Math 307 (Section 103) Applied Linear Algebra

SEP 5   Lecture notes from today's class are posted below.
SEP 6   Homework 1 (due on Tue, Sep 17 in class) is posted below.
SEP 12   First office hour today at 11am in AUDX 142; Lecture notes posted below.
SEP 16   Quiz 1 will cover everything until the end of our coverege of condition number (all of I.1 in the typed lecture notes).
SEP 16   Here are some old midterm exams for additional practice. The following problems in these old midterms are on material covered in Quiz 1:
         Midterm (2016 WT2): Problem 1c and all parts of 2.
         Midterm from 2016 WT1: Problem 1a,c and all parts of 2.
         Midterm from 2015: All parts of 1 and 2a
         Midterm from 2014: All parts of 1 except 1d
SEP 23   The lecture notes from Thursday Sep 19 are posted below.
SEP 23   The solutions to Quiz 1 are posted below.
SEP 23   Homework 2 (due on Tue, Oct 1 in class) is posted below.
SEP 25   The following files are for section I.2.6 from the lecture notes (which we will cover tomorrow). You will need plotspline2.m for Problems 3 and 4 in Homework 2, problems_1.2.pdf. Note that plotspline2.m needs the other two files below (splinemat2.m and plotcubic2.m) to be in the same folder as plotspline2.m. So, save these three files in the same folder and make sure your MATLAB command window is working in that folder.
         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(x_l)=y_l, p(x_u)=y_u, p"(x_l) = z_l, p"(x_u) = z_u.
         plotspline2.m   plots the cubic spline through points X,Y when you type plotspline2(X,Y).
SEP 27   Quiz 2 will cover everything we did on interpolation (I.2.1, I.2.2, I.2.6, I.2.7). The following problems in the old midterms are on material covered in Quiz 2:
         Midterm from 2016 WT1 : All parts of 4.
         Midterm from 2015 : All parts of 4
         Final exam from 2013 : Problem 2
         Final exam from 2011 : Problem 1
OCT 8   Homework and Quiz grades are now recorded in Canvas.
OCT 8   Homeworks, Quizzes, and Midterms can be picked up from the Math Learning Center, located in LSK 301.
OCT 9   Starting tomorrow, office hours will take place in my office, ESB 4128.
OCT 9   Homework 3 and its solutions have been posted below. It is for your own exercise.
OCT 9   The midterm will take place next Friday at 6:30PM in MATH 100. It will cover
        Chapter 1: everything except for I.2.4 and I.2.
        Chapter 2: all subsections of II.1 and all subsections of II.2 except II.2.3, II.2.7, II.2.8, and II.2.9.
OCT 14   The following problems from the old midterms involve the material that will be covered in our midterm:
        Midterm from 2016 WT2: everything except 1g;
        Midterm from 2016 WT1: everything;
        Midterm from 2015: everything;
        Midterm from 2013: everything except 4.
OCT 22   The lectures on Thursday, Oct 24 and Tuesday, Oct 29 will be lead by Prof. Yaniv Plan
OCT 22   Office hours this Thursday are cancelled.
OCT 27   Homework 4 has been posted and is due on Tuesday, Nov 5.
NOV 4   Quiz 3 (on Thu, Nov 7) will cover Sections II.3 (Graphs and resistor networks), III.1.1, and III.1.2. The following problems in the old midterms and finals are on material covered in Quiz 3.
        Midterm from 2014: Problem 4,
        Final exam from 2013: Problem 3,
        Another final from 2013: Problem 5,
        Final from 2011: Problem 4.
NOV 14   Here are the solutions to the midterm.
NOV 14   Quiz 4 will cover III.1.3, III.1.4, III.2, III.3, and IV.1.1-IV.1.7. The following problems in the old finals are on material covered in Quiz 4:
        Final exam from 2013: Problems 3,4
        Another final from 2013: Problems 2c,4
        Final exam from 2011: Problems 5c, 8a

DEC 2   We will have a review session (all Sections) on Thursday. Dec 5, 10:30am-12:00pm, in room MATH 100.
DEC 3   I will hold additional office hours this week on Wednesday and Friday 2-3pm. Note that the usual office hour on Thursday is at the same time as the review session.


The final exam will be on Saturday, December 7, 8:30AM in CIRS 1250.

It will cover the following sections:

Chapter 1: everything except for I.2.4 and I.2.5
Chapter 2: all of II.1; all of II.2 except II.2.3; all of II.3
Chapter 3: all of III.1 except for III.1.5; all of III.2; all of III.3
Chapter 4: all of IV.1 except IV.1.10, IV.2.1-4 (to the extent to which it was covered in class), all of IV.3, IV.4, IV.6.1-2.

Past final exams with solutions: 2013, another 2013, 2011.

