Math 307 

 Applied Linear Algebra



ANNOUNCEMENTS

Aug 31 See you in class on Wednesday, Sep 7.
Sep 09  Homework 1 is posted below. The due date is Friday, Sep 16.
Sep 09  You all have undergraduate lab accounts now. Check your email (for an email from me) for more information regarding your username/password.
Sep 09  Please do not ask me "to register you into the course" as I do not have the authority to sign you into the course. All such requests need to be sent to the Undergraduate Chair Prof. Mark Mac Lean -- maclean-at-math.ubc.ca
Sep 12 Some MATLAB/OCTAVE resources are posted below.
Sep 14 Matlab examples from our last lecture are posted below.
Sep 16 Homework 2 is posted below. The due date is Friday, Sep 23.
Sep 19
Solutions of problems 1-15 in problem set 1.1 (including the problems in homework 1) are posted below.
Sep 19
Matlab examples from today's lecture are posted below.
Sep 21
Matlab examples from today's lecture are posted below.
Sep 26
Matlab examples from today's lecture are posted below.
Sep 26
Homework 3 is posted below. The due date is Monday, Oct 3.



INSTRUCTOR INFORMATION

Instructor: Ozgur Yilmaz
Email : oyilmaz-at-math.ubc.ca
Office: Math Annex 1113
Office Hours:  By appointment
Phone: (604) 822-5963

COURSE INFORMATION

Section: 101
                          
Class times and location: 
Day Start Time End Time Building Room
MWF 13:00 14:00 Chem C124


Course web page: http://www.math.ubc.ca/~oyilmaz/courses/m307/m307.html will be updated throughout the term.

Pre-requisite: One of MATH 152, MATH 221, MATH 223 and one of MATH 200, MATH 217, MATH 226, MATH 253, MATH 263.


COURSE OUTLINE


This course is organized around a collection of interesting applications. Examples from past years are:

Interpolation
Finite difference approximations
Formula matrix of a chemical system
Least Squares
Fourier series
Graphs and Networks
FFT
JPEG compression
Power method
Recursion relations
The Anderson tight binding model
Markov chains
Google PageRank

We will study a selection of these in this class. Each application will be preceded by discussion of the relevant concepts from Linear Algebra. These will be partly review from your previous linear algebra course and partly new material. You will also learn how to do Linear Algebra on a computer using MATLAB or Octave.

Learning Goals: See here for a detailed list of prerequisites and learning goals of Math 307.

Text: There is no required textbook for this course. Instead there is a set of typed notes designed for this course, which is available here:

Chapter 1   :  Linear Equations

Chapter 2   :  Subspaces, bases, and dimension

Chapter 3   :  Orthogonality

Chapter 4   :  Eigenvalues and Eigenvectors
Computational aspects: 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. You 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. Your username and password will be given out in class. Please contact me if you have difficulty logging in. Student versions of MATLAB are also available (although quite expensive). 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, the professor will only be able to answer questions regarding MATLAB.



Grades


Homework: There will be weekly written homework assignments, due at the beginning of class each Friday. These assignments will be posted below.  

WeBWork: There will also be webwork assignments with a schedule to be determined. 

Late homework will not be accepted.  However, your lowest (written) homework score will be dropped (so you can miss one homework if necessary).  Nevertheless, even if you miss a deadline, its a good idea to do the problems, since this is the best way to prepare for the tests and exam. You are welcome to discuss the homework problems with your friends, but are expected to hand in your own work.

There will one midterm exam on Wednesday, October 26 in class. Note that the final exam date is currently unavailable, but will be released during the term. Do not make end-of-term travel plans until this date has been fixed.

You will not be permitted to bring calculators to the test and exam.

Missing a homework or a midterm normally results in a mark of 0. Exceptions may be granted in two
cases: prior consent of the instructor or a medical emergency. In the latter case, the instructor must
be notified within 48 hours of the missed test, and presented with a doctor's note immediately upon
the student's return to UBC. Failure to comply results in a 0 mark. If a midterm was missed for legitimate reasons, the weight of the missed midterm will be transferred to the final. Make-up midterms will, in general, not be provided.

Your grade for the course will be computed roughly as follows:

Homework:  10%
WebWork:      5%
Midterm:      35%
Final exam:  50%


Resources


  • Piazza: You may find Piazza a useful resource for all class-related questions and discussion. Piazza is a question-and-answer platform specifically designed to expedite answers to your questions, using the collective knowledge of your classmates and instructor. It has several features that facilitate discussion of mathematics, most notably support of mathematical typesetting (LaTeX). You are encouraged to answer your classmates' questions, or to brainstorm towards answers, every bit as much as you are encouraged to ask questions. Here are the links:

            You will need a UBC email address to sign up for Piazza.

  • Math Learning Center: The Math Learning Centre (MLC) is a space for undergraduate students to study math together, with support from math tutors, who are graduate students in the math department. Please note that while students are encouraged to seek help with homework, the MLC is not a place to check answers or receive solutions, rather, its aim is aid students in becoming expert learners; to develop critical thinking and skills in a mathematical setting.

If you need help, or would like to discuss any aspect of this course, please make an appointment to see me in my office.

MATLAB/OCTAVE Resources


Material regarding installation/general tutorials

Examples, formulas, etc

Examples from lectures


Homework Assignments


The weekly (written) homework assignments are posted below.


Homework 1 (due Fri, Sep 16) 1a, 2, 5, 7, 13, 14 in problems_1.1.pdf
  Solutions of 1-15 in  problems1.1 
Homework 2 (due Fri, Sep 23)
16, 18 in problems_1.1.pdf,
1, 2, 3, 4 in problems_1.2.pdf
   Solutions of problems1.1 (full)
   Solutions of problems1.2 (full)
Homework 2 (due Mon, Oct 3 )  1, 2, 3, 4, 5, 6 in problems_1.3.pdf


Supplementary MATLAB files useful for the homework and more
  • The following files are for section 1.2.5 for completeness (we did not cover this section in class and it will NOT be covered in the tests)
    • splinemat.m computes the spline matrix of size 3*(n-1) when you type splinemat(n)
    • plotspline.m plots the cubic spline through points X,Y when you type plotspline(X,Y)
  • The following files are for section 1.2.6 (which is covered in class)
    • splinemat2.m splinemat2(X) returns the spline matrix for the points X=[x1,,xn].
    • plotcubic2.m  plotcubic2(x_l,x_u,y_l,y_u,z_l,z_u) plots the cubic polynomial p(x)on the interval [xl,xu] with values p(xl)=yl, p(xu)=yu, p′′(xl)=zl, p′′(xu)=zu.
    • plotspline2.m plots the cubic spline through points X,Y when you type plotspline2(X,Y)


Calendar

Wednesday, Sep 7
First lecture                                             
Monday, Oct 10
Thanksgiving day -- university closed.
Wednesday, Oct 26
Midterm
Friday, Nov 11
Remembrance Day -- university closed.
Friday, Dec 2
Last lecture
Tue, Dec 6 Examinations begin...
TBA
Final exam