## Course Summary

This is an introductory course in matrix algebra (also called linear algebra). Matrix algebra is an extremely important area of both pure and applied mathematics. The basic ideas present themselves in any higher lever math course, and they also appear in other fields such as physics, engineering, industry, finance, and computer science.

The basic idea of matrix algebra is to explore a particular class of functions with (linear transformations) over a particular kind of object (vector spaces). We'll talk about the motivation for this exploration, but this describes a lot of processes that might be of interest. For example, one class of objects we'll talk about is points of space, and the functions that we're interested in on this space correspond to different geometric contortions of the space.

There are no offical prerequisites for this course. As will all math courses at CMU, a fluency with pre-calculus is required. A familiarity with calculus (21-120 and 21-122) is also helpful for some examples we'll see. Concepts of Mathematics (21-127) would be a very helpful course to take before this course as this course will require the writing of formal proofs. But, the course will be (to the best of my efforts) self contained.

There are two goals in this course. The first is to explore theorems and ideas related to linear algebra that will directly help you tackle more difficult course material. The second is to learn and practice your ability to make formal and convincing arguments going indepth into one particular area.