MATH 2LA3
Applications of Linear Algebra
Fall 2022

Announcements:

• 10 December: Next week, Dr. Valeriote's office hours on Monday, Wednesday, and Thursday, from  1:00 to 3:00pm, will all be held virtually, via zoom.  Here is the link for these office hours:  https://mcmaster.zoom.us/j/92038485690?pwd=OGlNbnZLUlVwS3RmYlZJSFpLM3F4QT09  He will also be available by appointment.
  
• 5 December: Information on the MATH 2LA3 final exam can be found here.  The exam will be held on Friday, December 16 from12:30pm to 3:00pm in PGCLL room 127.
• 5 December: During the week of December 12, Dr. Valeriote will hold office hours  at the following times: Monday, Wednesday, and Thursday  1:00 to 3:00pm.  He is also available by appointment.
• 5 December: The MATH 2LA3 tutorial that is scheduled for Tuesday, December 6 at 12:30pm will be conducted, as scheduled, by Dr. Valeriote. The tutorial will be held in HSC 1A6.  All 2LA3 students are welcome to attend.
• 30 November: The third midterm test has been graded.   A scanned copy of your graded test has been emailed to you. Your grade will also be entered in the childsmath system soon.  Please check in a day or two to see if your grade has been properly entered on the system. Solutions for the two versions of the test can be found here: Version 1, Version 2.  The version number of your test can be found at the bottom of page 6 of your test.  If you have any questions on how your test was graded, or about any of the solutions, please send an email message to Dr. Valeriote.  The average and the median score are 22.5/30 (75%) and 24/30 (80%) respectively.
  
• 28 November: The MATH 2LA3 tutorial that is scheduled for Tuesday, November 20 at 12:30pm will be conducted, as scheduled, by Dr. Valeriote. The tutorial will be held in HSC 1A6.  All 2LA3 students are welcome to attend.
  
• 20 November: The MATH 2LA3 midterm test #3 will be held as scheduled on Thursday, 24 November from 5:30 to 6:20pm. Due to the TA strike (scheduled to start on Monday, 21 November) all students will write the test in TSH Room 120.
  
• 20 November:  Due to the TA strike (scheduled to start on Monday, 21 November), the MATH 2LA3 tutorial that is scheduled for Monday, 21 November at 3:30pm has been cancelled.  The tutorial scheduled for Tuesday, 22 November at 12:30pm (in HSC 1A6) will be held and will be conducted by Dr. Valeriote. It will be used to review the material for the upcoming midterm test.  All MATH 2LA3 students are welcome to attend this tutorial, even those that have been assigned to the Monday tutorials.  The MATH 2LA3 lectures on Monday and Wednesday of this week will be held as scheduled.
  
• 18 November: The midterm test #3 information webpage has been updated with a checklist of topics to study, along with suggested sample problems from the textbook.
  
• 18 November: The following are some additional practice problems to look over while preparing for the upcoming midterm test.  They  deal with using the least-squares method to fit a line to some given points, and to finding the spectral decomposition of a symmetric matrix:  Section 6.6:1-4, Section 7.1: 39, 40, Section 7.3:1, 3 (a), (b), 7, 9, 11.
  
• 15 November: The second midterm test has been graded.   A scanned copy of your graded test has been emailed to you. Your grade will also be entered in the childsmath system.  Please check in a day or two to see if your grade has been properly entered on the system. Solutions for the three versions of the test can be found here: Version 1, Version 2, Version 3.  The version number of your test can be found at the bottom of page 6 of your test.  If you have any questions on how your test was graded, or about any of the solutions, please send an email message to Dr. Valeriote.  The average and the median score is 19/30 (63%).
  
• 14 November:  Information on the upcoming MATH 2LA3 midterm test #3 has been posted here. Please read it over carefully and contact Dr. Valeriote if you have any questions or concerns with it. The test will be held in person on Thursday November 24 from 5:30pm to 6:20pm. It is important that you know the testing room that you have been assigned to (either ITB AB102 or TSH 120).  The room assignment for this test is not the same as for the first two tests.
  
• 2 November:  The Student Success Centre is hosting an Online Volunteer & Part-time Job Fair on November 8.  Click here to find out more details on this event.
  
