Fall-2014. Math 110 (ccn 54149): Linear Algebra
Instructor: Alexander Givental
Lectures: TuTh 8-9:30, 2040
Valley Life Science Building
Office hours: Tu 1-3 , in 701 Evans
Textbook: Linear Algebra by Alexander Givental
This is a (yet unfinished and unpublished) textbook, which will be made
freely available online. The current version
(which is to evolve during the semester) can be found
Grading policies: Homework 20%, Quizzes 20%, Midterm 20%, Final
The general idea is that you don't compete with
each other. Your goal should be to learn the material as well as
you can, and if all of you do really well, all will get an "A". What exactly
it means to learn well will become more clear during the semester
(probably after the midterm exam, or some quizzes).
Do not ask your instructor: "Is this particular theorem on the
curriculum?" Naturally, your teachers want you to know everything they know;
so, the only answer that would encourage you to learn is "yes, it is".
Instead, you should realize that your instructor and GSIs have absolutely
no motive to ruin your transcript, career, and prospects for a better life.
Just do your best in trying to understand everything, and hope that your
teachers are reasonable in their expectations.
Linear Algebra, if not as a research topic, then at least as a
college course, has a scope well-defined by tradition. It is a very
efficient subject, whose main attraction is that it gives quite complete
answers to several clearly posed problems.
(I would not say this about abstract algebra, and especially analisys,
which provides a number of useful approaches to a great variety
of problems, but a miracle's touch is needed to make the approaches work
all the way through).
Linear Algebra is also a very simple subject, and those several problems
(more specifically, four) can be easily explained in lay terms --
and will be explained, together with their complete answers, in the very
first week of classes. One could also make an effort and learn the
detailed solutions to those four problems in the next couple of
weeks, and go home. But since we have the entire semester at our disposal,
we will spend it wisely by slowly developing the adequate language,
studying various preliminaries, variations, and applications of the main
problems, and hopefully gaining a good intuitive understanding of what Linear
Algebra can do, and what it cannot.
There are many quite reasonable textbooks on Linear Algebra, and their main
content is roughly the same. Our text (even if it may look different at a
glance) is not in any way a deparure from the traditional content. Perhaps,
the main difference with other existing texts, is that we provide a simple
unifying view of the subject, and spell out the main problems quite
Although the terminology of our subject is almost a century old,
and most of the content is even older, we will have a chance to see during the
RRR week how some of our material fits into -- well, if not entrely modern,
then -- only 40-year-old research.