Linear Algebra: Fall 2008

Day/Time: MW 11:00am-12:15pm; Location: 417 Mathematics Building

Instructor
Mirela Ciperiani (mirela at math dot columbia dot edu)

Office
Math 629

Office Hours
MW 2:00pm-3:00pm in Math 629.

Contacting me
I strongly prefer communicating in person to email. Therefore, unless the issue is urgent, it should be discussed with me either after class or during my office hours.

Text
Elementary Linear Algebra: A Matrix Approach, by Lawrence E. Spence, Arnold J. Insel, and Stephen H. Friedberg, 2th edition, Prentice Hall. The book should be available at the Columbia bookstore.

Teaching Assistants
Emily Clader (ecc2112 at columbia dot edu)
Samantha John (smj2118 at columbia dot edu)
Office hours
Math 622 (- only for students in this class)    Thursday 12-1pm (Samantha), Friday 11am-12pm (Emily).
Math Help Room (Math 406)    Thursday 11am-12pm (Samantha), Tuesday 2-3pm (Emily).

Written work
We write to communicate. Please bear this in mind as you complete assignments and take exams. You must explain your work in order to obtain full credit. AN ASSERTION IS NOT AN ANSWER. For specific suggestions see A guide to writing in mathematics classes.

Midterm exams
There will be two midterm exams, the first on Monday, Oct. 6 and the second on Monday, Nov. 10 in class. Make-up exams will NOT be given. Students will only be excused from the midterms because of a serious illness or another emergency of similar gravity, and a note from a doctor or a dean will be required.

Final exam
Dec. 15, 2008:  9:00am-Noon    (according to the projected exam schedule)
All students must take the final at the time scheduled by the university.

Homework
There are weekly homework assignments which can be found below along with the due date and time. Late homework will not be accepted. Students are encouraged to discuss the homework with other students but should write their solutions individually. You can see your grades in the Courseworks Grade Book. The two lowest homework grades will be dropped.

Extra Knowledge
Each week, I assign one or two harder problems which will be graded even if they do not count towards your grade in any way. They are there only for students who would like to deepen their understanding of the material or simply enjoy challenging themselves.

Submitting homework
The homework should be submitted in Mailbox 4446. In order to find the mailbox you should go downstairs once you enter the building and you will see a bunch of mailboxes. You are responsible for putting your homework in the right mailbox by the right time. The mailbox is locked and the papers will be picked up at the homework due time. Whatever is submitted after that time may not be graded and nobody is responsible for returning it to you.

Picking up graded homework
Your graded homework will be in a box on the fourth floor starting at 6pm on Monday. In order to find this box you should turn left once you get to top of the stairs on the fourth floor, you will see a door, after entering the hall the box will be on your right, on a table, and it has the course information on it.

Grading
Homework %25
Midterms %20 (each)
Final exam %35

Conflicts
If you have a conflict with any of the exams (for example, due to a religious holiday), please contact the instructor as soon as possible and at least one week before the exam.

Disabilities
Students who may need disability related accomodations should contact the professor as soon as possible.

Help Room
If you would like help with the material, in addition to the office hours you can take advantage of the Math Help Room (Math 406) which is staffed by graduate students. No appointment is necessary.

Academic Honesty
Copying your written work from somebody else or from any other source is considered cheating and will be dealt with severely. Any cheating during midterms or finals will result in you failing the course and the matter being reported to your dean.


Schedule of lectures
This schedule is tentative and may be modified as necessary.

Date
Reading
Homework
Practice problems
  Sept. 3   1.1: Matrices and Vectors   Due on 9/5/2008 at 3pm
  1.1: 6, 29, 31, 33, 71, 74, 76
  Extra Knowledge 1.1: 82
  1.1: 1, 3, 5, 8, 17, 18, 37 - 46
  Sept. 8, 10   1.2, 1.3: Linear Combinations, Matrix-Vector Products and Special Matrices; Systems of Linear Equations   Due on 9/12/2008 at 3pm
  1.2: 2, 7, 33, 42, 70
  1.3: 6, 8, 9, 45
  Extra Knowledge 1.3: 83
  1.2: 3, 5, 29, 45 - 52
  1.3: 4, 20, 24, 46, 57 - 63
  Sept. 15, 17   1.4, 1.6, 1.7: Gaussian Elimination, The Span of a Set of Vectors, Linear Dependence and Linear Independence   Due on 9/19/2008 at 3pm
  1.4: 10, 35, 46(a), 47
  1.6: 1, 17, 26, 34, 43
  1.7: 5, 15, 31, 41, 55
  Extra Knowledge 1.6: 67
  1.4: 4, 53 - 57
  1.6: 1, 21, 45 - 50
  1.7: 1, 63 - 67, 99
  Sept. 22, 24   2.1, 2.3, 2.4: Matrix Multiplication, Invertibility and Elementary Matrices, The Inverse of a Matrix  Due on 9/26/2008 at 3pm
  2.1: 12, 19, 23, 68
  2.3: 2, 13, 17, 26, 60, 67
  2.4: 12, 58, 64
  Extra Knowledge 2.4: 86
  2.1: 2, 3, 33 - 39
  2.3: 33 - 39
  2.4: 35-46
  Sept. 29,   Oct. 1   2.7, 2.8, 3.1: Linear Transformations and Matrices, Composition and Invertibility of Linear Transformations, Cofactor Expansion   Due on 10/3/2008 at 3pm
  2.7: 1, 7, 21, 29, 33, 59, 72, 79, 101
  2.8: 6, 12, 15, 26, 37, 66, 97
  3.1: 2, 9, 14, 29, 37
  Extra Knowledge 2.7: 100
  2.7: 35 - 40
  2.8: 41-52
  3.1: 56-58
  Oct. 6
1st Midterm