• 23 October:  Information on the upcoming MATH 2LA3 midterm test #2 has been posted here. Please read it over carefully and contact Dr. Valeriote if you have any questions or concerns with it. The test will be held in person on Thursday November 3 from 5:30pm to 6:20pm. It is important that you know the testing room that you have been assigned to (either ITB AB102 or TSH 120).  The room assignment for this test is not the same as for the first test.
  
• 17 October: The first midterm test has been graded.   A scanned copy of your graded test has been emailed to you. Your grade has also been entered in the childsmath system.  Please check to see if your grade has been properly entered on the system. Solutions for the three versions of the test can be found here: Version 1, Version 2, Version 3.  The version number of your test can be found at the bottom of page 6 of your test.  If you have any questions on how your test was graded, or about any of the solutions, please send an email message to Dr. Valeriote.  The average score on this test is 21.9/30 (73%) and the median score is 23/30 (76/6%).
  
• 29 September:  Dr. Valeriote's office hour on Tuesday, October 4 will run from 3:30 to 4:20pm (instead of from 3:00 to 4:20pm).
  
• 22 September:  Information on the upcoming MATH 2LA3 midterm test #1 has been posted here. Please read it over carefully and contact Dr. Valeriote if you have any questions or concerns with it. The test will be held in person on Thursday October 6 from 5:30pm to 6:20pm. It is important that you know the testing room that you have been assigned to (either ITB AB102 or TSH 120).
  
• 14 September: For information on STEM Week activities, please click here.  STEM week runs during the week of September 19.
  
• 8 September: If you would like to volunteer to provide copies of your lecture notes (hand written or typed) to be posted on the course website, please contact Dr. Valeriote via email (matt@math.mcmaster.ca).  He will coordinate with those who volunteer to set up some sort of schedule, with the aim of having some version of each lecture posted online.  Note that notes from Lecture #1 have been provided by a student in the class and have been posted on the course website (here).
  
• 8 September: A copy of the pdf file that contains a statement of the Invertible Matrix Theorem that was shown in class can be downloaded here.
  
• 7 September: Assignment #1 is available to view and to work on on childsmath.  It is due by 11:59pm on Tuesday, September 20.
  
• Practice problems from the textbook will be posted each week.  They can be found below in the Lecture Schedule of this webpage (here).  You should know how to solve these problems by hand, but should do most of them using some suitable software, such as Wolfram Alpha (see the previous announcement).
  
• McMaster has a site license for Wolfram Alpha Pro as well as for Mathematica.  To use this software (for free), please follow this link:  www.wolfram.com/siteinfo.  Dr. Valeriote will make use of Wolfram Alpha in the lectures from time to time.
  
• Dr. Valeriote will hold office hours on Tuesdays from 3:00 to 4:20pm and on Thursdays from 2:00pm to 3:20pm in his office, HH 323.
• Tutorials for this class will be held on Mondays from 3:30 to 4:20pm and Tuesdays from 12:30 to 1:20pm.  They will start during the week of September 12.
• Students should review the contents of Chapters 2 and 4  from the textbook during the first week of class.
• A record of the topics covered in each lecture can be found near the bottom of this webpage (here).  It will be updated on a regular basis.
• The required textbook for this course is Linear Algebra and its Applications (6th edition) by Lay, Lay and McDonald.  There are several options for getting access to this book.  The publisher, Pearson, has an online site MyLab where you can get access to the book and also other resources; the Pearson course ID for this course is: valeriote62132.  To access the resources, including the online version of the textbook, go to the site MyLab and login or register.  Instructions on how to do this can be found here.  You can also rent or buy a pdf copy by following this link.  Remember that you want the 6th edition; all references I make to the text will be to that edition.  You might find better pricing at the campus store.  Click here to see what is available.  Note that the MyLab component of the text that is offered as an option by the bookstore is not needed for this course, but you might find it to be useful.
  
• The Avenue to Learn site for this course will not be used this semester.  All relevant course information will be posted on this website.
• The course announcement can be found here.
• The first class will be held on Wednesday, 7 September at 5:30pm in ITB AB102.

