Spring 2009 Linear Algebra

Last updated on Apr. 28, 2009.

Course Schedule

Time: Tuesday and Thursday, 9:10 am–10:25 am
Location: Room 312, Mathematics Building

Instructor

Name: Weizhe Zheng
Office: Room 626, Mathematics Building; Phone: 212-854-2719
Email: zheng at math dot columbia dot edu
Office hours: Tuesday, Wednesday and Thursday, 10:30 am–11:30 am, in instructor's office

Teaching Assistants

Sheau-Juinn Ho Email: sh2502 at columbia dot edu
Dili Wang Email: dw2320 at columbia dot edu; Help Room Hours: Wednesday, 11 am–1 pm

Help Room

The Mathematics department maintains the Columbia Help Room for students needing help with their upper-level mathematics courses.
Hours: 10 am–6 pm Monday through Thursday, 11 am–4 pm Friday (detailed schedule of who will be staffing the room)
Location: Room 406, Mathematics Building

Textbook

Elementary Linear Algebra: A Matrix Approach, by Lawrence E. Spence, Arnold J. Insel, and Stephen H. Friedberg, 2nd edition, Prentice Hall, 2008. (Errata)
The book should be available at the Columbia bookstore.

Grades

The overall course grade is determined as follows:

• Homework (20%):
  There will be weekly problem sets, which can be found below, due at 9:10am on Tuesdays. Homework for one session (#5, #10 or #14) is worth only half a homework. Hand in your homework set in the locked box labeled for the course on the south side of the 4th floor near room 408 of the Mathmatics Building. Graded homework will be returned after class. Uncollected homework will be left in the receptacle in room 406 for a period of two weeks. It may be discarded after that period of time.
  Late homework will only be accepted under exceptional circumstances and you will need a note from a dean.
  Solutions will be will be available as Courseworks' Class Files.
• Midterm 1 (20%): Thursday February 19, in class
• Midterm 2 (20%): Thursday April 2, in class
• Final Exam (40%): Thursday May 14, 9:00 am–12:00 Noon, room 312
  Exams will not be rescheduled because of travel arrangements: it is your responsibility to schedule travel appropriately. Makeup exams will be given only under exceptional circumstances and you will need a note from a dean.
  Practice problems for exams will be available as Courseworks' Class Files.

Homework and exam grades will be posted on Courseworks' Grade Book.

Syllabus

This syllabus is subject to change.

Date	Topic	Reading	Homework
Jan. 20	vectors and matrices	1.1	#1 due on Jan. 27 1.1: 6, 24, 33, *81, 82; 1.2: 6, 9, 33, 42, 70, 80
Jan. 22	linear combinations, matrix-vector products	1.2
Jan. 27	systems of linear equations	1.3	#2 due on Feb. 3 1.3: 6, 9, 32, 45, 77; 1.4: 10, 40, 47, 88
Jan. 29	Gaussian elimination	1.4
Feb. 3	Span and linear dependence	1.6, 1.7, Proofs	#3 due on Feb. 10 1.6: 2, 17, 26, 67; 1.7: 5, 40, 55; 2.1: 1, 12, 27, 65
Feb. 5	matrix multiplication	2.1
Feb. 10	invertible and elementary matrices	2.3, 2.4	#4 due on Feb. 17 2.3: 3, 14, 27; 2.4: 10, 22, 67; 2.7: 1, 10, 60, 78; 2.8: 3, 24, 69
Feb. 12	linear transformations	2.7, 2.8
Feb. 17	determinants	3.1	#5 due on Feb. 24 3.1: 5, 20, 24, 37, 72, *80
Feb. 19	Midterm 1: covers Chapters 1 and 2 (except 1.5, 2.2, 2.5 and 2.6)
Feb. 24	determinants (cont'd)	3.2	#6 due on Mar. 3 3.2: 1, 18, 28, 63, 72, *82; 4.1: 5, 11, 26, 40, 77
Feb. 26	subspaces	4.1
Mar. 3	basis and dimension	4.2, 4.3	#7 due on Mar. 10 4.2: 5, 18, 63; 4.3: 10, 35, 63, 74; 4.4: 8, 30, 99; 4.5: 5, 15, 48
Mar. 5	coordinate systems	4.4, 4.5
Mar. 10	eigenvalues and eigenvectors	5.1	#8 due on Mar. 24 5.1: 1, 16, 29, 34, 69; 5.2: 15, 23, 38, 75, 78, *86
Mar. 12	characteristic polynomial	5.2
Mar. 24	diagonalization	5.3, 5.4	#9 due on Mar. 31 5.3: 17, 49, 64, 84, *88; 5.4: 26, 75; 6.1: 5, 12, 41, 95
Mar. 26	the geometry of vectors	6.1
Mar. 31	orthogonal vectors	6.2	#10 due on Apr. 7 6.2: 3, 14, 17, 55
Apr. 2	Midterm 2: covers Chapters 3 to 5 (except 5.5)
Apr. 7	orthogonal projections	6.3, 6.4	#11 due on Apr. 14 6.3: 3, 12, 19, *60, 68; 6.4: 3; 6.5: 6, 38, 44, 46, 54
Apr. 9	orthogonal matrices and operators	6.5
Apr. 14	symmetric matrices	6.6	#12 due on Apr. 21 6.6: 18, 41, 48, *55, 59, 68; 7.1: 2, 29, 60, 62, 91
Apr. 16	vector spaces and their subspaces	7.1
Apr. 21	linear transformations	7.2	#13 due on Apr. 28 7.2: 1, 15, 25, 30, *49; 7.3: 3, 10, 51, 68; 7.4: 7, 14, 16
Apr. 23	basis and dimension	7.3, 7.4
Apr. 28	inner product spaces	7.5	#14 due on May 5 7.4: 42, 46; 7.5: 11, 47, 71, *81
Apr. 30	Review

* Starred problems are extra credit.

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