Math 236: Aims

The aims are:

  1. Learn computational skills of linear algebra.
  2. Understand fundamental concepts about vectors, matrices, vector spaces, and linear transformations.
  3. Develop skills of reasoning about algebraic and geometric linear algebra concepts, and of expressing that reasoning in writing.
  4. Learn when and how to use linear algebra in several key applications.
  5. Learn enough of the Mathematica programming language to implement linear algebra algorithms effectively on a computer.
  6. Learn how to learn more about linear algebra and Mathematica.

Mathematica is used for three purposes: First, as a tool for doing numeric calculations and forming graphical representations. Second, as a means for exploration and discovery. Third, as an aid in understanding key ideas and methods: by expressing linear algebra procedures in the precise form that Mathematica can execute, you "teach the computer" how to do them.

In calculus, you might have become accustomed to blindly memorizing a few formulas and, for solving problems, matching them to standard “types” of examples whose solutions you mimicking.  That way won’t get you very far in Math 236; you really have to understand and reason things through!44

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