Course Information:

• Course Announcement

Assignments:


There will be 6 assignments this semester.  Your lowest assignment score will be droped when computing your assignment average in the course. Assignments are worth 10% of your final grade in this course, so each assignment will be worth 2% of your final grade (not counting your lowest assignment grade).  Assignments are conducted online through childsmath.  You can access them by clicking on the following link and following the posted instructions:  https://www.childsmath.ca/childsa/forms/main_login.php

The assignment due dates (tentative) are as follows:

1. Assignment #1 is due on Tuesday, September 20 by 11:59pm.
2. Assignment #2 is due on Tuesday, October 4 by 11:59pm.
3. Assignment #3 is due on Tuesday, October 25 by 11:59pm.
4. Assignment #4 is due on Tuesday, November 8 by 11:59pm.
5. Assignment #5 is due on Tuesday, November 22 by 11:59pm.
6. Assignment #6 is due on Tuesday, December 6 by 11:59pm.

Test Dates:

There will be three 50-minute tests held in person on October 6, November 3, and November 24 (tentative dates) during the scheduled class time. Further details on the tests will be given in class and announced on the course web page. The McMaster standard calculator is allowed on all tests. 

Final Exam Information:

A final exam for this courses will be scheduled by the registrar.  Details will be posted on the course website as they become available.

Lecture Schedule (tentative):

Lecture schedule for Math 2LA3 (tentative)

The following lecture schedule is tentative and could change as the term proceeds.  The chapter and section information are relative to the 6th edition of Linear Algebra and Its Applications by Lay, Lay and McDonald.

A more detailed, lecture by lecture schedule can be found below this list.

Week 1, September 6-9

        Review from Math 1B3 (Chapters 1, 2, and 4)

        Practice Problems: Section 2.8 #11, 13, 18, 19, 20, 31, 33, 45 (use WolframAlpha or some other software); section 2.9, #9, 13.

Week 2, September 12-16

        Continuation of Review.

        Practice problems: 4.1, #11, 13, 43 (don't do this by hand); 4.2 #5, 49 (use technology); 4.3 #15, 17; 4.4, #3, 7, 39 (not by hand); 4.5, #9, 11, 13, 53 (use tech)

Week 3, September 19-23

         Introduction to linear programming (Chapter 9, sections 2, 3), Optimization problems.

         Practice problems:  Section 9.2: #1, 3, 5, use desmos to solve 7, 9, 15, 16, 17

Week 4, September 26-30

        Optimization problems continued (Section 9.3)

        Practice problems:  Section 9.3: #1, 3, 5, 13, 15, 16  (do some of these by hand, and some using Wolfram Alpha, Matlab, or some other software)

Week 5, October 3-7  (test 1, October 6, in class)

         Review of eigenvalues and eigenvectors; Chapter 5 sections 1 - 3

         Practice problems: Section 5.1, #13, 15, 45, 47 (for 45, 47 - use WolframAlpha or equivalent), 5.2: 9, 11, 35 , 5.3: 17, 19, 41 (with any available tech)

Week 6, October 10-14

Reading week, no classes

Week 7, October 17-21

        Review, continued, orthogonality;  Chapter 6, sections 1- 3

Week 8, October 24-28

Gram-Schmidt, QR decomposition, projection matrices, Least-squares; Chapter 6, sections 4, 5

Practice problems: Section 6.1:  1-18; Section 6.2: 1-10, 13, 15, 21, 22; Section 6.3: 1, 5, 9, 17; Section 6.4: 1, 3, 5, 9, 11  13,  15

Week 9, October 31-November 4 (test 2, November 3, in class)

Least-squares, Orthogonal diagonalization; Chapter 6, sections 5, 6, Chapter 7, section 7.1

        Practice problems: Section 6.5: 2 - 6, 9-11, 15  Section 7.1: 13-22

         Added:  Section 6.6:1-4, Section 7.1: 39, 40

Week 10, November 7-11

        The spectral theorem, quadratic forms. Chapter 7, sections 1 and 2

        Practice problems: Section 7.2: 9-20

Week 11, November 14-18

         Constrained Optimization Singular value decomposition (SVD); Chapter 7, sections 3 and 4

         Section 7.4: 1-16, 26-29 (use Wolfram Alpha or other software).

