Mon, Tue, Wed, and Thu, 1pm - 2:35pm, Room 417, Mathematics
July 2 - August 10
All important course announcements will appear here. So check back regularly.
Class meets in the Mathematics building, room 417!
The first day of class is July 2nd. See you there.
There will be no class on July 4th so that we can all celebrate Independence Day accordingly. To make sure no course time is missed, class will meet on Friday July 6th.
How do I prove something in Linear Algebra? I practice. But here is a guide that you might find helpful: Proofs.
Here is a handout on Gaussian Elimination.
Here are the selected Solutions to Homework 1. Some of the words got cut off. In 1.20 it was "group". In 1.46a) it was "trace B". In 1.46c) it was "transpose doesn't change the diagonal", and in 3.44 it was "variables" in line 3, and "it works for any b in R^m because b was arbitrary". Let me know if there are questions.
Here is the midterm I gave last summer. Note that the last two problems aren't relevant to this class yet because we went in a different order last summer.
Here are the solutions to the first five questions from the above midterm. Let me know if you have any questions.
Here are the solutions to the fifth homework assignment (the one that has yet to be returned. There is a typo in problem 16 from 4.2.16, can you find it?
Here are the solutions to homework six and seven. It's just one file, all the answers should be there.
Here are the midterm solutions finally. Let me know if there are any questions.
Here is a link to the page about Google and linear algebra that I never made it to during class. It's relatively interesting and not that difficult. Enjoy the rest of the summer.
Instructor: Matt DeLand (x45886, 408 Mathematics, deland@math.columbia.edu)
Office Hours: 11am-12pm Monday through Thursday. I'll also be around the math department at other odd hours (usually in my office).
Teaching Assistant: Irena Penev Office Hours: TBA
Syllabus: Tentative Syllabus. The word TENTATIVE will change to OFFICIAL on or shortly after the first day of class.
| Date | Topics/Sections covered | Remarks | Homework | Date Due |
|---|---|---|---|---|
| July 2 | Introduction Vectors and Matrices (1.1) Linear Combinations (1.2) | Welcome to the first day! | Homework 1 | July 5 |
| July 3 | Linear Combinations (1.2) Systems of Linear Equations (1.3) Gaussian Elimination (1.4) | |||
| July 4 | NO CLASS | |||
| July 5 | Gaussian Elimination Applications (1.5) | Homework 2 | July 9 | |
| July 6 | Spans Linear Dependence (1.6-7) | Note Friday Class! | ||
| July 9 | Matrix Multiplication Applications (2.1-2) | QUIZ 1 | Homework 3 | July 11 |
| July 10 | Invertibility, Elementary Matrices, the Inverse (2.3-4) Systems of Linear Equations | |||
| July 11 | Applications: LU Decomposition Linear Transformations (2.5-6) | Homework 4 | July 16 | |
| July 12 | More about Transformations (2.7) Start talking about determinants? (3.1) | |||
| July 16 | Determinants (Chapter 3) | QUIZ 2 | Homework 5 | July 18 |
| July 17 | Subspaces Basis and Dimension (4.1-2) | |||
| July 18 | Subspaces associated to a Matrix Coordinate Systems (4.3-4) | Homework 6 | July 23 | |
| July 19 | Linear Operators and Matrices Eigenvalues and Eigenvectors (4.5-5.1) | |||
| July 23 | MIDTERM: The exam will cover chapters 1-4 | Homework 7 | July 25 | |
| July 24 | Characteristic Polynomials Diagonalization of Matrices (5.2-3) | |||
| July 25 | More About Diagonalization (5.4) | Homework 8 | July 30 | |
| July 26 | Application Day : Markov Chains -- Differential Equations | |||
| July 30 | Geometry of Vectors Orthogonal Vectors (6.1-2) | QUIZ 3 | Homework 9 | August 1 |
| July 31 | Least Squares Approximation Orthogonal Matrices (6.3-4) | |||
| August 1 | Symmetric Matrices Singular Value Decompositions (6.5-6) | Homework 10 | August 6 | |
| August 2 | Application Day : Rotations in Euclidean Space | |||
| August 6 | Vector Spaces Dimension and Isomorphisms | QUIZ 4 | ||
| August 7 | Linear Transformations and Matrices Inner Product Spaces | |||
| August 8 | Finish Chapter 7 | |||
| August 9 | Google? and Review | Homework 11 - Optional | ||
| August 10 | FINAL |
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