Linear Algebra: Summer session (D): May 27 - July 03 , 2008

Day/Time: MTWR 2:45pm-4:20pm; Location: 417 Mathematics Building

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

Office
Math 629

Office Hours
Monday 4:30pm-5:30pm 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
Min Lee (enoia at math.columbia.edu) and Jian Wang (jw2464 at columbia.edu)
    Min's office hours: MTWR 12-2pm in the Math help Room (Math 406)
    Jian's office hours: Tuesday 2pm-6pm, Thursday 5pm-6pm, Friday 1pm-4pm in the Math help Room (Math 406)

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.

Exams
There will be a midterm and a final exam. The midterm will be in class on June 19, 2008 and the final will be again in class on July 3, 2008. Make-up exams will not be given. Students will only be excused from the exams because of a serious illness or another emergency of similar gravity, and a note from a doctor or a dean will be required.

Homework
There are weekly homework assignments. Students are encouraged to discuss the homework with other students, but should write their solutions individually. Each student is allowed to submit one late homework. You can see your grades in the Courseworks Grade Book.

Submitting your homework
Your homework shoud be handed to Min Lee or Jian Wang in the math help room on Tuesday before class.

Picking up graded homework
Your graded homework will be in a box on the fourth floor starting from after class on Wednesdays. 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 %30
Midterm %30
Final exam %40
Conflicts
If you have a conflict with any of the exams (for example, due to a religious holiday), please contact the instructor by May 30, 2008.
Disabilities
Students who may need disability related accomodations should contact the professor by June 5, 2008.


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

Date
Reading
Homework
Practice problems
  May 27-30   1.1, 1.2, 1.3, 1.4, 1.6, 1.7: Matrices and Vectors, Linear Combinations, Matrix-Vector Products and Special Matrices, Systems of Linear Equations, Gaussian Elimination, The Span of a Set of Vectors, Linear Dependence and Linear Independence  Due on 6/3/2008
  1.1: 6, 29, 31, 33, 71, 74, 76
  1.2: 2, 7, 33, 42, 70
  1.3: 6, 8, 9, 45
  1.4: 10, 35, 46(a), 47
  1.6: 1, 17, 26, 34, 43
  1.7: 5, 15, 31, 41, 55
  1.1: 1, 3, 5, 6, 8, 17, 18, 29, 31, 33, 37 - 46, 71, 74, 76
  1.2: 2, 3, 5, 7, 29, 33, 42, 45 - 52, 70
  1.3: 4, 6, 8, 9, 20, 24, 45, 46, 57 - 63
  1.4: 4, 10, 35, 46(a), 47, 53 - 57
  1.6: 1, 17, 21, 26, 34, 43, 45 - 50
  1.7: 1, 5, 15, 31, 41, 55, 63 - 67, 99
  June 2-5   2.1, 2.3, 2.4, 2.7, 2.8, 3.1: Matrix Multiplication, Invertibility and Elementary Matrices, The Inverse of a Matrix, Linear Transformations and Matrices, Composition and Invertibility of Linear Transformations, Cofactor Expansion   Due on 6/10/2008
  2.1: 12, 19, 23, 68
  2.3: 2, 13, 17, 26, 60, 67
  2.4: 12, 58, 64
  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
   2.1: 2, 3, 12, 19, 23, 33 - 39, 68
  2.3: 2, 13, 17, 26, 33 - 39, 60, 67
  2.4: 12, 35-46, 58, 64
  2.7: 1, 7, 21, 29, 33, 35 - 40, 59, 72, 79, 101
  2.8: 6, 12, 15, 26, 37, 41-52, 66, 97
  3.1: 2, 9, 14, 29, 37, 56-58
  June 9-12   3.2, 4.1, 4.2, 4.3, 4.4, 4.5: Properties of Determinants, Subspaces, Basis and Dimension, The Dimension of Subspaces Associated with a Matrix, Coordinate Systems, Matrix Representations of Linear Operations  Due on 6/17/2008
  3.2: 1, 11, 29, 63, 69, 71
  4.1: 8, 11, 19, 29, 38, 77
  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
  3.2: 1, 11, 29, 39 - 51, 63, 69, 71
  4.1: 2, 8, 11, 19, 29, 38, 43 - 62, 77
  4.2: 2, 11, 18, 26, 33 - 43, 60, 64, 69, 75
  4.3: 4, 6, 15, 20, 40, 41 - 50, 66
  4.4: 8, 14, 30, 31 - 43, 54
  4.5: 5, 15, 19 - 30, 40, 48
  June 16-18   5.1, 5.2, 5.3, 5.4, 6.1: Eigenvalues and Eigenvectors, The characteristic Polynomial, Diagonalization of Matrices, Diagonalization of Linear Operators, The Geometry of Vectors  Due on 6/24/2008
  5.1: 7, 17, 30, 37, 66, 69, 73
  5.2: 18, 31, 40, 41, 74, 75, 78
  5.3: 6, 17, 49, 54, 63, 74, 84
  5.4: 2, 18, 25, 50, 75
  6.1: 4, 12, 42, 53, 87
   5.1: 7, 15, 17, 30, 37, 41 - 51, 66, 69, 73
  5.2: 2, 5, 18, 31, 40, 41, 53 - 65, 74, 75, 78, 81, 83
  5.3: 3, 8, 17, 29 - 45, 49, 54, 63, 74, 84
  5.4: 2, 18, 25, 29 - 39, 50, 75
  6.1: 4, 12, 42, 53, 61 - 70, 87 , 90, 104
  June 19
Midterm

This midterm will cover the material covered in the first three weeks. 		In order to prepare for this midterm you should redo the homework sets of the first three weeks.
  June 23-26,   6.2, 6.3, 6.4, 6.5, 6.6, 7.1: Orthogonal Vectors, Orthogonal Projections, Least-Squares Approximation and Orthogonal Projection Matrices, Orthogonal Matrices and Operators, Symmetric Matrices, Vector Spaces and their Subspaces  Due on 6/30/2008
  6.2: 4, 14, 17, 53, 58
  6.3: 3, 11, 19, 57, 59, 68
  6.4: 17
  6.5: 6, 38, 39, 44, 46, 54
  6.6: 42
  7.1: 1, 31, 60, 68, 72, 91
  6.2: 4, 14, 17, 41 - 51, 53, 58
  6.3: 3, 11, 19, 33 - 44, 57, 59, 68
  6.4: 17
  6.5: 6, 17 - 28, 38, 39, 44, 46, 54
  6.6: 17, 21 - 31, 42
  7.1: 1, 11, 31, 33 - 47, 60, 68, 72, 91
  June 30- July 2   7.2, 7.3, 7.4, 7.5: Linear Transformations, Basis and Dimension, Matrix Representations of Linear Operators, Inner Product Spaces  Due on 7/1/2008
  7.2: 6, 29, 31
  7.3: 11, 54, 71

 Due on 7/2/2007
  7.4: 1, 9, 41
  7.2: 1, 6, 29, 31, 32, 39 - 42
  7.3: 3, 11, 31 - 38, 54, 71
  7.4: 1, 3, 9, 28 - 39, 41, 47, 48
  7.5: 3, 10, 19, 25 - 37, 47, 55
  July 3
Final Exam

The final will cover the whole material of this course but it will concentrate on what was not covered in the midterm. 		In order to prepare for the final you should redo the homework sets.   Solutions to some proof related homework problems