# Math 307 Applied Linear Algebra

ANNOUNCEMENTS
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
approximations.
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.

FINAL EXAM INFORMATION

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):

LECTURE NOTES

 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 Midterm(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 INFORMATION

Instructor: Claire Guerrier
Email : guerrier-at-math.ubc.ca
Office: Math Annex 1110
Office Hours: Fri 10-11am, MATX1102 (in Math Annex).
COURSE INFORMATION

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: http://www.math.ubc.ca/~guerrier/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
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:
https://it.ubc.ca/services/desktop-print-services/software-licensing/matlab#getMATLAB.

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:

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.

HOMEWORK ASSIGNEMENTS

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 Solutions Homework 2 (due Wed, May 30) 1, 2, 3, 4 in  problems_1.2.pdf   1, 2, 3, 4 in  problems_1.3.pdf Solutions 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 Solutions 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) problems_4.1.pdf problems_4.2.pdf problems_4.4.pdf 1 to 6 in problems_4.6.pdf problems_4.7.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

PRACTICE EXERCISES

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

 Norm and cond. number Interpolation Subspaces Graphs and networks Projections Fourier Eigenvalues and eigenvectors Markov Chains Singular value decomposition

CALENDAR

 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 Midterm 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