MATH 307


Notes for the solutions of the second final exam from 2008S have now been posted.

The final exam is on Saturday, April 25, 8:30 am (in BUCH A204 for section 201; BUCH A205 for section 202). The exam will be based on the following comprehensive set of learning goals for the course. To prepare for the final exam, we recommend that you review the learning goals, the lecture notes and the homework problems. You will be provided with the usual sheet of MATLAB/Octave functions for the exam: formula sheet

The Math Club sells a MATH 307 exam package (for $5); however, all the exams in this package are based on the old syllabus of the course.  We do not recommend using this for studying purposes.  If, however, you already bought the package or insist on using it, the following is a list of questions from the package that are relevant given the new  course syllabus.  Note that many topic are not covered at all in these questions - more relevant sample exams can be found on the Documents and Files page.

Relevant questions from the exam package
Dec 2008: 1, 2, 3, 4, 5
Dec 2005: 2(a), 5(a), 7 (there is a typo in the solution, the factor of "e^t/4i" should not be there), 8(a)
Apr 2005: 2(a), 3(a), 5
Apr 2004: 2(i)(ii), 4
Apr 2003: 1, 4

Reminder: the second test will be on Friday Mar. 13.  It will cover material from sections II.2 (the four fundamental subspaces) to III.4.6 (Fourier Series) inclusive.
You will provided with the following sheet of MATLAB/Octave functions for the test: formula sheet

Reminder: the first test will be on Friday Feb 6. It will cover material up to section 2.1.4 and be based on the learning goals listed at the beginning of each section.

The homework solutions for Section 1.1, #8, Section 1.2, #7 and Section 2.1, #2e have been corrected (Mon Feb 2).

You can take this quiz (it is on the Test Page) to test your basic MATLAB skills.

Course Information

Welcome to Math 307, a course in applied linear algebra. This course is organized around a collection of interesting applications. Here is list of applications that have be covered in this course in recent years
  • Interpolation
  • Finite difference approximations
  • Least Squares
  • Fourier series
  • FFT
  • JPEG compression
  • Power method
  • Recursion relations
  • The Anderson tight binding model
  • Markov chains
  • Google PageRank
  • Principal component analysis

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.

There is no required textbook for this course. Instead we will post lecture notes in pdf format on the Documents and Files page. However, if you would like to consult a book you may find these useful:

Linear Algebra and its Applications by Gilbert Strang.
Elementary Linear Algebra with Applications by Howard A. Anton and Chris Rorres.

There is also a wealth of information on the internet. This MIT course site has many interesting links.

To complete the work for this course, you will need access to MATLAB/Octave software. MATLAB is a widely used program for numerical computations with matrices. You can access MATLAB in the math department computer labs. These are location in LSK 121, 302 and 310. You may use the labs at any time if there is a terminal free. Your username and password (the same as you use for this site) wil be given out in class. Please contact your instructor you have difficulty logging in. Student versions are also available (although quite expensive). GNU Octave 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.

This year we have received special funding from Skylight and the Carl Weimann Science Education Initiative to hire a TA, Avishka Raghoonundun, to help you with the MATLAB/Octave component of the course. She will hold regular office hours and be available by email to provide help. She will compile and FAQ list and maintain the MATLAB Octave Help page on this site. The goal is to make this page a resource that will be useful for future students in this course. So please contact Avishka with any MATLAB/Octave problems or comments.

The regular TA's for the course are Thomas Wong (section 201) and Ana Culibrk (section 202). They will be grading your homework assignments. In addition, they will be available to answer your questions at
This page contains information relevant to both sections of the course. Each section also has a separate page with section specific information. Here is a list of all the pages on this web site:
Homework and Tests

There will be weekly homework assignments. They will be posted on the assignments page.
They are due in class on the posted day. Late homework will not be accepted. But even if you miss the deadline, its a good idea to do the problems, since this is the best way to prepare for the tests and exam.

There will be two midterm tests in class on Friday, February 6 and Friday March 13 as well as a final exam during the April exam period. You will not be permitted to bring calculators or formula sheets to the tests and exam. You will be provided with a formula sheet, which you may view in advance.


The following weightings will be used in computing your final grade:

Homework: 10%
Midterms: 40%
Exam: 50%

If you miss the test for a legitimate reason (e.g., illness with doctor's note), the weight of the final exam will be increased.


Chapter 1: Linear Equations
Topics: Solving linear equations, vector and matrix norms, condition number.
Applications: Lagrange interpolation, splines, finite difference approximation
8 hours
Chapter 2: Subspaces, Basis and Dimension
Topics: Vector spaces, subspaces, basis, dimension, basis for N(A), R(A), N(A^T) and R(A^T)
Applications: Graphs and resistor networks
8 hours
Chapter 3: Orthogonality
Topics: Inner products, orthogonality, Gram-Schmidt orthonormalization, QR decomposition
Applications: Least squares, Fourier series, discrete Fourier transforms, FFTs
9 hours
Chapter 4: Eigenvalues and Eigenvectors
Topics: Eigenvalues and eigenvectors
Applications: Power method, Markov chains, Anderson tight binding model, Google PageRank, Singular Value Decomposition
9 hours 

Monday, May 4, 2009

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Department of Statistics


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