Math 1B03 - Linear Algebra I
(Fall 2019)
| |||||||||||
Course Information
There are two sections of Math 1B03 during the Fall 2019 semester. Both sections are identical (they will follow the same schedule, have the same homework, midterms, and final). This webpage is for both sections.
Instructors:
Section C01: Andres Zuniga
Office: Hamilton Hall 407
Office Hours: Monday 2:20-3:20PM, Wednesday 3:20-4:20PM
Email: andres.zuniga@math.mcmaster.ca
Section C02: Adam Van Tuyl (Course Coordinator)
Office: Hamilton Hall 419
Office Hours: Monday 2:30-3:20PM, Thursday 10:30-11:20AM
Email: vantuyl@math.mcmaster.ca
Place and Time:
Section C01: Monday, Wednesday, Thursday 4:30PM-5:20PM
in TSH (Togo Salmon Hall) B128
Section C02: Monday, Thursday 9:30AM-10:20AM, Tuesday 10:30-11:20AM
in TSH (Togo Salmon Hall) B128
Tutorial T01: Mo 3:30PM - 4:20PM in TSH B128
Tutorial T02: Fr 2:30PM - 3:20PM in TSH B128
TAs:
Tutorials T01 and T02: Aaron Crighton
Office Hours: Aaron will be working the Math Help Centre
Email: crightoa@mcmaster.ca
Lab Tutors: Andrii Turchenko and Aghigh Farhadicheshmehmorvari
Hours: See the Lab Schedule.
Email: aturchenko98@gmail.com and farhadia@mcmaster.ca
Math Help Center: The Math Help Center will have dedicated TAs for Math 1B03.
Hours: See the Math 1B03 TA Schedule.
Textbook:
-
Elementary Linear Algebra: Applications Version 11th Edition
by Howard Anton, Chris Rorres
- We will also use Chapter 10 of the 9th Edition of this textbook on complex numbers.
News (Last Updated: Dec 10, 2019)
|
FINAL EXAM Information
The final for Math 1B03 will be on Friday Dec. 13, 2019 at 7:30PM. Please find a review sheet below:
Here are some practice tests.
|
|
MIDTERM 1 INFORMATION
Midterm 1 was on October 2, 2019 at 7:00PM. It has now been graded and you can see your results in the homework portal (childsmath). Here are the solutions to this year's midterm:
|
|
MIDTERM 2 INFORMATION
Midterm 2 was on November 6, 2019 at 7:00PM. The midterm is graded. Here are the solutions to this year's midterm: Please note that the wording in Question 9 was unclear, so we will not count this question. The midterm will be out 19 instead of 20. |
|
The following online app on linear algebra may be of interest.
We were contacted by the developers, and we decided that it may help
you learn some of the concepts in this class. Try it out
and let us know what you think!
|
You can access the latest version of the lecture notes here:
Below is a summary of any relevant news and/or information. To see what we covered in class, see the lecture notes above and the schedule below.
- Oct. 29, 2019 For our third lecture on complex numbers,
I gave an example using Matlab. Here is the code that I used:
# Matrix from class A = [1 -2; 1 3] w = [1; 0] ## Create all x-coordinates x=[] for i=1:1:24 x(end+1)= (1/(sqrt(5)^i)*(A^i*w)(1,1)) endfor ## Create all y-coordinates y=[] for i=1:1:24 y(end+1)= (1/(sqrt(5)^i)*(A^i*w)(2,1)) endfor ## Plot x vs y plot(x,y) ## The above example was rescaled so you can see the rotation. If we change rescalling slightly, we can make a spiral. ## x=[] for i=1:1:24 x(end+1)= (1/(2^i)*(A^i*w)(1,1)) endfor ## Create all y-coordinates y=[] for i=1:1:24 y(end+1)= (1/(2^i)*(A^i*w)(2,1)) endfor ## Plot x vs y plot(x,y) - Sept. 5, 2019 Missing information (Adam's office hours, TA information, lab schedule) has been added to this web page. The course outline also includes some of this updated information.
- Sept. 3, 2019 The Math Help Centre will open Wednesday, Sept. 11, 2019. The hours will be M-Th 2:30-8:30 and Fr 2:30-6:30.
- Aug. 30, 2019 A couple of minor updates.
- Aug. 22, 2019 Some minor updates throughout the webpage, plus the course outline has been added to the webpage.
- July 30, 2019 Webpage was started (it will be added to over the next couple of weeks).
Return to TOP
Schedule
We will be using the following schedule. Please note that there may be changes; always refer to the news section above for most recent information.
In addition, I have included some links to some videos to complement the
lectures. It is suggested that you also do the following practice problems.
