Home Page for Math 2R03: Linear Algebra II 2007-2008

Instructor: Dr Deirdre Haskell
Contact information: 905-525-9140 x27244 Hamilton Hall 316
haskell@math.mcmaster.ca
Office hours: Wednesday, Friday 10:30-12:00, or by appointment10

Teaching assistant: Laurel Miller-Sims
Contact information: millerlg@math.mcmaster.ca
Office hours: Wednesday 15:30-17:30 in the math help centre

Course Outline

Course goals: develop properties of abstract vector spaces, building on the intuition that came from the study of real euclidean space in Linear Algebra I. Includes the study of inner product spaces, orthogonality, and linear transformations. Applications to other parts of mathematics.

Announcements
17 December 2007: Several people have queried me about the suggested review problems posted for Chapter 6. I inetended to post problems that did not include any from section 6.1. Thus all the indicated problems should be moved over by one section. Thus the recommended problems are: section 6.2: 3, 14; section 6.3: 6, 11, 28; section 6.4: 3, 13. Of course, the material of section 6.1 is contained in everything else that we have done in the course.

10 December 2007: Review comments for the final exam are posted here. Laurel's review session is on Dec 13, 2-4 in HH 109. Notes for the last week of classes are posted below.

6 December 2007: Marks  up to Project 2 are posted here. Laurel will hold a review session on Thursday, December 13, 14:00-16:00. Room to be announced, but probably somewhere in Hamilton Hall. Also she will have office hours on Monday, December 17, 11:00-13:00 in the Math Help Centre. My office hours are the same as term time, except the Wednesday Dec 19 hours are moved to Tuesday.

29 November 2007: Recommended problems for section 10.3 are now posted on the calendar.

23 November 2007: There is a typo in the project, which makes the problem considerably harder. In the discussion before Question 4, the matrix given for e^{tM} should have the same angle for each of the trigonometric functions. The argument for each of these functions should be 2t, and not 3t. My apologies.

22 November 2007: Question 3 on the project (showing that the exponential of a matrix follows the usual rules for multiplication when the matrices commute) is a bit subtle. I will discuss it in class on Friday, but YOU DO NOT HAVE TO DO IT.

21 November 2007; the marks file that I posted yesterday had mistakes. Here it is again.

20 November 2007: Project 2 is now available. It will be due on Wednesday, November 28.

20 November 2007: My apologies for not posting the marks earlier (I thought I had done this before I left). This file contains all marks to date.

9 November 2007: Solutions to Midterm II.

5 November 2007: Solutions to practice problems for midterm II.

2 November 2007: Here are some practice problems for the midterm. Brief solutions will appear later.

1 November 2007: Midterm II is on Wednesday, 7 November, 19:00-20:30. Send email with your name and student number if you have a scheduled conflict  and want to take the exam at the alternate time 17:15-18:45. The test rooms are organised alphabetically by family name: REF 104 A-Loza, T13 125 Lytwyn - Z.

24 October 2007: Project 1 was returned in tutorial on Tuesday and in class on Wednesday. The marks to date, including all corrections, are posted here. Note that all marks recorded for the project are one point higher than the mark noted on your paper, as Laurel and I decided that the marking was a little harsh. As a result, we will be very reluctant to consider any requests for extra marks. Problems for sections 9.3, 9.4 and 9.5 are posted on the calendar below.

18 October 2007: Deadline for Lab 9.1 is postponed until Sunday, Oct 21. I will be anwering questions about it in office hours on Friday.

8 October 2007: By popular request, the deadline for Project 1 has been extended to Tuesday, 16 October. Remember that you may work in groups of up to 4 people. For each project handed in with more than one author, there must also be an assessment of each person's contribution, individually by each group member. Assessments are on a scale of 0 (low) to 3 (high).



