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This is a (yet unfinished and unpublished) textbook, which will be made freely available online.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 here.

Grading policies:

Homework 20%, Quizzes 20%, Midterm 20%, Final 40%
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.

Course Description

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 explicitly.

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.