The midterm will cover the material of chapter I and II (up to and including 2.4) only. 		  Sample midterm
In order to prepare for this midterm you should redo the homework sets preceding the one due on 10/3/2008.
   Solutions to some previous proof related homework problems
  Oct. 8   3.2, 4.1 Properties of Determinants, Subspaces  Due on 10/10/2008 at 3pm
  3.2: 1, 11, 29, 63, 69, 71
  4.1: 8, 11, 19, 29, 38, 77
  Extra Knowledge 4.1: 79
  3.2: 39 - 51
  4.1: 2, 43 - 62
  Oct. 13, 15   4.2, 4.3, 4.4, 4.5: Basis and Dimension, The Dimension of Subspaces Associated with a Matrix, Coordinate Systems, Matrix Representations of Linear Operations  Due on 10/17/2008 at 3pm
  4.2: 11, 18, 26, 60, 64, 69, 75
  4.3: 4, 6, 15, 20, 40, 66
  4.4: 8, 14, 30, 54
  4.5: 5, 15, 40, 48
  Extra Knowledge 4.2: 77, 4.4: 99
  4.2: 2, 33 - 43
  4.3: 41 - 50
  4.4: 31 - 43
  4.5: 19 - 30
  Oct. 20, 22   5.1, 5.2: Eigenvalues and Eigenvectors, The characteristic Polynomial  Due on 10/20/2008 at 3pm
  5.1: 7, 17, 30, 37, 66, 69, 73
  5.2: 18, 31, 40, 41, 74, 75, 78
  Extra Knowledge 5.1: 72, 5.2: 84
  5.1: 15, 41 - 51
  5.2: 2, 5, 53 - 65, 81, 83
  Oct. 27, 29   5.3, 5.4, 6.1: Diagonalization of Matrices, Diagonalization of Linear Operators, The Geometry of Vectors  Due on 10/31/2008 at 3pm
  5.3: 6, 17, 49, 54, 63, 74, 84
  5.4: 2, 18, 25, 50, 75
  6.1: 4, 12, 42, 53, 87
  Extra Knowledge 5.3:86
  5.3: 3, 8, 29 - 45
  5.4: 29 - 39
  6.1: 61 - 70, 90, 104
  Nov. 5   6.2: Orthogonal Vectors  Due on 11/7/2008 at 3pm
  6.2: 4, 14, 17, 53, 58
  Extra Knowledge 6.2: 55
  6.2: 41 - 51
  Nov. 10
2nd Midterm

This midterm will cover the material up to section 6.1. 		In order to prepare for this midterm you should redo the five homework sets preceding the one due on 11/7/2008.
   Solutions to some previous proof-related homework problems
  Nov. 12   6.3: Orthogonal Projections  Due on 11/14/2008 at 3pm
  6.3: 3, 11, 19, 57, 59, 68
  Extra Knowledge 6.3: 75, 79
  6.3: 33 - 44
  Nov. 17, 19  6.4, 6.5, 6.6: Least-Squares Approximations and Orthogonal Projection Matrices, Orthogonal Matrices and Operators, Symmetric Matrices  Due on 11/21/2007 at 3pm
  6.4: 17
  6.5: 6, 38, 39, 44, 46, 54
  6.6: 42
  Extra Knowledge 6.6: 70
  6.5: 17 - 28
  6.6: 17, 21 - 31
  Nov. 24, 26   7.1, 7.2, 7.3: Vector Spaces and their Subspaces, Linear Transformations, Basis and Dimension  Due on 12/1/2008 at 3pm
  7.1: 1, 31, 60, 68, 72, 91
  7.2: 1, 6, 29, 31, 32
  7.3: 3, 11, 54, 71
  Extra Knowledge 7.1: 94
  7.1: 11, 33 - 47
  7.2: 39 - 42
  7.3: 31 - 38
  Dec. 1, 3   7.4, 7.5: Matrix Representations of Linear Operators, Inner Product Spaces  Due on 12/5/2007 at 3pm
  7.4: 1, 3, 9, 41, 47, 48
  7.5: 3, 10, 19, 47, 55
  7.4: 28 - 39
  7.5: 25 - 37
  Dec. 8
Review
   Midterm 1A,Midterm 1B
  Midterm 2A,Midterm 2B
  Solutions to some previous proof-related homework problems