pre-approved Substitutions
The substitution of 18.443 by 15.075 or of 18.05 by 6.041 will be granted upon request for math majors, but not for minors. Send an email request to Debbie Bower. Other non-course-18 classes at MIT are very unlikely to be considered for substitution.
For all other inquiries send an email to Professor Ju-Lee Kim (julee@math.mit.edu).
RESTs
There are five Restricted Electives in Science and Technology subjects in Mathematics: 18.03, 18.034, 18.05, 18.06, and 18.700.
Narrative Account of the Course 18 Undergraduate Subjects
The subject numbers in Course 18 give a clue to the mathematical area of the subject. The first digit indicates the field. Each item below is linked to a brief annotation of the undergraduate subjects in the area, including comparisons among analogous subjects. These comments are informal. Consult the catalogue for authoritative information on content, prerequisites, availability of the subject, semester, and so on.
18.0x Lower level and specialty subjects
18.1x Analysis
18.2x Mathematical physics (graduate subjects only)
18.3x Applied mathematics
18.4x Theoretical computer science, and Probability and statistics
18.5x Logic and set theory
18.7x Algebra and number theory
18.8x Laboratory subjects
18.9x Topology and geometry, and specialty subjects.
