| Call number: | 67337 | |||||||||
| Room/Time: | TR 1:10pm--2:25pm, Schermerhorn 614 | |||||||||
| Instructor: | Eric Urban | |||||||||
| Office: | 608 Math | |||||||||
| Office hours: | Monday 10-12pm or email for appointment | |||||||||
| E-mail: urban at math dot columbia dot edu | ||||||||||
| Teaching assistants: |
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| Midterm 1: | Thursday, February 9th | |||||||||
| Midterm 2: | Thursday, March 23rd | |||||||||
| Final: | Tuesday, May 9th (tentative) | |||||||||
| Webpage: | www.math.columbia.edu/~urban/linar_algebra.html | |||||||||
Our teaching assistants hold their office hours in the Help Room in Math 406. The Help Room is open Monday-Thursday 9am-6pm and Friday 9am-4pm. You can go there any time during open hours to get help with the material (not just from our TAs).
Textbook Otto Bretscher Linear algebra with applications, Fifth edition. Cheaper 4th edition is fine too, except for the homework problems, which come from the 5th edition. If you buy the fourth edition, you'll need to get the correct problems from a friend who has the 5th edition
Syllabus: Our goal is to cover chapters 1 through 8 of the textbook, with few omissions. The topics are: systems of linear equations and Gaussian elimination, matrices, linear transformations, subspaces, linear spaces, orthogonality and the Gram-Schmidt, determinants, eigenvalues, eigenvectors, symmetric matrices.
Homework: Homework consists in reading the textbook sections before class according to the schedule of lectures and writing down (and turning in) the solutions of problems. The homework problems
will be assigned on Tuesdays in Class, due Tuesday the next week before class.
Drop the homework off to the hw box with my name on it on the 4th floor of the Math building
Two lowest homework scores will be dropped.
Graded homework can be
picked up from a tray on the 6th floor (up the stairs, turn left and
through the door, the table with hw trays is to your left half the hall way). LATE HOMEWORK WON'T BE ACCEPTED.
The numerical grade for the course will be the following linear combination:
15% homework, 25% each midterm, 35% final.
Homework 1, due Tuesday January 24th. Solve in Section 1.1: # 6, 18, 24, 37, 44 and in Section 1.2: # 2, 4, 9, 11, 18.
Homework 2, due Tuesday January 31st.
Solve in Section 1.2: # 29, 37, 67, in Section 1.3: # 2. 8, 9, 24, 50 and in Section 2.1: # 6, 8.
Homework 3, due Tuesday February 7th.
Solve in Section 2.2: # 14, 32, 39, in Section 2.3: # 7, 20, 47, 60 and in Section 2.4: # 4, 30, 84.
Homework 4, due Tuesday February 28th.
Solve in Section 3.1: # 7, 20, 34, 46, 50 in Section 3.2: # 3, 14, 15, 37, 41.
Homework 5, due March 7th.
Solve in Section 3.2: # 46, 52, 57 in Section 3.3: # 16, 27, 33, 36, 39, 62, 69.
Homework 6, due March 21st.
Solve in Section 3.4: # 45, 60, 82, in Section 4.1: # 29, 49, 59, in Section 4.2: # 7, 53, 65, 70, in Section 4.3: # 38, 62.
Homework 7, due April 4th.
Solve in Section 5.1: # 12, 14, 16, 23, 31 and in Section 5.2: # 29, 35, 38, 44.
Homework 8, due April 11th.
Solve in Section 5.3: # 30, 38, 42, 67 and in Section 5.5: # 5, 10, 16, 20.
Homework 9, due April 18th.
Solve in Section 6.1: # 10, 15, 28, 50 and in Section 6.2: # 5, 23, 31, 43, 45, 54.
Homework 10, due April 25th.
Solve in Section 6.3: # 10, 11, 38, 39, in Section 7.1 : # 13, 44, 53, 64 and in section 7.2 # 2, 22, 33, 45.
| Dates | Topics | Book |
| TR 01/17,01/19 | Linear equations, matrices, vectors, GJ elimination | 1.1, 1.2 |
| TR 01/24, 01/26 | RREF, Solutions of lin. systems, linear transformations | 1.2, 1.3, 2.1 |
| TR 01/31, 02/02 | LT in geometry, products, inverses | 2.2, 2.3, 2.4 |
| T 02/07 | Image, Kernel of LT, subspaces, bases, independence | 3.1, 3.2 |
| R 02/09 | First Midterm | 1.1-3.2 |
| TR 02/14, 02/16 | Dimension of subspace, Coordinates | 3.3, 3.4 |
| TR 02/21, 02/23 | Linear spaces, linear transformation | 4.1,4.2 |
| TR 02/28, 03/02 | Matrix of linear transformation, orthonormal bases | 4.3, 5.1 |
| TR 03/07, 03/09 | Gram-Schmidt Process, Orthogonal matrices, Inner products, | 5.2, 5.3, 5.5 |
| TR 03/14, 03/16 | NO CLASS (Academic Holiday) | |
| T 03/21 | Review | |
| R 03/23 | Second Midterm | 3.3-5.5 |
| TR 03/28,03/30 | Determinants | 6.1, 6.2 |
| TR 04/04, 04/06 | Cramer's rule, Diagonalization | 6.3, 7.1 |
| TR 04/11, 04/13 | Eigenvalues, Dynamical systems | 7.2-7.4 |
| TR 04/18, 04/20 | Complex eigenvalues | 7.5, 8.1 |
| T 04/25, | Symmetric matrices | 8.1-8.3 |
| R 04/27 | REVIEW | 1.1-8.3 |
| T 05/09 | FINAL EXAM 1:10-4pm |