Answers are in the back of the book, and worked out solutions are in the student manual.
I recommend that you first attempt the questions, and then check your
answers.
| Week 1: September 3-7 |
||||
|---|---|---|---|---|
| No Tutorials, Assignments, or Labs |
||||
| Lecture |
Topic |
Videos |
Practice |
|
| Lecture 1 |
Introduction 1.1 Systems of Linear Equations |
Section 1.1: 5a, 7a, 11, 15, 17, 19, True-False Questions |
||
| Lecture 2 |
1.2 Gaussian Elimination I |
Video 1 Video 2 |
Section 1.2: 3,15, 17, 19, 23, True-False Questions |
|
| Week 2: September 9-13 | ||||
| ASSIGNMENT #1: Due at 11:59PM on Friday Sept. 13 | ||||
| Lecture 3 |
1.2 Gaussian Elimination II |
|||
| Lecture 4 |
1.3 Matrices and Matrix Operations |
Section 1.3: 1, 5, 11a, 12a, 25, True-False Questions |
||
| Lecture 5 |
1.3 Matrices and Matrix Operations (Continued) 1.4 Inverses, Properties of Matrices |
Video | Section 1.4: 3, 5, 15, 21, 33, 39, True-False Questions |
|
| Week 3: September 16-20 | ||||
| LAB #1 (Matlab): Due at 11:59PM on Friday Sept. 20 NOTE: Matlab TA is available this week |
||||
| Lecture 6 |
1.4 Inverses, Properties of Matrices (Continued) |
Video | ||
| Lecture 7 |
1.5 Elementary Matrices |
Video
|
Section 1.5: 3, 5, 9, 13, 15, 19, True-False Questions |
|
| Lecture 8 |
1.5 Elementary Matrices (Contiued) 1.6 More Linear Systems and Invertible Matrices |
Section 1.6: 5, 7, 15, 17, 21, True-False Questions |
||
| Week 4: September 23-27 | ||||
| ASSIGNMENT #2: Due at 11:59PM on Friday Sept. 27 |
||||
| Lecture 9 |
1.6 More Linear Systems and Invertible Matrices (Continued) |
|||
| Lecture 10 |
1.7 Diagonal, Triangular, and Symmetric Matrices 1.8 Linear Transformations |
Section 1.7: 5, 13, 15a, 17, 27, True-False Questions |
||
| Lecture 11 |
1.8 Linear Transformations (continued)
|
Video | Section 1.8: 1, 5, 11, 15, 27, 31, True-False Questions |
|
| Week 5: September 30 - October 4 | ||||
|
MIDTERM #1: Evening of Wednesday, October 2 LAB #2 (Matlab): Due at 11:59PM on Friday Oct. 4 NOTE: Matlab TA is available this week |
||||
| Lecture 12 |
10.5 Application (Graph Theory) |
|||
| Lecture 13 |
2.1 Determinant by Cofactor Expansion
|
Video 1 Video 2 Video 3 |
Section 2.1: 9, 11, 13, 21, 23, 34, True-False Questions |
|
| Lecture 14 |
2.2 Evaluating Determinants by Row Reduction
|
Video |
Section 2.2: 1, 9 15, 23, 31, True-False Questions |
|
| Week 6: October 7-11 | ||||
| ASSIGNMENT #3: Due at 11:59PM on Friday Oct. 11 |
||||
| Lecture 15 |
2.3 Properties of Determinants (including Cramer's Rule)
|
Video | Section 2.3: 7, 9, 15, 19, 27, 33, True-False Questions |
|
| Lecture 16 |
5.1 Eigenvalues and Eigenvectors
|
Video | Section 5.1: 3, 5, 7, 9, 13, 25, True-False Questions |
|
| Lecture 17 |
5.1 Eigenvalues and Eigenvectors (continued) |
Video | ||
| Week 7: October 14-18 | ||||
| FALL BREAK - no classes | ||||
| Week 8: October 21-25 | ||||
| LAB #3 (Matlab): Due at 11:59PM on Friday Oct. 25 NOTE: Matlab TA is available this week |
||||
| Lecture 18 |
5.2 Diagonalization
|
Video
|
Section 5.2: 3, 5, 7, 11, 13, 15, 19, 27, True-False Questions |
|
| Lecture 19 |
5.2 Diagonalization (continued)
|
Video
|
||
| Lecture 20 |
10.1 (from 9th Edition) Complex Numbers
10.2 (from 9th Edition) Division of Complex Numbers |
Video 0 Video 1 NOTE: You need Flash enabled |
Section 10.1: (9th ed.): 11, 19 | |
| Week 9: October 28-November 1 | ||||
| ASSIGNMENT #4: Due at 11:59PM on Friday Nov. 2 |
||||
| Lecture 21 |