4 October 2007: Corrections to the deadlines for next week are posted on the calendar below. Lyryx lab 7.2 is moved to the subsequent week to allow time to work on the project. The project is posted here and is due in class on Friday, 12 October.

26 September 2007: Solutions to the practice problems are posted here. Two typos in the problems: problem 3) is to show that (-1)v=-v (not (01)v=-v); 4) should ask if the intersection of X and Y is non-empty (not x and Y).

26 September 2007: The first midterm is on Wednesday, October 3, 19:00--20:30. It will cover sections 6.1, 6.2, 6.3, 6.4 of the text. Some practice problems are posted here. The test rooms are organised alphabetically by family name: MDCL 1309 A--L, MDCL 1110 M--Z.

For anyone who is unable to make the scheduled time there will be an advance seating of the exam. You must email me your name and reason for being unable to make the regular exam time by Friday afternoon in order to take the exam at the alternate time.

11 September 2007: For all students who have not yet managed to buy a book or register on LYRYX: Lyryx has provided us with a temporary access code which will allow you to login, register as a student in this course and complete your lab assignment. This code will be available until the end of the month; by then you should have your permanent registration set up.  I will postpone the deadline for the first lab  6.1 until Monday, September  17. As this is the last day for drop/add, all registration issues should be settled by then. Follow the instructions below to register with the temporary code.
TEMPORARY PINCODE FOR
    McMaster University
    Linear Algebra II
    Fall 2007
    MATH 2R03
    D. Haskell

Students in the above course can use the following special pincode at any time:
             SN3W52TR
Their license will remain valid until 2007-09-28 by which time they should enter their true pincode after they logon to their account.

Instructions for students:
    1: Go to https://login.lyryx.com
    New to Lyryx: Follow the Registration Link and fill the student form
    Previous Lyryx account: Logon and click "ADD COURSE"
    Insert the pincode where requested.
    2: Once the new pincode has been purchased,  insert it in the indicated box after logon.
*****************************************


11 September 2007: Notes from the lectures are posted below the calendar.

7 September 2007: Tutorials begin the first full week of classes; 11 Sept 2007.

Course Calendar: All entries on the calendar should be considered provisional. Any changes will be posted here, and announced in class.


Dates
 Tuesday
 Wednesday
 Friday
 Comments
Sept 3 - 7

Introduction
Sept 10 - 14
 Sec: 6.1
Problems: pp 257-259, 2f, l, 12
Tutorial: lab 6.1, concepts 6.1, 6.2
 Sec: 6.2
 Sec: 6.2
Problems: pp 263-264, 1f, 3f, 4, 8, 16, 21
 Lyryx Lab 6.1 due Sept 13
Sept 17 - 21
 Sec: 6.3
Tutorial: labs and concepts 6.2, 6.3
 Sec: 6.3
Sec: 6.3
Problems: pp  270-272, 1b, 3b, 6d, 7d, 10b, 12, 22, 34b
 Lyryx Labs 6.2, 6.3 due Sept 20
Sept 24 - 28
 Sec: 6.4
Tutorial: labs and concepts 6.4
 Sec: 6.4
 Sec: 6.4
Problems: pp 278-279, 1b, 2b, 3b, 7b, 8, 15, 18, 20
 Lyryx Lab 6.4 due Sept 27
Oct 1 - 5
 Sec: 7.1
Problems: pp 295-297, 1f, 2d, 3e, 4b, 5b, 16
Tutorial: review for Midterm I
 Sec: 7.2
Sec: 7.2
Problems: pp 304-305, 2b,i, 3, 4b, 7, 10, 14
 Midterm I Oct 3 19:00-20:30
Oct 8 - 12
 Sec: 7.3
Tutorial: Project I
 Sec: 7.3
Problems: pp 310-312, 1d, 4c, 6e, 9a, 10b, 12, 16
 Sec: 9.1
 Lyryx Lab 7.1 due Oct 11
Project I due Oct 12
Oct 15 - 19
 Sec: 9.1
Problems: pp 400-402, 1b, 2b, 3b, 4d, 5d, 8b, 9
 Sec: 9.2
 Sec: 9.2
Problems: pp 408-410, 1b, 3, 4b, 5b, 12
 Lyryx Labs 7.2, 7.3, 9.1 due Oct 18
Oct 22 - 26
 Sec: 9.3
 Sec: 9.3
Sec: 9.3
Problems: pp 418-421, 2, 8b, 9b, 10d, 13, 16, 22b, 24
 Lyryx Lab 9.2 due Oct 25
Oct 29 - Nov 2
 Sec: 9.4
 Sec: 9.4
Problems: pp427-428, 1b, 3, 4
 Sec: 9.5
 Lyryx Lab 9.3 due Oct 31
Nov 5 - 9
 Sec: 9.5
Problems: p432, 2
Tutorial: review for Midterm II
 Sec: 5.3 (review), 10.1
 Sec: 10.1
Problems: pp 439-440, 1b, 3b, 4b, 12b, 13b, 22b, 26		 Midterm II Nov 7 19:00-20:30
Nov 12 - 16
 Sec: 10.2
Tutorial: labs and concepts 10.1
 Sec: 10.2
 
