Prerequisite: Math 126

Text: Introduction to Linear Algebra by Johnson, Riess and Arnold, 5th ed. Note: Although the Student's Solutions Manual for the textbook will not be ordered by the University Bookstore, students may be able to locate their own copy. This contains detailed solutions to all odd-numbered exercises.

Math 308 is an introductory linear algebra course and it is assumed that students have a higher level of mathematical maturity. Math 308 is not supposed to be a course in abstract vector spaces.

Math 308 should stress some difficult abstract ideas in concrete form (e.g., linear dependence, subspace) but there should also be substantial time spent on examples of applications of linear algebra. The applications which are found in Johnson and Riess are included in the syllabus below; some instructors may wish to pick applications from other sources, such as Applications of Linear Algebra by Rorres and Anton.

Note: Please contact Brooke Miller, 3-6830, if you have questions or suggestions concerning the syllabus.

This syllabus refers to sections of the textbook.

§1 - Matrices and Systems of Linear Equations (9 lectures):

§1.1-1.4: Gaussian Elimination (3 lectures)

.§1.5,1.6: Matrix operations (2 lectures)

§1.7: Linear independence (1 lecture)

§1.9: Data Fitting (1 lecture)

If time is limited, just do the first interpolation application on pp. 76-81; introducing students to the idea of interpolation should help them be prepared for the later section on least squares approximation. These pages also provide a good example of linear independence.

§1.9: Matrix inverses (2 lectures)

§2 - Chapter 2 is a review of material that the students should have learned in Math 126. Remind the students that they should review the material.

§3 - Rⁿ (11 lectures):

§3.1-3.3: Subspaces (3 lectures)

§3.4-3.5: Bases and dimension (3 lectures)

§3.6-3.7: Orthogonal bases and linear transformations (3 lectures)

§3.7 is not really a good place to try to teach abstract linear transformations, but one can teach how to construct the matrix representations of geometric transformations such as rotations and reflections.

§3.8,3.9: Least Squares (2 lectures)

§4 - Eigenvalues and eigenvectors (6 lectures)

§4.1-4.3: Introduction to eigenvalues and determinants (2 lectures)

§4.4-4.5: Eigenvalues, characteristic polynomial, eigenspaces. (2 lectures)

§4.8: Applications (2 lectures)

This section can be integrated with the prior eigenvalue sections to furnish further examples of eigenvalue problems.

§4 - More on eigenvalues (optional)

§4.6,4.7: Complex eigenvalues, similarity, diagonalization

These ideas are clearly very important for linear algebra, so it would round out the course if this material could be introduced at some level. However this part of the theory will be introduced and studied in Math 309 preparatory to the study of systems of linear differential equations, so these sections are made optional here. Perhaps one could show how diagonalization works in simple cases here, without going into detail about the fine points.

Updated 10-6-04