Mathematics 115AH - Linear Algebra - Fall 2019 - UCLA

Instructor: Burt Totaro.
E-mail: totaro@math.ucla.edu.

Course webpage: www.math.ucla.edu/~totaro/119ah.1.15f/index.html

Book: K. Hoffman and R. Kunze, Linear Algebra, Prentice Hall, second ed., ISBN: 978-0135367971. The book is out of print, but you can buy a reprint from the UCLA Store for about $15.00. Or you can buy an electronic copy from the UCLA Store for about $10.00.

Alternate book: S. Friedberg, A. Insel, and L. Spence, Linear Algebra, Pearson, ISBN: 9780134860244. This is sometimes used for 115A and 115B; the material is similar to Hoffman-Kunze, but with more emphasis on applications.

Course Description: Linear algebra is a subject that permeates almost all of mathematics, both pure and applied. For example, calculus is based on approximating arbitrary functions by linear maps, which are easy to analyze. This simple idea makes linear algebra fundamental to algebra, analysis, geometry, physics, and statistics.
Your primary goals in the course should be to understand linear algebra from a rigorous point of view and to learn to write clear and precise proofs.

Material to be covered: Vector spaces, linear transformations, determinants, inner product spaces, orthogonal and unitary transformations, diagonalization, dual spaces. You should have seen much of this material from a computational point of view. Familiarity with complex numbers is also required.

Course outline: My plan is to cover sections 2.1-4, 3.1-5 and 3.7, 6.2, 6.4, and 8.1-5 in the book by Hoffman and Kunze.

Grading: Grades will be assigned based on the higher of the following two schemes:
10% homework + 25% first midterm + 25% second midterm + 40% final
10% homework + 35% (best of two midterms) + 55% final

Evaluation:

Every exam will include at least one problem taken from the homework, possibly with minor variations.
Part of the homework grading will be based simply on whether you hand in the problems (without copying from someone else). However, at the top of each homework, you may mark a problem you wish to be read carefully. We will read that problem carefully and give you detailed feedback so that you can get better and better at writing solutions.
It is your responsibility to know how to do the problems. Practicing that is the only way to study for the exams.
A grade of 'F' will be assigned to any student who misses the final. Incompletes are reserved for those who have completed all of the work for the class, including both midterms, but who, for a legitimate, documented reason, miss the final.
Exams (or copies) will be returned, but I will keep copies (or originals) of the exams, as required by the math department.

Miscellanea:

If you wish to request an accommodation due to a disability, please contact the Center for Accessible Education as soon as possible at A255 Murphy Hall or via their web site.

Catalog description: 115AH. Linear Algebra. (5) Lecture, three hours; discussion, two hours. Requisite: course 33A with grade of B or better. Techniques of proof, abstract vector spaces, linear transformations, and matrices; determinants; inner product spaces; eigenvector theory. Honors course parallel to course 115A. P/NP or letter grading.