Algebra is much more than solving real-number equations for *x*. Rather, it is the study of **structure**: the way the rules of a system influence its behavior, *e.g. *the fact that addition, multiplication, and exponentiation of real numbers can all be inverted allows us to solve aforementioned equations. Linear algebra, the study of the structure of **vector spaces**, generalizes these ideas for the first time. You will see the first but by no means last appearance of **structure-preserving maps **between mathematical objects. These will be understood by means of **matrices** looked at from both the concrete point of view—**systems of equations**, **row reduction**, **determinants**—and the abstract point of view—**linear independence**, **linear transformations**, **bases**, **eigenvectors** and **eigenvalues**.

You will be assessed by way of weekly homework (40%), a midterm exam (30%), and a final (30%). Extra credit will be available. Note well that a C (70-79) is awarded to students who have met expectations; a B (80-89), to students who have met expectations well; and an A (90-100), to students who met expectations and knocked my socks off doing so.

**Notes:**

- Systems of linear equations (5/25 & 5/26)
- Matrix algebra (5/31 – 6/2)
- Determinants (6/6 & 6/7)
- Introduction to vector spaces (6/13 – 6/16)
- Linear transformations (6/16 – 6/20)
- The big idea: coordinatization (6/21)
- The eigenvalue problem (6/22)

Syllabus (subject to change in fair ways)

**Homework: **1 2 3 4

**Extra credit: **1 2 3 4 5

Midterm study guide

Final study guide

Shelton State Community College homepage

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