**Overview**

We will be studying the mathematics of phenomena that depend linearly on several parameters. As a first example, to develop geometric intuition, we consider linear transformations of vectors in the plane. We then study systems of linear equations, which motivate the study of matrix equations and matrix decompositions. We also investigate a variety of applications. Finally we will study abstract vector spaces and inner product spaces.

**Course Documents**

- Syllabus (
*Last updated 9/16/2011*) - Course Schedule (
*Last updated 11/28 /2011*) - What is a proof?

**Supplemental Course Notes**

- Linear Transformations of the Plane (
*Last updated 9/7/2011*) - Subspaces Associated to Linear Transformations (
*Last updated 10/10/2011*) - Fourier Series Example (
*12/05/2011*) - Demo: approximating the step function (
*Short QuickTime movie*)

** Homework **

Weekly written homework, consisting of practice problems and mathematical arguments, typically due in class on Monday and returned within the week. See assigned homework problems.

** In-class activities **

- Linear Combinations (
*8/31/2011*) - Geometry and the Dot Product (
*9/2/2011*) - Examples of Linear Transformations of the Plane (
*9/5/2011*) - Linear Transformations of the Plane: Exercise (
*9/7/2011-9/9/2011*) - Matrix Multiplication (
*9/21/2011*) - Transpose Matrices (
*9/26/2011*) - Elementary Matrices (
*9/28/2011*) - Subspaces Associated to a Matrix (
*10/05/2011*) - Eigenvalues/vectors-I (
*10/12/2011*) - Eigenvalues/vectors-II (
*10/21/2011*) - Diagonalization (
*10/24/2011*) - Distinct Eigenvalues (
*10/31/2011*) - Orthogonal Complement (
*11/07/2011*) - Isometries of the Plane (
*11/11/2011*) - Diagonalizing Symmetric Matrices (
*11/16/2011*) - Orthogonality in a function space (
*11/30/2011*)

**Group project for Nov 18**

- Matrix factorizations from a geometric perspective (
*11/16/2011*) - Group evaluation (
*11/16/2011*)

** Project**

Each student will study a topic independently, explain their findings to the group in a 7-10 minute presentation, and discuss their findings in a written paper.

- Project Selection Hand-out
*Please sign up for a project (using the sign-up sheet on the M-drive) by Sept 9.* - Presenting the results of your project
- Presentation practice report form

Goshen College Math