 Sec: 10.2
Problems: pp 447-449;1b, 4b, 6b,d, 12, 18		 Lyryx Labs 9.3, 9.4, 10.1 due Nov 15
Nov 19 - 23
 Sec: 10.5, Project II
Tutorial: labs and concepts 10.2, Project II
 Sec: 10.3

 Sec: 10.3
Project II due Nov 23
Nov 26 - 30
 Sec: 10.3
Problems: p543-454, 1b, 2, 4, 5b,d
Tutorial: labs and concepts 10.3
 Sec: 10.4

 Sec: 10.4
Problems:		 Lyryx Labs 10.2, 10.3 due Nov 29

Slides created during lectures

Lecture 2: 11 Sept 2007

Lecture 3: 12 Sept 2007 I did not succeed in saving the notes created during the lecture, so I have posted my own notes here instead.

Lecture 4: 14 Sept 2007
                                                                                                 Lecture 20: 23 Oct 2007
Lecture 5: 18 Sept 2007
                                                                                                 Lecture 21: 24 Oct 2007
Lecture 6: 19 Sept 2007
                                                                                                 Lecture 22: 26 Oct 2007
Lecture 7: 21 Sept 2007
                                                                                                 Lecture 23: 30 Oct 2007
Lecture 8: 25 Sept 2007
                                                                                                 Lecture 24: 31 Oct 2007
Lecture 9: 26 Sept 2007
                                                                                                 Lecture 25: 2 Nov 2007
Lecture 10: 28 Sept 2007
                                                                                                 Lecture 26: 6 Nov 2007
Lecture 11: 2 Oct 2007
                                                                                                 Lecture 27: 7 Nov 2007
Lecture 12: 3 Oct 2007
                                                                                                 Lecture 28: 9 Nov 2007
Lecture 13: 5 Oct 2007
                                                                                                 Lecture 29: 12 Nov 2007   Note: these slides are in reverse order.
Lecture 14: 9 Oct 2007
                                                                                                 Lecture 30: 13 Nov 2007(first page)   Lecture 30: 13 Nov 2007(later pages)
Lecture 15: 11 Oct 2007
                                                                                                 Lecture 31: 15 Nov 2007
Lecture 16: 12 Oct 2007
                                                                                                 Lecture 32: 20 Nov 2007
Lecture 17: 16 Oct 2007
                                                                                                 Lecture 33: 21 Nov 2007
Lecture 18: 17 Oct 2007
                                                                                                Lecture 34: 27 Nov 2007
Lecture 19: 19 Oct 2007
                                                                                                Lecture 35: 28 Nov 2007
                                                                                                Lecture 36: 30 Nov 2007