Math 115A/5, Fall 2012
Linear Algebra

Instructor

George J. Schaeffer
Email: gschaeff@math.ucla.edu
Office: MS 5226 (Mathematical Sciences Building)
Office Hours: Tuesdays 2:30 to 5:30 PM (tentative)

Teaching Assistant

TBA

Class Meetings

There will be class every day in MS 6229 from 1:00 to 1:50 PM.
Classes on MWF are lectures (given by myself) while classes on TR are discussion sections (given by your TA).

Textbook

Friedberg, Insel, and Spence, Linear Algebra, 4th edition (custom UCLA edition).
Unavoidably, the book contains small errors. A list of known errata can be found here.

Prerequisites

Math 33A or equivalent.

Homework

Homework will be collected in lecture on Fridays every week except for 09/28 (2nd day of class), 11/02 (midterm), and 11/23 (day after Thanksgiving), and assigned on Friday afternoons.
The homework assignments will nominally cover material up to and including the week's Wednesday lecture, but they will mostly concentrate on reinforcing earlier material.
Collaboration on homework is encouraged, as long as it is beneficial to your understanding of the material!
Late homework will not be accepted.

Quizzes and Examinations

There will be two short quizzes, a midterm exam, and a final exam.
The quizzes are scheduled for 10/16 and 11/28 (in class). The midterm is scheduled for 11/02 (in class).
The final exam is scheduled for 12/13, 8:00 to 11:00 AM (Final Examination Code 06).
Make-up exams are strongly discouraged. If you have a legitimate reason for missing an exam, contact me as soon as possible (preferably the week before) and we will attempt to make alternate arrangements.

Grading

Your grade will be determined as follows: 25% Homework and Quizzes, 25% Midterm, 50% Final.

Syllabus

We will follow the sequence of topics in the course outline with some modifications. Subject to change, this is the plan:

Week 1 (of 10/01): Vector spaces, subspaces, linear independence
Week 2 (of 10/08): Bases, dimension, linear transformations, nullspace and range
Week 3 (of 10/15): Some review, Quiz 1 (Tuesday), matrix of a linear transformation
Week 4 (of 10/22): Matrices, invertibility, change of basis
Week 5 (of 10/29): Review, Midterm (Friday)
Week 6 (of 11/05): Determinants, eigenvalues and eigenvectors
Week 7 (of 11/12): Diagonalizability
Week 8 (of 11/19): Review, Quiz 2 (Monday), linear recurrences
Week 9 (of 11/26): Inner products and norms, Gram-Schmidt orthogonalization
Week 10 (of 12/03): Adjoints, normal operators, self-adjoint operators.

Additional topics related to writing proofs (e.g., basic logic and proof by induction) will be covered in the discussion section.