# 18.7x

## Algebra and Number Theory

There is a wide range of basic algebra offerings, and the choices can be confusing.

A basic and illuminating introduction to modern algebra is provided by linear algebra. There are two undergraduate subjects focusing entirely on linear algebra:

• 18.06 (Linear Algebra) listing 18.02 as prerequisite, is a basic subject on matrix theory and linear algebra, emphasizing topics useful in other disciplines. Compared with 18.700, there is more emphasis on matrix algorithms and many applications.
• 18.700 (Linear Algebra) also lists 18.02 as prerequisite. It is a rigorous treatment of linear algebra. Compared with 18.06, there is more emphasis on theory and proofs. Along with 18.100, this subject provides a good place to learn how to construct and write proofs.

In addition, the subject 18.C06 (formerly 18.061) provides an alternative to 18.06 which combines linear algebra with an introduction to optimization, especially suitable for students of Computer Science.

Other offerings in Algebra and Number Theory include:

• 18.701 (Algebra I) lists 18.100 as prerequisite. The actual subject matter of 18.100 is not directly relevant to that of 18.701, but the experience with mathematical reasoning and expression is.
• 18.702 (Algebra II) is a continuation of 18.701. Together they provide an introduction to modern algebra that is more extensive and theoretical than the 18.700-18.703 sequence.
• 18.703 (Modern Algebra) has only 18.02 as a prerequisite. It is a one term treatment of Modern Algebra, covering the traditional algebra topics that have found greatest application in science and engineering as well as in mathematics.
• 18.781 (Number Theory) is an elementary class on the topic, developed independent of algebraic preliminaries. It has no formal prerequisites.

There are two Undergraduate Seminars in this area:

• 18.704 (Seminar in Algebra) Prerequisite: 18.701; or 18.06 and 18.703; or 18.700 and 18.703.
• 18.784 (Seminar in Number Theory) The topics tend to be more algebraic than those treated in 18.781, so there are Prerequisites: 18.701; or 18.06 and 18.703; or 18.700 and 18.703.