Course outline, policies, and syllabus

Main text: Chapter I | Chapter II | Chapter III | Chapter IV

Supplementary texts (not required): Linear Algebra and Its Applications (Strang); Elementary Linear Algebra with Applications (Anton and Rorres)

Lecture times: 11:00AM - 12:30PM TuTh in LSK 200

Instructor: Justin Tzou

Email: jtzou at math dot ubc dot ca

Office hours: 12:30PM - 1:30PM Wednesdays in LSK 300, and by appointment - I am in everyday, but try to make your appointments on Tuesdays and Thursdays if possible. I will also usually be available right after class for quick questions.

Office location: My office is in a no-student area - the default meeting place will be in the seating area on the fourth floor of ESB by the elevator unless otherwise agreed upon. I will also usually be available right after class for quick questions.

Grading scheme

- assignments (approximately 6-8 over the term; late homework will not be accepted; worst one will be dropped): 25%
- midterm (Thursday Mar. 2 during class time in LSK 200): 25%
- final exam (date set by UBC): 50%

The midterm grade of those students who miss the midterm exam (with proper documentation given within 72 hours of the midterm) will be replaced by that obtained on the final exam. There will be no makeup exams given under any circumstances.

For the midterm and final exam: no calculators, no notes, no books, no cell phones or other electronic devices of any kind.

MATLAB/GNU Octave

To complete the work for this course, you will need access to MATLAB software. MATLAB is a widely used program for numerical computations with matrices. As a UBC student, you may obtain a free Student Version here -- this version will be sufficient for this course, and I strongly recommend you go with this option. You also can access MATLAB in the math department computer labs. These are located in LSK 121 and 310. The labs hours are posted here. You may use any free terminal in the labs during these times. You will need an account to use the terminals -- please let me know if you need access. If you prefer, you may also use GNU Octave, which is an open source MATLAB clone that is available for free. It is included in most Linux distributions. Windows and Mac versions are available for free download. However, I will probably only be able to answer questions regarding MATLAB.

Course plan

From the main text above, we will plan to cover approximately the following sections (time considerations will dictate what we are ultimately able to cover):

- Chapter I: everything except for I.2.4 and I.2.5
- Chapter II: all of II.1, all of II.2, II.3.1-7 (inclusive)
- Chapter III: all of III.1 except for III.1.5, all of III.2, all of III.3, (III.4 is not covered in the exam), III.5.1
- Chapter IV: all of IV.1 except for IV.1.10, IV.2.1-3
(inclusive), IV.2.5, all of IV.3, IV.4,
IV.6.1-2 (inclusive), IV.7.1-3 (inclusive)

Useful links

Academic integrity

Class notes

- 01/03/2017: (Ch.1) linear systems, vector norms, matrix norms | TYPO: on p.6, every 3/5 should be a -3/5; sorry! | MATLAB intro
- to run the MATLAB script, save it in a directory, open MATLAB, navigate to that directory, open the file, then run it by either pressing F5 or the 'run' icon
- alternatively, once in that directory, type jan_03_mat in the command window
- please let me know if you have issues with running the script
- the link to the MATLAB download is above

- 01/05/2017: (Ch.1) review, matrix norms | least squares fitting demo
- for the MATLAB code, please see p. 17 and p. 21 in the notes for the setup of the problem

- 01/10/2017: (Ch.1) matrix norms, condition number, Lagrange interpolation | proof of the first inequality on the bottom of p. 35 | map of circle by a random matrix: run file and function | other useful commands
- save these two files in the same directory; then run the run file, which is jan_10_mat.m
- notice
that the variables t, x_1, x_2 are created in the function computex(N),
but you do not have access to these variables once the function
exits
- 01/12/2017: (Ch.1) Lagrange interpolation, cubic spline interpolation | Lagrange interpolation demo
- for the code, please refer to notes on Lagrange interpolation
- take
a look at the output of the code - for the second example, the code
outputs the difference in the coefficients resulting from the small
change in one of the data points;the change is very large because of
the large condition number of the Vandermonde matrix when there are
many data points

- 01/17/2017: lecture by Brian Wetton, (Ch.1) cubic spline interpolation (cont'd)

- 01/19/2017: lecture by Anthony Peirce, (Ch.1) finite differences | Matlab session (text file)

