The aims are:
- Learn computational skills of linear algebra.
- Understand fundamental concepts about vectors, matrices, vector spaces, and linear transformations.
- Develop skills of reasoning about algebraic and geometric linear algebra concepts, and of expressing that reasoning in writing.
- Learn when and how to use linear algebra in several key applications.
- Learn enough of the Mathematica programming language to implement linear algebra algorithms effectively on a computer.
- 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