This page is www.math.columbia.edu/~bayer/S04/linalg

Section 002 (Bayer)
Tuesdays and Thursdays, 11:00am-12:15pm
304 Barnard Hall

Dave Bayer (x42643, 426 Mathematics, www.math.columbia.edu/~bayer)
Bulletin page | Directory of Classes : Mathematics
Student Services Online

Email

My email address is  

Please include the phrase "Linear Algebra Spring 2004" in the subject line of any correspondence with me concerning this course.

In particular, if for any reason you do not take and hand in each exam in our regular classroom at the regularly scheduled time, it is your responsibility to document the status of your exam by sending me an email with this subject line, including your full name in the body of the message. Ask anyone writing on your behalf to do the same.

Office Hours

Exams

There will be two exams (30 points each) and a final (40 points). The final is not cumulative.

These dates do not coincide with any religious holiday which causes suspension of New York City's alternate side parking regulations; see NYC Parking Calendar. Please discuss other conflicts with me well in advance of the exam in question.

Master University Examination Schedule
University Academic Calendar

Text: Linear Algebra with Applications Sixth Edition, by Steven J. Leon. Prentice Hall, 1998, ISBN 0130337811. University bookstore ($105) or AddALL ($60 and up). This semester we will cover chapters 1, 2, 3, 4, 5, 6.

Teaching Assistants

The teaching assistant for this course is Debbie Grier (debbie@math.columbia.edu). See Columbia Help Room Schedule for Debbie's help room hours.

Course materials

Course materials will be posted in Acrobat 4 PDF format (PDF 1.3). Your browser can be trained to automatically open these files with Acrobat Reader, a free program which you can download from (If you have trouble reading or downloading these files, check to see if you're using an outdated version of Acrobat, and upgrade to the latest version, or try using a different computer.)

Course materials from previous semesters

I have taught this course before; you can find further practice materials on the web pages from previous semesters:

Review Session:

Debbie Grier will host a review session for the final on Thursday, May 6, 11:00 AM to 12:30 PM, in 207 Math.

Homework Assignments

  1. Matrices and Systems of Equations
    1. Systems of Linear Equations. Exercises 1-8
    2. Row Echelon Form. Exercises 1-3, 5, 6
    3. Matrix Algebra. Exercises 1-10, 12, 20
    4. Elementary Matrices. Exercises 1-5, 7, 9
  2. Determinants
    1. The Determinant of a Matrix. Exercises 1-4, 6
    2. Properties of Determinants. Exercises 1, 3, 4, 7, 10
    3. Cramer's Rule. Exercises 1-6
  3. Vector Spaces
    1. Vector Spaces. Exercises 1-10
    2. Subspaces. Exercises 1-8
    3. Linear Independence. Exercises 1-9
    4. Basis and Dimension. Exercises 1-8, 11
    5. Change of Basis. Exercises 1-5, 8-10
    6. Rowspace, column space. Exercises 1-7
  4. Linear Transformations
    1. Linear transformations, definitions and examples. Exercises 1, 3-5, 12
    2. Matrix representation of linear transformations. Exercises 1-5
    3. Similarity. Exercises 1, 3-6
  5. Orthogonality
    1. The scalar product. Exercises 1-8
    2. Orthogonal subspaces. Exercises 1, 2
    3. Inner product spaces. Exercises 1-4
    4. Least squares problems. Exercises 1-6
    5. Orthonormal sets. Exercises 1, 2, 4, 7, 8
    6. The Gram-Schmidt orthogonalization process. Exercises 1-4
  6. Eigenvalues
    1. Eigenvalues and eigenvectors. Exercises 1-5
    2. Systems of linear differential equations. Exercise 1
    3. Diagonalization. Exercises 1-4
    4. Hermitian matrices. Exercises 1, 4
    5. Quadratic forms. Exercises 1, 3
    6. Positive definite matrices. Exercises 1, 3, 4

Class schedule

Sun Mon Tues Wed Thur Fri Sat
18 Jan
 		 19
 		 20
1.1		 21
 		 22
1.2		 23
 		 24
 
25
 		 26
 		 27
1.3		 28
 		 29
1.4, 1.5		 30
 		 31
 
1 Feb
 		 2
 		 3
2.1		 4
 		 5
2.2		 6
 		 7
 
8
 		 9
 		 10
2.3		 11
 		 12
Review		 13
 		 14
 
15
 		 16
 		 17
EXAM		 18
 		 19
3.1		 20
 		 21
 
22
 		 23
 		 24
3.2		 25
 		 26
3.3		 27
 		 28
 
29
 		 1
 		 2
3.4, 3.5		 3
 		 4
3.6		 5
 		 6
 
7 Mar
 		 8
 		 9
4.1		 10
 		 11
4.2		 12
 		 13
 
14
 		 15
 		 16
 		 17
 		 18
 		 19
 		 20
 
21
 		 22
 		 23
4.3		 24
 		 25
Review		 26
 		 27
 
28
 		 29
 		 30
EXAM		 31
 		 1
5.1, 5.2		 2
 		 3
 
4 Apr
 		 5
 		 6
5.3		 7
 		 8
5.4, 5.5		 9
 		 10
 
11
 		 12
 		 13
5.6		 14
 		 15
6.1, 6.2		 16
 		 17
 
18
 		 19
 		 20
6.3		 21
 		 22
6.4, 6.5		 23
 		 24
 
25
 		 26
 		 27
6.6		 28
 		 29
Review		 30
 		 1
 
2 May
 		 3
 		 4
 		 5
 		 6
 		 7
 		 8
 
9
 		 10
 		 11
FINAL		 12
 		 13
 		 14
 		 15