10.2 (from 9th Edition) Division of Complex Numbers
10.3 (from 9th Edition) Polar Form of a Complex Number |
Section 10.2: (9th ed.): 9, 10, 35 Section 10.3: (9th ed.): 1, 3, 4 |
||
| Lecture 22 |
5.3 Complex Eigenvalues and Eigenvectors
|
Section 5.3: 1, 3, 5, 7, 9 15, 17, 19, 21, 23, 25, True-False Questions |
||
| Lecture 23 |
3.1 Vectors in 2-space, 3-space and n-space
|
Section 3.1: 3, 7, 9, 11, 15, 19, 21, True-False Questions |
||
| Week 10: November 4-8 | ||||
| MIDTERM #2: Evening of Wednesday Nov. 6 LAB #4 (Matlab): Due at 11:59PM on Friday Nov. 8 NOTE: Matlab TA is available this week |
||||
| Lecture 24 |
3.2 Norm, Dot product, and Distance in R^n |
Video | Section 3.2: 1, 5, 9, 15, 17, True-False Questions |
|
| Lecture 25 |
3.3 Orthogonality 3.4 The Geometry of Linear Systems |
Video | Section 3.3: 1, 13, 15, 19, 29, True-False Questions Section 3.4: 17, 19, 25, True-False Questions (c,d,e,f) |
|
| Lecture 26 |
3.4 The Geometry of Linear Systems (Continued) 3.5 Cross Product |
Video | Section 3.5: 1, 7, 9, 13, True-False Questions |
|
| Week 11: November 11-15 | ||||
| ASSIGNMENT #5: Due at 11:59PM on Friday Nov. 15 | ||||
| Lecture 27 |
4.1 Real Vector Spaces
|
Section 4.1: 3,5, 9, 11, 13, 17, 21, True-False Questions |
||
| Lecture 28 |
4.1 Real Vector Spaces (Continued) 4.2 Subspaces |
Video |
||
| Lecture 29 |
4.2 Subspaces (Continued)
|
Section 4.2: 1ace, 3ac, 7, 9, 11, 19, True-False Questions |
||
| Week 12: November 18-22 | ||||
| LAB #5 (Matlab): Due at 11:59PM on Friday Nov. 22 NOTE: Matlab TA is available this week |
||||
| Lecture 30 |
4.3 Linear Independence
|
Section 4.3: 1ab, 3a, 5, 9, 11, 15, 29, True-False Questions (not h) |
||
| Lecture 31 |
4.3 Linear Independence (Continued) 4.4 Coordinates and Basis |
Video 1 Video 2 |
||
| Lecture 32 |
4.4 Coordinates and Basis (Continued)
|
Section 4.4: 1, 3, 5, 7, 11, 13, 25, True-False Questions |
||
| Week 13: November 25-November 29 | ||||
| No assignments or labs this week |
||||
| Lecture 33 |
6.3 Gram-Schmidt Process
|
Video | Section 6.3: 1, 7, 9, 11, 13, 27, 29, 31 | |
| Lecture 34 |
6.3 Gram-Schmidt Process (Continued) 4.5 Dimension |
Video | Section 4.5: 1, 3, 9, 15, 17, True-False Questions |
|
| Lecture 35 |
4.5 Dimension (Continued) 4.7 Row Space, Column Space, and Null Space |
Section 4.7: 3, 9, 11, 13a, 15, True-False Questions a,b,c,d,i,j |
||
| Week 14: December 2-5 | ||||
| ASSIGNMENT #6: Due at 11:59PM on Wednesday, Dec. 3 (NOTE CHANGE!!!) | ||||
| Lecture 36 |
4.7 Row Space, Column Space, and Null Space (Continued) 4.8 Rank, Nullity, and the Fundamental Matrix Spaces |
Video | Section 4.8: 3, 5, 7, True-False Questions a,c,e |
|
| Lecture 37 |
Review | |||
Return to TOP
Homework and Labs
There will be six assignments and five labs
made available through online submission.
They will be automatically graded if submitted before the deadline expires.
You can access the assignments though this portal:
There will be five labs which will require the use of Matlab (version 7 or later). These will be submitted using the online system given via the link above. Here is the Lab Schedule. Specifically, this is a time and place that you can go to ask questions about Math 1B03 and Matlab. In addition, the department has put together a series of online video tutorials:
You can access Matlab in the campus computer labs in BSB anytime in the
opening hours (check opening hours), as long as there is not another
class using them. There are scheduled lab times exclusive for MATH1B03.
