214 Math 204 served as an introduction to the abstract concepts and theory of vector spaces. The focus is on understanding the relations among vector spaces, linear transformations, bases, dimension, linear systems, subspaces such as row, column and null spaces, and determinants. On one level, Math 204 is a great introduction to abstraction in mathematics because it is largely self-contained with few mathematical prerequisites. For this reason, the subject plays a central role in your development as a mathematics major. However, another of the reasons that linear algebra plays such a central role is the comes from our ability to interpret abstract concepts in various concrete ways.
Abstraction is what makes applied mathematics possible.
A matrix can be interpreted as the way that this machine, animal, or process changes states. This is the theory of Markov chains. In a different situation, vectors can be interpreted as codewords with matrix multiplication representing the encoding and decoding processes. As a motivation and introduction to this course we will start with an application of linear algebra to the world of genetics. Vectors represent the proportions of certain alleles in the entire population and matrices provide the way to see how those proportions change from one generation to the next.