Instructor: Nadia Masri
email: nmasri@math.uiuc.edu
Office hours: Tuesday, Thursday after class or by appointment
Lectures: TR 2:00 - 3:50 PM, Room 2 Illini Hall
Textbook: David C. Lay, Linear Algebra and its Applications, 3rd edition (Updated), Addison-Wesley, Reading, MA, 2002.
Preamble:
This course is an introduction to linear algebra. We will begin by looking at ways of solving systems of linear equations, and then translating these solutions into the language of matrices. In effect, by the end of the course we should be able to talk about algebraic questions in the language of geometric objects: a property that makes linear algebra tremendously useful for solving real-world problems.
The analogy of language is a useful one. You can think of linear algebra as just a very practical language for talking about the sets of solutions of systems of equations. As such, this will probably be a slightly different type of math course than what you might be used to. Linear algebra is usually the first class in which a student experiences mathematical abstraction beyond college-level calculus. Our goal will not be to learn a bunch of new formulas, but rather, to learn how best to approach solutions analytically. The best strategy for doing well in this course is thus very similar to what you would do when learning a new language: try to internalize the definitions and the grammar, and (with some practice, of course) you will be able to apply it in all kinds of situations.
Administrative stuff:
We will have two midterms and a final exam. Tentative dates of tests (subject to change):
Thursday November 1
Thursday November 29
I'll provide more precise information on the dates of the tests later. All tests will be held during regular class time in Illini Hall, Room 2.
Final exam: 1:30-4:30 PM, Friday, December 14 in Illini Hall, Room 2.
Grading:
The grade for the course will be based on the total points from the two midterm exams (the maximum score will be 100 in each test), the final exam (maximum score 200), and on points from homework (normalized to a maximum score of 50; the lowest homework score will be dropped). Since the time of this course is very constrained, no make-up tests will be given, and no late homework will be accepted. Exceptions will be considered only in the case of a prolonged illness indicated by a doctor's note.
No books, notes or calculators will be allowed in the tests and the final exam.
There will be weekly homework assignments, due in class at the beginning of the lecture specified for each assignment. Again, no late homework will be accepted. Graded homework will be returned in class.
A few words of advice: This is a full semester course that has been condensed into an eight week one. This means that it is especially important to not miss classes. I will not take attendance but typically students find it very difficult to keep up if they skip lectures. Also, it is very normal to have difficulty with some new concepts here and there. The material builds on itself so it is very important to catch any difficulties right when they come up, rather than letting them build up. Come to office hours as soon as possible!
Suggested Problems: Almost all the suggested problems listed below have solutions at the back of the book. The homework assignments will be pulled from these as well as some additional even-numbered problems. To do well in the course, you should at the very least be able to solve all the problems listed below.
Chapter 1, section 1: 3,5,7-9,11,13,15,19,21,23,25,31
Chapter 1, section 2: 1-3,5,9,11,15,19,21,25-27,31
Chapter 1, section 3: 1,3,5,7,9,11,15,21,23,25
Chapter 1, section 4: 1,3,5,7,9,11,15,17,19,21,24,27,29,31
Chapter 1, section 5: 1,7,9,11,15,17,19,21-23,27,28,33
Chapter 1, section 7: 1,3,5,11,13,17,19,21,23,25,29,31,34-37
Chapter 2, section 1: 1,3,5,7,10-13,25
Chapter 2, section 2: 1,3,7,9-11,13,17,19,23,27,31
Chapter 2, section 3: 3,5,9,13,15,18,21,27
Chapter 3, section 1: 3,7,13,17,19,21,23,25,37-40
Chapter 3, section 2: 1,3,5,9,13,17,19,23,26,29,35-37,39-42,44
Chapter 3, section 3: 1,5,9,13,19,23,25
Chapter 4, section 1: 1,3,9,11,13,15,16,21
Chapter 4, section 2: 1,3,5,7,11,15,19,23,27
Chapter 4, section 3: 2,3,8,9,11,13,15,19,21-25
Chapter 4, section 5: 3,7,11,13,19,20
Chapter 4, section 6: 3,5,7,9,11,13,15,17,21,23,25
Chapter 5, section 1: 3,5,9,13,15,17,19,21
Chapter 5, section 2: 3,7,11,13,17,18,21,23,27
Chapter 5, section 3: 1,3,5,7,15,19,21,25,29
Chapter 6, section 1: 1,3,5,7,11,13,15,17,19,21,22,29,31
Chapter 6, section 2: 3,5,9,11,13,15,21,23
Chapter 6, section 3: 1,5,9,11,13,15,17,19,21
Chapter 6, section 5: 3,5,9,11,13,15,17,19,21,25
Chapter 6, section 6: 1,7a,10a