Math 307 Applied Linear Algebra

MAY 14   You may register to piazza using the class sign up link.
MAY 15   See below for Homework 1 (due on Wed, May 23).
MAY 16   Quiz 1 (May 22) will cover everything until the end of condition number (all of I.1 in                     the typed lecture notes).  
MAY 20   I posted some old midterm exams for additional practice. 
                Midterm from 2016 (WT2)
                Midterm from 2016 (WT1)
                Midterm from 2015
                Midterm from 2014
MAY 22  The solutions of the first quiz are here.
MAY 23  
See below for Homework 2 (due on Wed, May 30).
               You can use plotspline2.m for Problems 3 and 4 in Homework 2, problems_1.2.pdf.
               Make sure that the file is in the same folder as your MATLAB command window.

MAY 25   Quiz 2 (May 29) will cover everything we did on interpolation and finite difference
                The following problems in the old midterms are on material covered in Quiz 2:
                Midterm from 2016 (WT2): Problem 3
                Midterm from 2016 (WT1): Problem 1d and all parts of 4
                Midterm from 2015: All parts of 3, 4
                Midterm from 2014 : All parts of 2                     

MAY 28   The file heat.m for exercise 4 in problems 1.3 is here.
               The rubric for Quiz 1 is here
MAY 30   The midterm will cover everything we did until the end of the Null space.
                Homework 3 (not due) is posted below together with its solutions. You may use these
                problems for practice. 
JUN 3      The solutions of the second quiz are here.
JUN 4      The midterm with solutions are given below.
JUN 7      Quiz 3 will cover Chap.2, until Graphs and networks (not included).
JUN 8      I compiled several exercises coming from different sources such as old finals and                    midterms for those of you who want more practice.
               They are organised by theme, and are posted below.
JUN 11    The following assignement will replace your lowest quizz if it is in you favor:
                Midterm correction assignement
                The solutions of the third quiz are here
JUN 13   
Find here a short review on complex numbers.
JUN 14    Quiz 4 will cover chap.3 until Fourier analysis (not included).
JUN 18   
The solutions of quiz 4 are here
                Find info about the grading scheme below
                There will be two additional hours of office hours on Monday June 25, to help you prepare the                 final. I will give back the last homework that day.
                It will be Monday June 25th, from 2 to 4pm, in Geography building, room 147.
                Homework 6 (not due) is posted below together with its solutions and will be updated through                 the week.


The final exam will be on: Wednesady, June 27, 12 noon in LSK 201.

It will cover everything we did during class , that corresponds roughly to the following sections in the typed notes:

Chapter 1:
1.1 (Systems of linear equations)
1.2 (Interpolation) except 1.2.4 and 1.2.5
1.3 (Finite difference approximation)
Chapter 2:
2.1 (Vector spaces and subspaces)
2.2 (Fundamental subspaces of a matrix) except 2.2.3 and 2.2.9
2.3 (Graphs and networks)
Chapter 3:
3.1 (Projections) except 3.1.5
3.2 (Complex vector spaces)
3.3 (Orthonormal bases)
3.4 (Fourier series)
3.5 (Discrete Fourier transform)
Chapter 4:
4.1 (Eigenvalues and Eigenvectors)
4.2 (Hermitian matrices) except 4.2.6
4.4 (Recursion relation)
4.6 (Markov Chains) until 4.6.4 (not included) -- see this article for Google PageRank
4.7 (Singular value decomposition) until 4.7.4 (not included)

Check out this link to UBC Wiki for some more past exams (possibly with solutions):


Week 1
    May 14
class notes
May 15   
class notes
matlab script
May 16            
class notes
matlab script
May 17            
class notes
matlab script
Week 2
    May 21
    No class
May 22
class notes
matlab script
May 23
class notes

May 24
class notes
matlab script
Week 3
    May 28
class notes
May 29
class notes
May 30
class notes
May 31
class notes
Week 4
    June 4
(with solutions)

