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There are four undergraduate programs in mathematics. The
first three (General Mathematics, Applied Mathematics and Theoretical Mathematics) lead to the degree Bachelor of Science in Mathematics,
and the fourth (Mathematics with Computer Science) to the degree Bachelor of Science in Mathematics with Computer Science. The requirements for these programs are given in the
following sections.
The breadth of careers envisioned by Mathematics Majors has led to
the
creation of a number of subjects with similar content. The
following limitation applies to all four degree options: Subjects
taken
to satisfy the Mathematics degree requirements must not have
essentially
similar content
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COURSE 18 OPTION I: GENERAL MATHEMATICS
This option is the one followed by most students who major in mathematics. In addition to the General Institute Requirements, the requirements consist of 18.03 Differential Equations, or 18.034 Differential Equations, and eight 12-unit subjects in Course 18 of essentially different content, including at least six advanced subjects (first decimal digit one or higher). This leaves available 84 units of unrestricted electives. The requirements are flexible in order to accommodate several categories of students: students who pursue programs that combine mathematics with a related field (such as physics, economics, or management); students who are interested in both theoretical and applied mathematics; and students who choose mathematics as a general Institute major.
COURSE 18 OPTION II: APPLIED MATHEMATICS
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 18.310 and 18.311 Principles of Applied Mathematics. Subject 18.310, given only in the first term, is devoted to the discrete aspects of the study and may be taken concurrently with 18.03. Subject 18.311, 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.
COURSE 18 OPTION III: THEORETICAL MATHEMATICS
Theoretical mathematics (or "pure" mathematics) is the study of the basic concepts and structures that underlie the mathematical tools used in science and engineering. Its purpose is to search for a deeper understanding and an expanded knowledge of mathematics itself. Traditionally, pure mathematics has been classified into three general fields: analysis, which deals with continuous aspects of mathematics; algebra, which deals with discrete aspects; and geometry. The undergraduate program is designed so that students become familiar with each of these areas. Students may also wish to explore other topics such as logic, number theory, complex analysis, and subjects within applied mathematics. The subject 18.100B Analysis I is basic to the program. Since this subject is strongly proof oriented, many students find an intermediate subject such as 18.06 Linear Algebra or 18.700 Linear Algebra useful as preparation. The subject 18.701 Algebra I is more advanced and should not be elected until the student has had some experience with proofs (as in 18.100B or 18.700).
COURSE 18C MATHEMATICS WITH COMPUTER SCIENCE
Mathematics and computer science are closely related fields. Problems in computer science are often formalized and solved with mathematical methods. It is likely that many important problems currently facing computer scientists will be solved by researchers skilled in algebra, analysis, combinatorics, logic and/or probability theory, as well as computer science. The purpose of this program is to allow students to study a combination of these mathematical areas and potential application areas in computer science. Required subjects include linear algebra (18.06 or 18.700) because it is so broadly used; discrete mathematics (18.062J or 18.310) to give experience with proofs and the necessary tools for analyzing algorithms; and software construction (6.005 or 6.033 or 6.170) where mathematical issues may arise. The required subjects covering complexity (18.404J or 18.400J) and algorithms (18.410J) provide an introduction to the most theoretical aspects of computer science. Some flexibility is allowed in this program. In particular, students may substitute the more advanced subject 18.701 Algebra I for 18.06, and if they already have strong theorem-proving skills, may substitute 18.314 for 18.062 or 18.310.
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