Fall 2009 Linear Algebra

Last updated on Aug. 30, 2010.

Course Schedule

Time: Monday and Wednesday, 9:10 am–10:25 am
Location: Room 203, Mathematics Building

Instructor

Name: Weizhe Zheng
Office: Room 606, Mathematics Building; Phone: 212-854-3003
Email: zheng at math dot columbia dot edu
Office hours: Monday 3 pm–4 pm and Friday 9:30 am–10:30 am, in instructor's office

Teaching Assistants

Alexandru Georgescu Email: abg2129 at columbia dot edu; Help Room Hours: Tuesday 4 pm–5 pm and Thursday 5 pm–6 pm
Ion Mihalescu Email: igm2103 at columbia dot edu; Help Room Hours: Tuesday and Thursday, 4 pm–5 pm

Help Room

The Department of Mathematics 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 is available at the Columbia University 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 Mondays. Homework for one session (#1, #5, #9 and #10) is worth only half a homework.
  Hand in your homework set in the locked box labeled for the course in the south wing of the 4th floor near room 408 of the Mathmatics Building. Graded homework will be returned in a basket in the south wing of the 6th floor near room 604.
  Late homework will not be graded and will not receive credit. Each student has one free pass on the homework during the semester, meaning that you can not turn it in and there will be no penalty. If you turn in all the homework, I will discard your lowest grade before computing your overall homework grade.
  Solutions will be available as CourseWorks' Class Files.
• Midterm 1 (20%): Wednesday October 7, in class
• Midterm 2 (20%): Wednesday November 11, in class
• Final Exam (40%): Wednesday December 23, 9:00 am–12:00 Noon, Mathematics 203
  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. Statistics will be posted here.

Syllabus

This syllabus is subject to change.

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

* Starred problems are extra credit.

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