You do not have to attend any scheduled lab times. But TAs will be available
if you need help at the times given on the Lab information page. Matlab can
be purchased at the campus bookstore or online directly from
Mathworks.
An alternative to Matlab is to use Octave. Octave doesn't have all the functionality of Matlab, but it is free, it uses the same syntax as Matlab, and can be accessed via the web: Octave Online. For the majority of your lab work, you can use Octave.
Return to TOP
Handouts
All class handouts are available as
PDF files.
Course Information (Updated Sept 5.)
Course handout from first day of class
Midterm 1 Review Sheet
Handout describing first midterm.
Midterm 2 Review Sheet
Handout describing second midterm.
Return to TOP
Grading Scheme
I will calculate your mark using two different weightings. Your final mark will be the higher of the two weightings. The two weightings are as follows:
Weighting 1
20% = Assignments and Labs (11 x 1.818%)
40% = Midterms (2 x 20%)
40% = Final Exam
Weighting 2
20% = Assignments (11 x 1.818%)
20% = Maximum of Midterm 1 and 2
60% = Final Exam
Return to TOP
Class Polices
1. Policy on Academic Ethics. You are expected to exhibit honesty and use ethical behaviour in all aspects of the learning process. Academic credentials you earn are rooted in principles of honesty and academic integrity.
Academic dishonesty is to knowingly act or fail to act in a way that
results or could result in unearned academic credit or advantage. This
behaviour can result in serious consequences, e.g. the grade of zero
on
an assignment, loss of credit with a notation on the transcript
(notation reads: Grade of F assigned for academic dishonesty),
and/or suspension or expulsion from the university.
It is your responsibility to understand what constitutes academic
dishonesty. For information on the various types of academic
dishonesty
please refer to the Academic Integrity Policy, located at:
http://www.mcmaster.ca/academicintegrity/
The following illustrates only three forms of academic dishonesty:
- plagiarism, e.g. the submission of work that is not one's own or for which other credit has been obtained.
- improper collaboration in group work,
- copying or using unauthorized aids in tests and examinations.
2. Academic Accommodation of Students with Disabilities.
Students with disabilities who require academic accommodation must contact Student Accessibility Services (SAS) to make arrangements with a Program Coordinator. Student Accessibility Services can be contacted by phone 905-525-9140 ext. 28652 or e-mail sas@mcmaster.ca. For further information, consult McMaster University's Academic Accommodation of Students with Disabilities policy.
3. Requests for Relief for Missed Academic Term Work. If you have missed work, it is your responsibility to take action. If you are absent from the university for medical and non-medical (personal) situations, lasting fewer than 3 days, you may report your absence, once per term, without documentation, using the McMaster Student Absence Form (MSAF). See Requests for Relief for Missed Academic Term Work
Absences for a longer duration or for other reasons must be reported
to
your Faculty/Program office, with documentation, and relief from term
work
may not necessarily be granted.
In Math 1B03, the percentages of the missed work will be
transferred
to the final examination.
Please note that the MSAF may not be used for term work worth 25% or
more,
nor can it be used for the final examination.
4. Academic Accommodation for Religious, Indigenous or Spiritual Observances
(RISO).
Students requiring academic accommodation based on religious, indigenous or spiritual observances should follow the procedures set out in the RISO policy. Students requiring a RISO accommodation should submit their request to their Faculty Office normally within 10 working days of the beginning of term in which they anticipate a need for accommodation or to the Registrar's Office prior to their examinations. Students should also contact their instructors as soon as possible to make alternative arrangements for classes, assignments, and tests.
5. Important Message.
The instructor and university reserve the right to modify elements of the
course during the term.
The University reserves the right to change the dates and deadlines for any or all courses in extreme circumstances (e.g., severe weather, labour disruptions, etc.). Changes will be communicated through regular McMaster communication channels, such as McMaster Daily News, A2L and/or McMaster email.
If either type of
modification becomes necessary, reasonable notice and communication with the
students will be given with explanation and the opportunity to comment on
changes. It is the responsibility of the student to check their McMaster
email and course websites weekly during the term and to note any changes.
6. On-line Statement for Courses Requiring Online Access or Work. In this course we will be using Crowdmark and https://www.childsmath.ca/childsa/forms/main_login.php, a local website hosted by the department. Students should be aware that, when they access the electronic components of this course, private information such as first and last names, user names for the McMaster e-mail accounts, and program affiliation may become apparent to all other students in the same course. The available information is dependent on the technology used. Continuation in this course will be deemed consent to this disclosure. If you have any questions or concerns about such disclosure please discuss this with the course instructor.
Return to TOP