         Added:  Section 7.3:1, 3 (a), (b), 7, 9, 11

Week 12, November 21-25 (test #3, November 24, in class)

        SVD

Week 13, November 28-December 2

        SVD, Principal component analysis

Practice problems: Section 7.5: 1, 2, 7

Week 14, December 5-8

        SVD applications, course wrap-up

Tentative Lecture by Lecture schedule (will be updated on a regular basis)

Lecture #	Date	topics covered	reading/resources/comments
1	7/09/22	course introduction, the vector space R^n	Invertible Matrix Theorem Lecture #1 notes Introduction, Section 1.3
2	8/09/22	matrices, matrix multiplication, subspaces of R^n	Sections 1.3, 1.7, 2.1, 2.8 of the textbook Lecture #2 notes
3	12/09/22	bases, rank,  reduced row echelon form	Sections 1.2, 2.8, 2.9 Lecture #3 notes
4	14/09/22	finding, extending a basis for a subspace. Basis for a null space.	Sections  2.3, 2.8, 2.9, 4.2, 4.3, 4.4, 4.5 Lecture #4 notes
5	15/09/22	invertible matrices, introduction to linear programming	Sections  3.2, 4.5, 9.2 Lecture #5 notes
6	19/09/22	geometric method for solving linear programming problems	Section 9.2 Desmos Graphing Website Lecture #6 notes
7	21/09/22	continued, the simplex method, introduction	Sections 9.2, 9.3 3-d graphing website Lecture #7 notes
8	22/09/22	continued	Sections 9.2, 9.3 Lecture #8 notes
9	26/09/22	the simplex method	Section 9.3 Lecture #9 notes Simplex Method Example from the lecture
10	28/09/22	continued	Section 9.3 Lecture #10 notes
11	29/09/22	continued, review of eigenvalues, eigenvectors	Sections 9.3, 5.1, 5.2 Lecture #11 notes
12	3/10/22	review of eigenvalues, eigenvectors	Sections 5.1, 5.2 Lecture #12 notes
13	5/10/22	similarity and diagonalizability	Sections 5.2, 5.3 Lecture #13 notes
14	6/10/22	midterm test #1
15	17/10/22	continued, diagonalization	Sections 5.1, 5.2, 5.3 Lecture #15 notes
16	19/10/22	orthogonality, orthogonal complement	Sections 6.1,  6.2 Lecture #16 notes
17	20/10/22	orthogonal and orthonormal bases, orthogonal projections	Sections 6.2, 6.3 Lecture #17 notes
18	24/10/22	orthogonal projections, Gram-Schmidt Process	Sections 6.3, 6.4 Lecture #18 notes
19	26/10/22	Gram-Schmidt Process, QR decomposition	Section 6.4 Lecture #19 notes
20	27/10/22	QR factorization, projection matrices	Sections 6.4, 6.5 Lecture #20 notes
21	31/10/22	least-squares	Section 6.5 Lecture #21 notes
22	2/11/22	least-squares	Section 6.5 Lecture #22 notes
23	3/11/22	midterm test #2
24	7/11/22	symmetric matrices	Section 7.1 Lecture #24 notes
25	9/11/22	symmetric matrices	Section 7.1 Lecture #25 notes
26	10/11/22	quadratic forms	Section 7.2 Lecture #26 notes
27	14/11/22	quadratic forms	Sections 7.2, 7.3 Lecture #27 notes
28	16/11/22	constrained optimization	Section 7.3 Lecture #28 notes
29	17/11/22	SVD	Section 7.4 Lecture #29 notes
30	21/11/22	SVD	Section 7.4 Lecture #30 notes
31	23/11/22	SVD	Section 7.4 Lecture #31 notes
32	24/11/22	midterm test #3
33	28/11/22	SVD	Section 7.4 Lecture #33 notes
34	30/11/22	Principal Component Analysis	Section 7.5 Lecture #34 notes
35	1/12/22	Principal Component Analysis	Section 7.5 Lecture #35 notes
36	5/12/22	image compression	Image compression demo Lecture #36 notes
37	7/12/22	facial recognition	Eigenfaces example Faces DataSet Face recognition Eigenfaces Lecture #37 notes
38	8/12/22	course wrap up, review	Lecture #38 notes

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Matt Valeriote