- 01/24/2017: (Ch. 1), review of matrix norms, condition numbers, cubic spline interpolation, finite differences | cubic spline demo

- 01/26/2017: (Ch. 1), review of finite differences, (Ch. 2), vector spaces | TYPO at the top of p. 72 has been fixed; sorry! | one-sided and centered difference demo | gambler problem

- 01/31/2017: (Ch. 2), linear independence, span

- 02/02/2017: (Ch. 2), basis, the four fundamental spaces of a matrix

- 02/07/2017: (Ch. 2), the four fundamental spaces of a matrix, orthogonality | angles in R^n

- 02/09/2017: (Ch. 2), orthogonality, orthogonality relations between the four fundamental spaces of a matrix, solvability conditions

- 02/14/2017: (Ch. 2), solvability conditions | derivation of the steady state heat equation u'' = -f(x)

- 02/16/2017: (Ch. 2), solvability conditions, chemical systems, directed graphs

- 02/28/2017: (Ch. 2), directed graphs, (Ch. 3), orthogonal projections onto a line

- 03/07/2017: (Ch. 3), orthogonal projections onto a line, orthogonal projection matrices, least squares solutions

- 03/09/2017: (Ch. 3), least squares data fitting, vectors of complex numbers, orthogonal bases, orthogonal and unitary matrices | least squares code Matlab data
- To run MATLAB script, save both files in the same directory, then run mar_07_mat.m

- 03/14/2017: (Ch. 3), unitary matrices, (Ch. 4) eigenvalues and eigenvectors, determinant, trace

- 03/16/2017: (Ch. 4), eigenvalues and eigenvectors of Hermitian matrices, power method for computing eigenvalues

- 03/21/2017: (Ch. 4), power method for computing eigenvalues, recursion relations, Markov chains

- 03/23/2017: (Ch. 4), Markov chains, properties of stochastic matrices, Google PageRank

- 03/28/2017: (Ch. 4), singular value decomposition

- 03/30/2017: (Ch. 4), singular value decomposition, application to image compression | map of unit circle by random matrix | image compression demo
- to run the image compression demo, first save a picture called pic.jpg in the same directory - press Enter to advance

- 04/04/2017: (Ch. 4), principal coordinates analysis | PCA code
- the code is divided into 3 sections separated by `%%'. To run a section, put your text cursor in that section (so that it turns yellow), and hit CRTL+ENTER

- 04/06/2017: final exam details, review of orthogonal projections, Markov Chains, SVD, condition number, cubic spline interpolation, finite differences
- I
know that some of the assignments were a lot of work and that some
lectures went a little (a lot?) fast, so I'd like to thank you for your
effort and for sticking with it this whole term. I wish you the best on
all of your finals.

Assignments

- this problem along with problems 1(b), 2, 4, 8, 13, 14, 16 from here | code for the umbrella problem | due Jan. 24 at the beginning of class
- SOLUTIONS | umbrella code | umbrella answers | solutions to the other problems
- supplementary problems and solutions on interpolation; DO NOT SUBMIT
- these problems along with problems 2-6 from here | For #3 in the second set of problems, disregard the reference to #1, as it is not assigned | heat.m code | Please start this early! | due Feb. 2 at the beginning of class |
- problems 1, 2, 7 from here | due Feb. 9 at the beginning of class
- SOLUTIONS | here

- these problems | due Feb. 16 at the beginning of class
- SOLUTIONS | here

- SOLUTIONS | here
- these problems | data for problem 6 | due Mar. 16 at the beginning of class
- SOLUTIONS | here

- SOLUTIONS | here
- these problems | data for problem 5 | due Mar. 28 at the beginning of class
- SOLUTIONS | here

- SOLUTIONS | here
- these problems | due April 4 at the beginning of class
- SOLUTIONS | here | 2(b) code | 2(f) code | setaxes function

Practice problems

- set 1 | solutions
- set 2 | solutions
- set 3 | solutions
- set 4 | solutions
- set 5 | solutions
- set 6 | solutions
- set 7 | solutions
- set 8 | solutions
- set 9 | solutions
- set 10 | solutions
- set 11 | solutions
- set 12 | solutions
- set 13 | solutions
- set 14 | solutions