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| Quick links to: | Announcements | General information | Assignments | Notes | External Resources |
09/28/2007 Solutions to midterm I Solution to the first midterm are posted in the notes section below.
09/28/2007 Solutions to review problems I've posted selected solutions to the review problems. Corrections have been made to some of the review problems.
09/27/2007 Review problems for first midterm Review problems for the first midterm have been posted in the notes section below. Solutions will appear shortly.
08/31/2007 Assignment 1 due date changed Assignment 1 is due Friday September 7 instead of Wednesday September 5. Future assignments will be due Wednesdays as usual.
08/24/2007 Course web page now online! The course web page now exists! This web page will be your central resource (outside of classes) for information about the course; please come here often to look for assignments, announcements and other information.
Course description This is a first course in linear algebra. Topics to be covered include: vector spaces, linear transformations, matrices, Gaussian elimination, determinants, eigenvalues and eigenvectors, and various additional topics.
Prerequisites Math 0413: Introduction to Theoretical Mathematics is the main prerequisite.
Assessment The final grade will be composed of grades for coursework, two midterm exams, and a final exam, in the following proportions.
Coursework will consist of a series of weekly homework assignments.
There will be around 12 homework assignments in total. Homework will
be assigned every Wednesday, and completed assignments will be
collected at the beginning of class on the following Wednesday.
You're encouraged to discuss homework problems with each other, but
you should write up your solutions individually. Homeworks should be
presented neatly and carefully.
Late homeworks will not
be accepted without prior arrangement (genuine emergencies excepted);
if for some reason you think you won't be able to get your homework in
on time, please come and discuss this with me before the due
date.
The exams will be based on the material presented in class, which may
differ from the material in the book. At exam time it will be
important to have a complete set of notes to review. Exams will be
closed book; calculators will not be permitted. If you need to miss a
class, make sure that you (1) get a copy of the notes for the class
you missed from a classmate, (2) read those notes, together
with the appropriate portion of the textbook, and (3) come and see me
if anything doesn't make sense, or if you want to know more about what
you missed.
Exam dates The final exam is on Thursday, December 13th from 4:00pm to 5:50pm, in a room to be announced. The two midterm exams will be held during class time and are provisionally scheduled for Wednesday, October 3 and Wednesday, November 7. Please let me know as soon as possible if any of these dates causes serious problems for you, so that alternative arrangements can be made.
Textbook The textbook for the course is ‘Linear Algebra: A Geometric Approach&rsquo by Theodore Shifrin and Malcolm R. Adams. ISBN-13: 978-0-7167-4337-8. It's published by W. H. Freeman and Company.
Syllabus Here's a rough syllabus for the course. Please bear in mind that the information below isn't exact: some sections listed may be only partially covered, and we may cover additional material not listed below. When exam time comes around your course notes should serve as the primary reference.
| Week beginning | Textbook sections | Topics to be covered |
|---|---|---|
| 08/27 | 1.1–1.2 | Vectors, Dot products and Euclidean spaces |
| 09/03 (No class Monday) | 1.3–1.4 | Systems of equations and Gaussian elimination |
| 09/10 | 1.4–1.5 | Existence of solutions and rank |
| 09/17 | 1.5–1.6, 2.1 | Uniqueness of solutions; applications |
| 09/24 | 2.2–2.3 | Matrices; Inverse matrices |
| 10/01 | Midterm 1, 3.1–3.2 | Vector spaces |
| 10/08 | 3.2–3.3 | Linear independence; bases |
| 10/15 | 3.4, 3.6 | Some important subspaces; abstract vector spaces |
| 10/22 | 4.1–4.2 | Projection and orthogonal bases |
| 10/29 | 4.3–4.4 | Linear transformations |
| 11/05 | Midterm 2, 5.1 | |
| 11/12 | 5.2–5.3, 6.1 | Determinants; eigenvalues |
| 11/19 (No class Wed/Fri) | 6.2 | Diagonalizability |
| 11/26 | 6.3–6.4 | Applications |
| 12/03 | Additional topics and review |
Assignments will be posted in this section. All assignments are due at the beginning of class on the indicated due date. Numbered problems refer to the textbook.
| Assignment | Problems | Due date |
|---|---|---|
| Assignment 1 | Exercises 1.1: 2, 5, 9, 14, 17 Exercises 1.2: 1, 3, 10, 14, 24 |
Friday September 7 |
| Assignment 2 | Exercises 1.2: 2, 17 Exercises 1.3: 1, 3, 6, 9 |
Wednesday September 12 |
| Assignment 3 | Exercises 1.3: 11 Exercises 1.4: 2, 4, 5, 9 Exercises 1.5: 2, 5, 7 |
Wednesday September 19 |
| Assignment 4 | Exercises 1.6: 4, 12, 15 Exercises 2.1: 1, 6, 11, 19 |
Wednesday September 26 |
| Assignment 5 | Exercises 2.2: 1, 3, 5, 12, 13, 17 Exercises 2.3: 2, 7, 18 |
Wednesday October 10 |
| Assignment 6 | Exercises 3.1: 1, 2, 3, 13, 14, 16, 26 | Wednesday October 17 |
| Assignment 7 | Exercises 3.2: 1, 3, 4, 5, 13 Exercises 3.3: 1, 4, 7, 11 |
Wednesday October 24 |
| Assignment 8 | Exercises 3.4: 1, 3, 4, 13 Exercises 3.6: 2, 3, 6, 7, 11 |
Wednesday October 31 |
| Assignment 9 | Exercises 4.1: 2, 4, 7, 13 Exercises 4.2: 2, 4, 11 |
Friday November 16 |
| Assignment 10 | Exercises 5.1: 4 Exercises 5.2: 1, 4, 5, 6, 9, 11 |
Friday November 30 |
I'll put digital copies of any handouts or overheads used during the course in this section, along with other course-related materials.
Here are some external links of varying relevance to the course. Let me know of anything that you'd like to see added here! A reminder: treat all information coming from any of these web pages with some caution; there's a lot of good information there, but errors and inaccuracies abound.
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