
Textbook: “Linear Algebra” by Friedberg, Insel and Spence (4th edition).
I will use my own lecture notes which follow the course outline. It is not necessary, but recommended, that you read the textbook concurrently and come to office hours if there is anything you do not understand.
Exams:
Lecture Notes, Homeworks, and Exams
Homeworks and lecture notes will be posted at the beginning of each week.
The homeworks should be turned in to the TA in the Thursday discussion section on the following week (So you have about 10 days to think about a homework).
No late homework will be accepted, unless with very good reasons. Please talk to the instructor before the homework is due if you have to miss the due date of that homework.
The lowest homework score will be dropped.
Grading:
Two schemes will be used.
The final grade will be the higher one from the two methods.
The grade “incomplete” will only be given in very special cases, when a student
Further readings:
How did linear algebra evolve over the last 4,000 years.
Chiu Chang Suan Shu (The Nine Chapters on the Mathematical Art),
Chapter 8 “Rectangular arrays” (System of linear equations). (In Ancient Chinese). (The full book is available here. English description of the book.)
From The MacTutor history of mathematics archive. Nice description of the evolution of linear spaces and matrices/determinants.
Kline, Morris. Mathematical Thought from Ancient to Modern Times,
Sections 1.5 (Babylonian algebra), 2.3 (Egyptian algebra), 25.3 (determinants) and Chapter 33 (19th century).
Dieudonné, Jean Alexandre. History of Functional Analysis.
Chapter IV (from finite to infinite dimensional “linear algebra”).
Analytical properties of linear transformations (Operator theory).
We have seen that we can assign norms to vectors, which allows us to estimate, approximate, etc.. It turns out that we can do the same thing to linear transformations. And furthermore, we can apply theories from calculus and complex analysis to study linear transformations...
Numerical linear algebra.
It's one thing to know that a linear system has a unique solution, it's a very very different thing to actually find it...