Linear algebra studies the theory of abstract vector spaces and linear transformations. Whenever one encounters a bunch of gizmos (functions, for instance) that can be added to form new gizmos and multiplied by scalars to form new gizmos, and for which a few familiar rules of algebra hold, one has what's called an "abstract vector space". The gizmos, whatever they may be, are called vectors, or abstract vectors. A linear transformation is a special kind of function from one abstract vector space to another. If you've ever wished that sin(A+B) could just be sin A + sin B and sin(kA) could be k sin A, you were wanting the sine function to be linear.
Math 206 defines "abstract vector space" and "linear transformation" axiomatically and then deduces a very pretty story. Geometry, perhaps unexpected, reappears -- and the abstract story that unfolds has some very concrete, computational aspects as well. The student who takes this course can learn computational techniques that have widespread applications, in the natural and social sciences as well as in industry, finance, and management.
Proof is the gold standard of mathematical discourse, and linear algebra is especially well suited for learning to do proofs. Many aspects of the course material are abstract, yet the logic involved is quite direct and the proof paths are often guided by very concrete ideas. In the course of learning some linear algebra, a student who takes this course can learn to read and understand proofs, to judge for herself whether a proof is valid or not, to write proofs clearly and carefully, and to create basic proofs on her own. This emphasis on reasoning skills is valuable for virtually any student, whether or not she intends to major/minor in mathematics.
Math 206 is required for both the mathematics major and the mathematics minor, and it satisfies the "proof-course" prerequisite for both Math 302 and Math 305. Students who wish to major in mathematics are advised to consider taking one of the following courses soon after they complete Math 205: Math 206, Math 223, Math 225, Math 214, or Math 212.
Prerequisite: 205 or Math 215/Phys 215
Distribution: Mathematical Modeling