Also, check out this link to UBC Wiki for some more past exams (possibly with solutions).


Week 1
  Sep 3
    no class
  Sep 5
class notes
Week 2
  Sep 10
class notes      
MATLAB script      
  Sep 12
class notes      
MATLAB script      
Week 3
  Sep 17
class notes      
  Sep 19
class notes
Quiz 1 Solutions
Week 4
  Sep 24
class notes
MATLAB Lagrange Interpolation
MATLAB Cubic Spline Interpolation
  Sep 26
class notes
MATLAB script
Week 5
  Oct 1
class notes
  Oct 3
class notes
MATLAB script
MATLAB script 2
Quiz 2 Solutions
Week 6
  Oct 8
class notes
  Oct 10
class notes
Week 7
  Oct 15
class notes
  Oct 17
class notes
Week 8
  Oct 22
class notes
  Oct 24
class notes
Week 9
  Oct 29
class notes
  Oct 31
class notes
Week 10
  Nov 5
class notes
  Nov 7
class notes
Quiz 3 Solutions
Week 11
  Nov 12
class notes
MATLAB script
  Nov 14
class notes
Week 12
  Nov 19
class notes
  Nov 21
class notes
Quiz 4 solutions
Week 13
  Nov 26
class notes
  Nov 28
class notes


Homework 1 (due Tue, Sep 17) 1a, 2, 5, 7, 13, 14 in problems_1.1.pdf
  Solutions of 1-15 in problems_1.1
Homework 2 (due Tue, Oct 1) 16, 18 in problems_1.1.pdf
1,2,3,4 in problems 1.2.pdf
  Solutions of all problems 1.1
Solutions of problems 1.2
Homework 3 (not due) 1,2,3,4,5,6 in problems_1.3.pdf
1,2,3,4 in problems 2.1.pdf
  Solutions of problems 1.3
Solutions of problems 1.2
Homework 4 (due on Tue, Nov 5) 1 in problems_2.2.pdf
1,2,3,4 in problems_2.3.pdf
2,3 in problems_3.1.pdf
  Solutions to problems 2.2
Solutions to problems 2.3
Solutions to problems 3.1
Homework 5 (not due) 4,5,7,9 in problems_3.1
1,2ab,3 in problems_3.2
1,3,8,9 in problems_3.3
1,2,3,4,5 in problems_4.1
  Solutions to problems 3.1
Solutions to problems 3.2
Solutions to problems 3.3
Solutions to problems 4.1
Homework 6 (not due) 1,2 in problems_4.2.pdf
1,2 in problems_4.3.pdf
1,2 in problems_4.4.pdf
  Solutions of problems 4.2
Solutions of problems 4.3
Solutions of problems 4.4


Instructor:   Elina Robeva
Office:   ESB 4128
Office Hours:   Th 11-12pm or by appointment.
Section 103
Class times and location: 
Day Start Time End Time Building Room
TTh 8:00 AM
9:30 AM
MATX 1100

Course web page for Section 103: 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 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: Sep 19, Oct 3, Nov 7, and Nov 21.  

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 you are expected to hand in your own work.

There will be one midterm exam on Friday, October 18 6:30pm-7:30pm in MATH 100 (Section 103). 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.

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

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

Missing a homework, quiz, or midterm:

If you miss an assesment (homework, quiz, or midterm) for a valid reason -- see UBC Vancouver Senate's Academic Concession Policy V-135, please fill out an academic request form and bring it to me. In this case, for a missed homework, the weight will be transferred onto the remaining homework assignment. For a missed quiz, the weight will be transferred to the remaining quizzes, If you miss the midterm, the weight will be transferred onto the final exam. Note that in accordance with UBC policy for academic concessions, this form may be used ONCE per course. On a second instance, students will be expected to provide documentation.

Any student who misses an assessment is to present to their instructor a self-declaration form (or relevant documentation if this is not the first time they miss an assessment) within 72 hours of the assessment date or their mark in the missed assesment will be 0. This policy conforms with the UBC Vancouver Senate's Academic Concession Policy V-135 and students are advised to read this policy carefully.


  • 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 is the link:

            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.


Thursday, Sep 5
First lecture                                             
Thursday, Sep 19
Quiz 1 
Thursday, Oct 3
Quiz 2
Monday, Oct 14
Thanksgiving Day -- university closed.
Friday, Oct 18
Midterm (6:30PM in MATH 100)
Thursday, Nov 7
Quiz 3
Monday, Nov 11 Remembrance Day -- university closed.
Thursday, Nov 21
Quiz 4
Friday, Nov 29
Last day of classes
Tuesday, Dec 3
Examinations begin...
Saturday, Dec 7
Final exam (8:30AM in CIRS 1250)