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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.

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: 18.06 and 18.100