An introduction to linear algebra, including linear transformations and determinants, eigenvectors and eigenvalues, and linear spaces. We will further study linear differential equations and applications.

This course is taught entirely in sections (taught by teaching fellows [TF]), with an additional weekly problem session (conducted by a Course Assistant [CA]). Sectioning must be done via computer by noon on Friday, Feb 5. You will be notified of your assigned section during the weekend. Classes will begin on Monday, Feb 8.

Course Head: Robert Winters, SC 432, 495-8796
rwinters@math.harvard.edu
http://www.math.harvard.edu/~rwinters
Office hours: Mon, Wed, Fri 1pm to 2pm and by appointment

Exams: There will be two midterm exams and a Final Exam.

Midterm Exam #1: Tuesday, March 16, 7:30pm in Science Center Hall C

Midterm Exam #2: Monday, April 26, 7:30pm in Science Center Hall C

Grades: Your overall course grade will be determined according to the following weights:

Midterm exams 20% each homework 20% final exam 40%

This scheme may be modified slightly, depending on circumstances.

Text: Linear Algebra with Applications, by Otto Bretscher.

Homework: Homework will be assigned each class and due at the next class. Graded homework will generally be returned the class after that. Your Course Assistant will put solutions on reserve in Cabot Library a few days after homework is due. Your Course Assistant will establish policies regarding submitting late homework. However, it is expected that you will do your homework on schedule.

Tentative assignments for the first week (Mon-Wed-Fri sections) are as follows:

HW #1: 1.1: 11,16,17,20,29,36
HW #2: 1.2: 6,9,20,33,37,42
HW #3: 1.3: 1,14,25,34,48,50

Homework problems are an integral part of this course. It is impossible to understand the material and do well on the exams without working through the homework problems in a thoughtful manner. Mathematics is not a spectator sport. Don’t just crank through computations and write down answers - think about the problems posed, your strategy, the meaning of the computations you perform, and the answers you get. Nothing prevents you from trying a few more problems in a given section if you feel it may do you some good.

We encourage you to form study groups with other students in the class so you can discuss the work with each other. Your Course Assistant will, upon request, distribute a list of names and phone numbers of those in class in order to facilitate this. Although we encourage you to talk to your classmates, work must be written up independently.

Many of the problems for homework will look different from problems you discussed in class and in the text. This is not an accident. We want you to think about the material and learn to apply it in unfamiliar settings and interpret it in different ways. Only if you understand the material (as opposed to merely knowing it) will you be able to go beyond the information you are given.

Many math students seem to subscribe to the "Ten Minute Rule": If you cannot solve it in ten minutes, you cannot solve it at all. Nothing could be further from the truth, of course. You will probably learn most from those problems which keep you busy more than ten minutes, whether you can ultimately solve them or not.

Use of Technology: In some of the homework problems you will be asked not to use any technology (calculators or software packages). If no restriction is made, you may use the form of technology of your choice, e.g. TI-85 calculator, Matlab, Maple, Mathematica. Make sure to have access to some form of technology. A few TI-85 calculators are on reserve in Cabot Library. At this stage, we do not plan to allow calculators on exams.

Syllabus: We will cover approximately one section of the text per class (MWF schedule). Your Section Leader will highlight the key concepts introduced in each section, but there may not be enough time to cover all the topics. You will need to study the text to fill in the details. Reading the text is an integral part of the course. On the exams, you will be responsible for all the material discussed in the text and in class. Below is the approximate syllabus for the course. Some topics may be omitted if time is limited.