# 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, 18.510, and 18.781.

A few more subjects open up as soon as you have credit for 18.01 — 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. (Note that in special cases the upper-level subjects 18.152 or 18.303 may be used in place of 18.03.)

There are a few subjects listing only 18.02 as a prerequisite:

18.05, 18.06, 18.100, 18.200, 18.600, 18.700, and 18.703.

Once you have completed 18.03, many additional undergraduate subjects open up, such as 18.04, 18.300, 18.330. The math-major roadmaps page provides guidance on relevant classes for different fields and applications of mathematics, sorted roughly into the order in which they might be taken.

## Pre-approved Substitutions

In place of 18.03, sufficiently advanced students may substitute either 18.152 or 18.303. In such a case these subjects will not count as RESTs nor will they be used as one of the eight required subjects beyond 18.03.

The substitution of 18.650 by 15.075 or of 18.05 by 6.041 or of 18.615 by 6.262 or of 18.600 by 15.079 will be granted upon request for math majors, but not for minors. Note, however, that only one such substitution will be permitted. Send an email request to Debbie Bower (debbie@math.mit.edu). 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 (juleekim@mit.edu).

## RESTs

There are six Restricted Electives in Science and Technology subjects in Mathematics: 18.03, 18.032 (formerly 18.034), 18.05, 18.06, 18.600, and 18.700.

## New Numbers for Math Subjects

Effective Fall 2019, the following subjects have been renumbered:

18.175 changed to 18.675

18.176 changed to 18.676

18.177 changed to 18.677

Many math subjects were renumbered effective the 2015-1016 academic year. For a chart of old number and new ones, look here.

## 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 Discrete applied mathematics

18.3x Continuous applied mathematics

18.4x Theoretical computer science

18.5x Logic and set theory

18.6x Probability and statistics

18.7x Algebra and number theory

18.8x Laboratory subjects

18.9x Topology and geometry, and specialty subjects