** Intructor:** Daniel Ruberman

** Office:** 310 Goldsmith

** Telephone:** x63074

** Email:** ruberman@brandeis.edu

** Office Hours:** For the first two weeks, Tuesday 10-12 and Friday
10-11, ** or by appointment.**

After my schedule has settled down, and I find out if these hours work for
most people, I may change the office hours. In general, I am in my office
quite a bit, and welcome visitors. You can try just dropping by, but it's
easiest if you contact me in advance by phone or email, or arrange something with
me before or after class. You may also find it worthwhile to consult my
schedule, which may be found on my web home page.

** Course Description:** This course covers linear algebra, which is the
study of linear equations, vectors and linear transformations. The ideas
of linear algebra are important in many fields of study, as well as being a
good starting point for the mathematics concentration. There will be a
dual emphasis on theory and techniques; one of the goals of the early part
of the course is for students to learn how to write a clear and complete
proof. * *

**Textbook: ** ``Linear Algebra with Applications'', by Otto Bretscher
(second edition), Prentice Hall (2001). We will cover almost all of
chapters 1-8, with some additional topics as time permits.

** Until the textbooks all come in:** The first two sections of the book,
enough to get started with the HW, can be found on the Library's ERES system.
Click here to go to
the Math 21a ERES page. You will need the password, which I sent you in an
email on Friday.

** Grading:** There will be one final (40%), two midterms (20% each),
quizzes (10%) and homework (10%).

** Homework: ** Homework will be given weekly, handed in, and graded.
The assignments can be found on the Math 21a Homework Page.
To further the course goal of learning to write good mathematics, at least
one problem will be to write a complete and well-organized proof. This
assignment will be graded separately, and should be handed in on a separate
sheet of paper. In keeping with the material, the first few of these will
be rather short, but we will work on more elaborate proofs as the class
progresses.

** First Quiz:** In class on Wednesday September 12. The results of the
quiz will be helpful for students who are still deciding between Math 21,
22, and 15.

** Midterm exams:** The first exam is tentatively scheduled for
Wednesday, October 10. The second exam will be sometime in mid-November.

** Final Exam: ** The final will be a 3-hour exam, given during exam
week. Time and place TBA

**Placement: ** There are two other linear algebra courses at Brandeis,
Math 15 and Math 22a, and choosing correctly is important. Roughly
speaking, the topics in covered in Math 22 are similar to those in this
course, but the treatment is more theoretical and somewhat faster paced.
The two courses have the same schedule, to simplify changing between them.
Math 15 is a much less theoretical course than either 21 or 22 (you won't
do very many proofs) and also covers much less ground. You are strongly
advised to discuss your placement with me and/or Professor Lian (Math 22),
or one of the department's undergraduate advisors, Professors Igusa and
Monsky.

** There will be a short diagnostic (ie grades don't count) quiz on the
first day of class, to help you decide which course is for you. The same
quiz will be given on the first day of Math 22.**

** Math 21a on the web:**
I will try to have everything concerned with the class posted on the class homepage,
http://www.math.brandeis.edu/Faculty/ruberman/math21f01/math21f01.html. On this page you will find up-to-date course information (eg changes in office hours or exam schedules), the homework assignments, and supplemental course materials. We will have a class mailing list; I will explain how to access this on the first day of class. If you are feeling adventurous, you can try to figure things out on your own by looking at the Brandeis lists page . Click on the link "Lists for classes offered at Brandeis" and then find math-21a on the list of offferings.