Math 33A: Linear Algebra and Applications
Fall 2022 - 1209B Bunche Hall - MWF 12pm-12:50pm
Instructor: Tom Gannon
Course website: https://bruinlearn.ucla.edu/courses/141790
How to reach me: If you have a question related to the course material, please post
it on the Piazza! (See below. You can post anonymously!) If you a grading question,
please check if it is answered in the syllabus below. Otherwise, feel free to email me at
gannonth@math.ucla.edu!
Office hours: Monday 2:50-3:50pm, Wednesday 5:10-6:10pm at Mathematical Sciences 5230
Other times by appointment.
Teaching assistants:
Discussion 3A/3B: Gurkiran Dhaliwal (gurkirand@math.ucla.edu)
Discussion 3C/3D: Alex Xue (alexxue@math.ucla.edu)
Discussion 3E/3F: Timothy Smits (tsmits@math.ucla.edu)
TA Office hours: Each TA has scheduled at least 1 drop-in office hour per week. These
are also listed on Bruin Learn. In short, always check the Bruin Learn course website for
the most up-to-date schedule of office hours, for both the instructor and the TAs.
Overview
How the course will work: Most of the course content will be delivered in our regular
lecture meetings (MWF from 12:00 to 12:50 PM). In recitation, you will have the opportunity
to ask questions about the homeworks and take quizzes which are explained in further detail
below.
Piazza/Collaboration: On all homeworks, you are allowed and indeed strongly encouraged
to work with other students. Work that you submit should be your own work; don’t simply
copy someone else’s work line for line–you don’t learn anything from copying! But forming
study groups to collaborate on the homework and study for exams is an excellent way to
learn, and is encouraged. Through Bruin Learn (Canvas), you can access Piazza, a place
where you can directly ask and answer questions related to the homeworks and the course
more generally.
Gradescope: The homework, quizzes, and exams except the final, will be turned in via a
website called Gradescope. You can access it through links on Bruin Learn (Canvas), so that
you don’t even need to create a Gradescope account. Just sign in to Bruin Learn (Canvas)
and click one of the Gradescope links. The assignments may be submitted to Gradescope
in one of two ways: uploading photos for each separate problem, or uploading a single PDF
file with all of the problems. If you do your work on a tablet or computer, the second
option (PDF file) is probably easiest. For a quick tutorial on this, see the following video:
https://youtu.be/u-pK4GzpId0
If you do your work on paper, the easiest way to submit it might be to upload separate
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photos for each problem. (You can use more than one photo per problem, e.g. if a problem
spans two pages.) Another option is to use a scanner app on your smartphone to create a
PDF file, and submit that. See https://tinyurl.com/GradescopeHW for more details on how
to do that.
BruinCast: A camera permanently mounted in the classroom and controlled from a remote
location will make high-definition video recordings (asynchronous, not livestreamed) of all
lectures. These lectures will be available from the BruinLearn (Canvas) under the ‘UCLA
Media Reserves’ tab. However, I strongly encourage you to attend the lectures–being in an
environment without distractions is the best way to learn math!
Course prerequisite: Completion of Math 3B, 31B or 32A with a grade of C- or better.
Textbook: There is no required textbook for this course. The textbook I will be primarily
following in this course is Linear Algebra with Applications, 5th edition, by Otto Bretscher.
You may find it helpful to read the relevant chapter or section before coming to lecture, even
if you do not understand everything the first time through.
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Schedule and learning goals
Approximately by the end of. . .
Week 1, you should be able to∗
• Solve a given system of many linear equations with many unknowns
• identify if a given matrix is in reduced row-eschelon form and explain what this
means in terms of the associated system of equations.
Week 2, you should be able to
• Identify whether a given function T : Rm → Rn is a linear transformation, where
m and n are some constants,
• multiply matrices and understand what it means to say that matrix multiplication
is not commutative, and
• define the notion of an invertible matrix and explain how to compute the inverse
of an invertible matrix.
Week 3, you should be able to
• Determine whether a given subset of Rn is a subspace of Rn , where n is some
constant
• define what it means for a given set of vectors to be linearly independent and
compute whether a given set of vectors is linearly independent
• define the span of a given subset of vectors in Rn and compute if a given spanning
set is a basis.
Week 4, you should be able to
• Compute the kernel and image of a given linear transformation,
• compute the coordinates of a given basis,
Week 5, you should be able to
• Determine if two given vectors in Rm are orthogonal, where m is some constant
and determine if a given set of vectors is orthonormal
• compute, for a given subspace of Rm and some vector in Rm , the orthogonal
projection of the vector onto the subspace,
• use the Gram-Schmit process to take a given basis of some vector subspace of Rm
and produce an orthonormal basis, and compute the associated QR factorization.
Week 6, you should be able to
• Directly compute the determinant of a given square matrix
• compute whether a matrix is invertible or not by computing the determinant and
∗
I.e. after the first three days of class!
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seeing whether it is zero or not
Week 7, you should be able to
• Give a geometric description of the determinant in the case of a 2 × 2 matrix
• compute the eigenvalues of a given square matrix and the eigenvectors
Week 8, you should be able to
• State the definition of what it means for a given square matrix to be diagonalizable
• Given a diagonalizable matrix, compute its eigenbasis.
Week 9, you should be able to
• Predict the limit behavior of a discrete dynamical system using eigenvalues and
eigenvectors.
Week 10, you should be able to
• Define a symmetric matrix, and be able to understand what the phrase ‘symmetric
matrices have only real eigenvalues’ means
• compute if a given quadratic form is positive definite, positive semidefinite, indefinite, negative definite, or negative indefinite
• write the singular value decomposition of a given matrix.