June 5
class notes
June 6
class notes
June 7
class notes
Week 5
    June 11
class notes
June 12
class notes
matlab script
June 13
class notes
June 14
class notes
Week 6
    June 18
class notes
June 19
class notes
June 20
class notes
matlab script
June 21
class notes


Instructor: Claire Guerrier
Email :
Office: Math Annex 1110
Office Hours: Fri 10-11am, MATX1102 (in Math Annex).
Class times and location: 
Day Start Time End Time Building Room
M 2:00 PM
3:00 PM
LSK 201
TuWTh 2:00 PM
4:00 PM
LSK 201

Course web page: 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.


This course is organized around a collection of interesting applications. Examples from past years are:
Finite difference approximations
Formula matrix of a chemical system
Least Squares
Fourier series
Graphs and Networks
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. Since September 2016, MATLAB is available to all active UBC students at no cost. For instructions on how to download and activate MATLAB, see:

You can also 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. If you prefer, you may also use GNU Octave instead of MATLAB, 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.


Homework: There will be weekly written homework assignments. These assignments will be posted below.  

Quizzes: There will be 4 quizzes over the term: May 22, May 29, June 11, and June 18. 

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, it is 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 you are expected to hand in your own work.

There will one midterm exam on Monday, June 4 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 quiz 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.

The midterm correction assignment is not mandatory. It will replace your lowest quiz if it is in you favor.

If the final is better than the midterm, the weight of the midterm will be transferred to the final.

To pass the course, you need to reach 50% total, and you need to reach at least 40% at the final.

The weights for computing the final grade for this course will be:

Homework:  10%
Quizzes:       10%
Midterm:      30%
Final exam:  50%

To make a grade over 10, each quiz/homework will be weighted the same (i.e. each quiz worth 2.5 points over 100, and each homework worth 3.3 points over 100, as the lowest homework will be ignored).
Follow the total of each written exam:

Midterm:          30
Quiz 1:              15
Quiz 2:              10
Quiz 3:              10
Quiz 4:              12
Homework 1:   27.5
Homework 2:   22
Homework 3:   20.5
Homework 4:   32
Midterm correction assignment: 5
Final exam: 


  • 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.


The homework assignments will be posted below.

Homework 1 (due Wed, May 23) 1, 2, 5, 7, 13, 14, 16, 18 in problems_1.1.pdf
Homework 2 (due Wed, May 30)
  1, 2, 3, 4 in  problems_1.2.pdf
  1, 2, 3, 4 in  problems_1.3.pdf
Homework 3 (not due)
  problems_2.1.pdf     Solutions
Homework 4 (due Wed, June 13)
  1, 2, 3, 4 in problems_2.3.pdf
 file hmkgraph.m
Homework 5 (due Wed, June 20)
4, 5 in problems_3.1.pdf
2 in problems_3.2.pdf
3, 8 in problems_3.3.pdf
1 in problems_3.4.pdf
Solutions of problems 3.1
Solutions of problems 3.2
Solutions of problems 3.3
Solutions of problems 3.4
Homework 6 (not due)
1 to 6 in problems_4.6.pdf
Solutions of problems 4.1
Solutions of problems 4.2
Solutions of problems 4.4
Solutions of problems 4.6
Solutions of problems 4.7


Below are some more exercises, organised by theme. They are mostly extracted from old finals and midterms.

Norm and cond. number
Graphs and networks
Eigenvalues and eigenvectors
Markov Chains
Singular value decomposition


Monday, May 14
First lecture                                               
Monday, May 21 
Victoria Day -- university is closed.
Tuesday, May 22
Quiz 1 
Tuesday, May 29
Quiz 2
Monday, June 4
Monday, June 11
Quiz 3
Monday, June 18
Quiz 4
Thursday, June 21
Last day of classes
Monday, June 25
Examinations begin...
Wednesday, June 27
Final exam