Fall 2010 Linear Algebra

Mathematics V2010 section 003

Last updated on Dec. 6, 2010.

Course Schedule

Time: Tuesday and Thursday, 2:40 pm–3:55 pm
Location: Room 633, Mudd Building

Instructor

Name: Weizhe Zheng
Office: Room 606, Mathematics Building; Phone: 212-854-3003
Email: zheng at math dot columbia dot edu
Office hours: Tuesday 10:30 am–11:30 am and Friday 9:30 am–10:30 am, in instructor's office

Teaching Assistants

Irena Penev graduate; Email: ipenev at math dot columbia dot edu; Help Room Hours: Monday 10 am–1 pm
Joshua Tobin undergraduate; Email: jpt2118 at columbia dot edu; Help Room Hours: Tuesday and Thursday 10:30 am–11:30 am

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

Linear Algebra with Applications, by Otto Bretscher, 4th edition, Prentice Hall, 2009.
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 2:40 pm on Tuesdays. Homework for one session (#5 and #11) 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.
  
• Midterm 1 (20%): Tuesday October 5, in class
• Midterm 2 (20%): Thursday November 4, in class
• Final Exam (40%): Thursday December 16, 1:10 pm–4:00 pm, Mudd 633
  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. 7	linear systems	1.1	#1 due on Sep. 14 1.1: 1, 4, 7, 18, 29; 1.2: 1, 4, 7, 18, 19, 45, *48
Sep. 9	Gauss-Jordan elimination	1.2
Sep. 14	matrices and vectors	1.3	#2 due on Sep. 21 1.3: 1, 2, 9, 18, 20, 24, 47, 49; 1.TF: 1–6; 2.1: 1, 43
Sep. 16	linear transformations	2.1, 2.2
Sep. 21	matrix product	2.3	#3 due on Sep. 28 2.2: 20, 29; 2.3: 14, 18, 27, 38, *68; 2.4: 1, 19, 48, 67, 76; 2.TF: 4, 6, 8, 26
Sep. 23	the inverse of a linear transformation	2.4
Sep. 28	subspaces	3.1	#4 due on Oct. 5 3.1: 2, 10, 14, 34, 40, 51; 3.2: 6, 8, 16, 33, 41, *51
Sep. 30	linear independence	3.2
Oct. 5	Midterm 1: covers Chapters 1 and 2
Oct. 7	dimension and coordinates	3.3, 3.4	#5 due on Oct. 12 3.3: 15, 22, 31, 83; 3.4: 3, 15
Oct. 12	linear spaces	4.1	#6 due on Oct. 19 3.4: 21, 61; 3.TF: 1–5; 4.1: 2, 10, 12, 36, 47; 4.2: 51, 55, 65, 70, 77, *78
Oct. 14	linear transformations	4.2
Oct. 19	linear transformations (cont'd)	4.3	#7 due on Oct. 26 4.3: 4, 10, 11, 30, 60, 70; 4.TF: 4–6, 12, 13; 6.1: 10, 20, 40, *47, 53; 6.2: 16
Oct. 21	determinants	6.1, 6.2
Oct. 26	Cramer's rule	6.3	#8 due on Nov. 9 6.2: 6, 20, 30, *31, 52; 6.3: 24, 25, 38; 6.TF: 2–6; 7.1: 12, 40
Oct. 28	eigenvalues and eigenvectors	7.1
Nov. 4	Midterm 2: covers Chapters 3, 4, and 6
Nov. 9	characteristic polynomials	7.2	#9 due on Nov. 16 7.2: 2, 9, 15, 22, 39; 7.3: 10, 16, 19, 31, 36, *52
Nov. 11	eigenspaces	7.3
Nov. 16	diagonalization	7.4	#10 due on Nov. 23 7.4: 13, 23, 32, 42, 54, *70; 7.TF: 1–4, 7; 5.1: 3, 8, 15, 22, 29
Nov. 18	orthogonality	5.1
Nov. 23	Gram-Schmidt process, orthogonal transformations	5.2, 5.3	#11 due on Nov. 30 5.1: 27; 5.2: 13, 18, 28, 34; 5.3: 28, *50
Nov. 30	least squares	5.4	#12 due on Dec. 7 5.3: 41, 44; 5.4: 7, *8, 17, 21, 31; 5.5: 3, 6, 14, 23; 5.TF: 1–5
Dec. 2	inner product spaces	5.5
Dec. 7	symmetric matrices	8.1	No homework. Have some fun.
Dec. 9	Review

* Starred problems are extra credit; TF refers to the true or false questions at the end of each chapter.

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