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Grades
Grading scheme: Your grade in this class is based on your own personal performance on
the assignments and exams. It will not be based on your ranking relative to your classmates,
and it will not be based on any sort of quota of how many students receive each letter grade.
In particular, grading in this class is not competitive. If every single student performs at
an A level, then every single student will receive an A.
At the end of the quarter, your course average will be computed as the maximum of the
following two schemes:
Homework:
Quizzes:
Midterms:
Final exam:
Scheme 1
Scheme 2
10%
15%
Two midterms,
20% each
35%
10%
15%
Highest of the two
midterms, 30%
45%
Each of these grade categories is described in more detail below. Note that you do not need
to choose one of these two schemes. I will calculate your average according to both of them,
and automatically choose the one that gives you the higher course average. In short, if you
must miss one of the midterms, the second grading scheme will ensure that this doesn’t harm
your grade.
A final average of 90% or higher will guarantee you at least an A−, a final average of 80% or
higher will guarantee you at least a B−, and a final average of 70% or higher will guarantee
you at least a C−. These letter grade cut-offs may be adjusted downward at the end of the
quarter, so that more students receive higher grades. But under no circumstances will the
grade cut-offs be higher than stated above: this policy can only help you, not hurt you.
Homework: You will be assigned homework every week except for the week of Thanksgiving. In particular, you will have homework due on the following days: September 29,
October 6, 13, 20, 27, November 3, 10, 17, and December 1. You can find your first homework assignment on Bruin Learn (Canvas) in the ‘Files’ tab. While no late homework will
be accepted, your lowest two scores will be dropped. Each of these nine homework assignments counts equally toward the final grade, even if the number of questions on individual
homeworks differ.
Quizzes: In recitation, you will receive a 20 minute, 1-2 question quiz on the following days:
Thursday Recitations
10/6, 10/13, 10/27, 11/10, 11/15
Tuesday Recitations
10/4, 10/11, 10/25, 11/8, 11/15
The questions on these quizzes are written as if they were test questions, and are designed
to provide a lower stakes environment to test your understanding of the course material.
Because of this, your lowest quiz score will be dropped. The quiz will cover the subjects of
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the homework the week before the quiz–I may be more specific in class!
Midterms and final exam: There will be two midterms, and a final exam. The dates for
the midterms are below; while these dates are tentative, they are very unlikely to change. I
cannot give make-ups for missed midterms, but if you must miss one midterm, your grade
will be computed using the second grading scheme above. The date of the final exam, listed
below, was set by the university months in advance, and cannot be changed. In accordance
with university policies, you must take the final exam in order to pass the class.
Make-ups for the final exam are permitted only under exceptional circumstances, as outlined
in the UCLA student handbook. If you have a conflict with any of these exam dates, let me
know as soon as possible, by the end of week two at the latest.
Midterm 1:
Friday, October 14 12pm-12:50pm
Midterm 2:
Monday, November 21, 12-12:50pm
Final exam:
Tuesday, December 6, 8am-11am
For each exam, you will be allowed to bring a handwritten reference sheet. For the midterms,
the reference sheet must be be written on a single 3" x 5" index card (double-sided). For the
final, the reference sheet may consist of one side of a single 8.5" x 11" sheet of paper. Sheets
that do not meet these requirements will be confiscated at the beginning of the exam.
Calculator Policy You are welcome to use calculators or Wolfram Alpha (a free online
calculator) on all homework assignments. However, the questions chosen on the homework
assignments do not require the use of a calculator, and no calculators will be allowed on
any of the exams or quizzes in this course. You are expected to be able to perform basic
arithmetic operations with fractions and decimals by hand, and know common values of
trigonometric and log functions.
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Other Information
Our inclusive learning environment: UCLA values diversity and inclusion. We expect
everyone in this class to contribute to a respectful, welcoming, and inclusive environment to
support the learning of all other members of the class. If there are aspects of the instruction
or design of this course that result in barriers to your inclusion or accurate assessment or
achievement, please tell me!
Student math center: The Student Math Center (SMC) is free resource available to
all students taking Math 1, 3A/B/C, 31A/B, 32A/B, 33A/B, and 61. It is open Monday
through Thursday from 9:00 AM to 3:00 PM. At any time during those hours, at least two
graduate student TAs will be available at the SMC to provide help with course content and
answer questions about the material. See here for more information:
https://ww3.math.ucla.edu/student-math-center/
Each of our own TAs will be staffing the SMC for one hour each week. However, if you go
to the SMC when they are there, be aware that they must divide their time among all of the
students who are there; if you want one-on-one time with your own TA, their drop-in office
hours are better for that.
Notice about academic integrity: From the office of the Dean of Students:
“With its status as a world-class research institution, it is critical that the University uphold the highest standards of integrity both inside and outside the
classroom. As a student and member of the UCLA community, you are expected
to demonstrate integrity in all of your academic endeavors. Accordingly, when
accusations of academic dishonesty occur, The Office of the Dean of Students is
charged with investigating and adjudicating suspected violations. Academic dishonesty, includes, but is not limited to, cheating, fabrication, plagiarism, multiple
submissions or facilitating academic misconduct.”
Students are expected to be aware of the University policy on academic integrity in the
UCLA Student Conduct Code:
https://www.deanofstudents.ucla.edu/Individual-Student-Code
Please note the sections on (1) cheating, (2) plagiarism, and (3) unauthorized study aids.
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