Linear Algebra

Fall 2007
Course Overview

Instructor: Dave Feldman Email: daveATh0rnacekDOTcoaDOTedu
Office: Second Floor, Turrets Annex Phone: x249, 276-5284
Mailing List: linalgATh0rnacekDOTc0aDOTedu Office Hours: Wed 6:30-8:00 in TAB, by appointment

Course Catalog Description: Through the study of linear algebra in this course, students will acquire powerful analytic techniques that are essential tools in almost any field of applied mathematics, including: physics, engineering, computer science, economics. Linear algebra is also commonly used in chemistry and mathematical biology. Our study of linear algebra will begin by abstracting and formalizing the idea behind solving familiar systems of linear equations. This will lead us to the study of matrices and determinants. We will study these mathematical objects both algebraically and geometrically, leading up to a general treatment of linear vector spaces. Additional topics covered will include: linear transformations; inner products and orthogonality; eigenvectors, eigenvalues, and their application. Where possible, applications to students' fields of interest will be emphasized. Students will leave this course with a solid foundation in the key ideas and techniques of linear algebra. Evaluation will be based on class participation and weekly problem sets.

Please note that this course meets the QR requirement. It does not meet the ES requirement.

I have several goals for this course:
  1. I want you to get a solid foundation in linear algebra which you can then apply to areas of your interest.
  2. I want you to increase your "mathematical sophistication," ability to reason abstractly, and give you an introduction to some of the more formal ideas of mathematics, including proofs.
  3. I want to help you improve your quantitative literacy, problem solving skills, and mathematical confidence. This includes using computers to help you set up and solve problems.
  4. I want to have fun while working hard and learning some challenging material.

Our textbook will be Linear Algebra by Jim Hefferon. This book is available in pdf form for free at the URL above. I would like to cover most of the first four chapters of this text. This will be a brisk pace, but I think it is doable.

Your evaluation will be based almost exclusively on weekly homework assignments. In most cases, you will be responsible for correcting your own assignments. I will assign grades (for those who so opt) by following the guidelines in the COA Course Catalog. I do not have any quota of A's, B's, etc. In general, I strongly recommend against grades; I believe they are more likely than not to interfere with genuine, reflective learning.

Policies and Course Details:
  1. The final version of this and related documents can be found on the course web page,
  2. Homework will usually be due Fridays at the end of the day. Chronically late homework assignments will result in me likely mentioning this in your narrative evaluation and may result in a lowering of your grade.
  3. You are strongly encouraged to work together on homework. You can also consult me, other faculty, friends, and family. However, the homework you hand in should represent your own understanding. This means that if your friends get a homework problem and you don't understand how they did it, you shouldn't photocopy their solution and turn it in.
  4. There will be some assignments for which you will need to use Maple to do numerical calculations.
  5. It is much easier for me if you send email to my hornacek account and not at any of my other addresses.
  6. Academic misconduct -- cheating, plagarizing, etc. -- is bad. Any cases of academic misconduct will result in a judicial hearing, as per pp. 14-15 of the COA handbook. Possible consequences range from failure of the assignment to expulsion. For more, see the revised statement on academic integrity passed by the faculty several winters ago.
  7. A more informal description of the course can be found here.