Course Objectives: Walking through Kemeny Hall, you will hear professors and students discussing a myriad of topics. A comment made suprisingly often in an explanation — independent of the subject — is It's just linear algebra. Whatever this subject is, one can be certain that linear algebra is as fundamental to higher mathematics as counting is to arithmetic. But what is it?
In your studies you have certainly heard the terms linear approximation or linear models. One inference is that these approximations or models (while far from perfect) are at least amenable to study, the tools of course being linear algebra. There are two linear algebra courses at Dartmouth, Math 22 and 24. This course is concerned more with computation and applications and less so with abstraction. The other is concerned with a broader context in which to view this subject, and learning to justify assertions with rigorous proofs. But both courses strive to reveal the power and beauty of this subject as well as some of its amazing applications.
So we will do our best to split our time. Theorems you learn are your tools, but tools are only useful if you know how to use them; a hammer is a great tool, but not terribly useful until you have learned not to bend too many nails. It is great to be able to determine whether a system of equations has a solution or not, but if it doesn't, you might still be interested in "how close" to a solution you can actually get. How does Netflix really make suggestions for what you would like to watch? How does Google rank pages returned from a search request? Applications abound.
If nothing else, linear algebra is a beautiful and elegant subject, and one that can easily convince you of the power of mathematics.
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Last updated November 15, 2017