# Course 18 Option 2: Applied Option

Applied mathematics is the mathematical study of general scientific concepts, principles, and phenomena that, because of their widespread occurrence and application, relate or unify various disciplines. The core of the program at MIT concerns the following principles and their mathematical formulations: propagation, equilibrium, stability, optimization, computation, statistics, and random processes.

Sophomores interested in applied mathematics typically survey the field by enrolling in 18.200 and 18.300 Principles of Applied Mathematics. Subject 18.200 is devoted to the discrete aspects of the study and may be taken concurrently with 18.03. It carries CI-M credit in mathematics. Subject 18.300, given only in the second term, is devoted to continuous aspects and makes considerable use of differential equations.

The subjects in Group I of the program correspond roughly to those areas of applied mathematics that make heavy use of discrete mathematics, while Group II emphasizes those subjects that deal mainly with continuous processes. Some subjects, such as probability or numerical analysis, have both discrete and continuous aspects.

Students planning to go on to graduate work in applied mathematics should also take some basic subjects in analysis and algebra.

## Required Subjects:

- 18.03 or 18.032 (formerly 18.034) (Differential Equations)

[sufficiently advanced students may substitute 18.152 or 18.303] - 18.04 (Complex Variables with Applications)

or 18.112 (Functions of a Complex Variable) - 18.06, 18.700 or 18.701 (Linear Algebra)
- 18.200 (Principles of Discrete Applied Mathematics)

or the non-CI-M variant 18.200A - 18.300 (Principles of Continuum Applied Mathematics)

## Restricted Electives:

At least four subjects from the following two groups with at least one subject from each group.

### Group I (Combinatorics, Computer Science, Probability and Statistics)

- 18.204 (Undergraduate Seminar in Discrete Mathematics)
- 18.211 (Combinatorial Analysis)

or 18.212 (Algebraic Combinatorics) - 18.400J/6.045J (Automata, Computability, and Complexity)

or 18.404J/6.840J (Theory of Computation) - 18.410J/6.046J (Introduction to Algorithms)
- 18.424 (Seminar in Information Theory)
- 18.453 (Combinatorial Optimization)
- 18.434 (Seminar in Theoretical Computer Science)
- 18.600 (Probability and Random Variables)
- 18.650 (Statistics for Applications)

### Group II (Numerical Analysis, Physical Mathematics, Nonlinear Dynamics)

- 18.303 (Linear Partial Differential Equations)
- 18.330 (Introduction to Numerical Analysis)
- 18.352J/12.009 (Nonlinear Dynamics: The Natural Environment)
- 18.353J/12.006 (Nonlinear Dynamics: Chaos)
- 18.354J/12.207 (Nonlinear Dynamics: Continuum Systems)
- 18.384 (Undergraduate Seminar in Physical Mathematics)