MAT344H1Y Summer 2022 Tentative Syllabus
Keegan Dasilva Barbosa and Reila Zheng
University of Toronto
May 16, 2022
Note: This document is subject to change. Please refer to the most recent version on the course website.
1 Contact Information
Please check the syllabus and announcements before you contact us as your questions may already be answered. For all
email enquiries, please put “MAT344” in the subject line as some of us are involved in multiple courses this semester.
For questions about logistics such as requests for extensions, please email the instructor for your section.
For grading concerns, please email the TA who marked the question. You can find this information on Quercus under
announcements after the assignments are graded.
For questions about course content such as confusion about lecture or assignment questions, we encourage you to ask on
Piazza.
We encourage you to start assignments early, we cannot guarantee responses to questions about assign-
ments the day of the deadline.
Instructor Email Lecture Times Location Office Hours
Keegan Dasilva Barbosa keegan.dasilvabarbosa@mail.utoronto.ca Tu 10-12, Th 11-12 Online Th 10-11
Reila Zheng reila@math.utoronto.ca M 6-7, Th 6-8 BA1170 M 8-9, Th 8-9
Please note the updated times for Reila’s lecture and office hour. Note that Monday’s office hour will be over Zoom only,
while Thursday’s office hour will be on Zoom and in-person.
TA Email Tutorial Times Tutorial Location Office Hours
Stanislav Balchev stanislav.balchev@mail.utoronto.ca M 10-11 Online M 5-6
David Ledvinka david.ledvinka@mail.utoronto.ca M 7-8; Th 5-6 SS1084; SF2202 none
Saeyon Mylvaganam saeyon.mylvaganam@mail.utoronto.ca M 7-8 SS2105 Tu 1-2
Shuyang Shen shuyang.shen@mail.utoronto.ca M 11-12 Online none
2 Course Description
We will cover basic counting principles, generating functions, permutations with restrictions. Fundamentals of graph
theory with algorithms; applications (including network flows). Combinatorial structures including block designs and
finite geometries.
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3 Prerequisite
MAT223H1/MATA23H3/MAT223H5/MAT240H1/MAT240H5
It is your responsibility to ensure you understand content from the prerequisite.
4 Course Objectives
Students will demonstrate the abilities to:
• Select and justify appropriate tools (induction, graphs, recurrences, complexity theory, generating functions, prob-
ability) to analyze a counting problem.
• Analyze a counting problem by proving an exact or approximate enumeration, or a method to compute one efficiently.
• Describe solutions to iterated processes by relating recurrences to induction, generating functions, or combinatorial
identities.
• Identify when an exact solution is intractable, and use estimates to describe its approximate size.
• Prove combinatorial identities by counting a set of objects in two ways.
• Construct counting problems which show the usefulness or limitations of combinatorial tools.
5 Textbook
We will use Applied Combinatorics by M.T. Keller and W.T. Trotter, 2017 edition as the required textbook for this
course. It is available at https://www.appliedcombinatorics.org/appcomb/get-the-book/editions/ . It will also be avail-
able on course reserves at the library.
We will use Introduction to Combinatorics by Richard A. Brualdi, fifth edition as a supplementary reference.
6 Course Structure
6.1 Course Website
The course website can be found on Quercus (https://q.utoronto.ca/courses/263776).
6.2 Lectures and Tutorials
Lectures start the week of May 9, tutorials start the week of May 16.
Reila’s lectures will be held in-person in BA 1170.
Keegan’s lectures will be held over Zoom (https://utoronto.zoom.us/j/84743811433).
Please ensure you attend the section of the lecture and tutorial you are registered in. Attendance is not mandatory and
the content covered will purely be for your own benefit. It is your responsibility to catch up on the content you missed.
Please note that due to the ongoing COVID-19 pandemic, the course delivery method may change after term has started
and this may alter the course organization. Students are expected to check the course site for updates as the contents of
this syllabus may change.
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6.3 Office Hours
Reila’s office hours on Thursday will be conducted simultaneously over Zoom and in-person in BA1170, and on Monday
will be conducted over Zoom (https://utoronto.zoom.us/j/86286690422).
Keegan’s office hours will be conducted over Zoom (https://utoronto.zoom.us/j/84743811433).
Stanislav will be holding office hours over Zoom (https://utoronto.zoom.us/j/81171495823).
Saeyon will be holding office hours over Zoom (https://utoronto.zoom.us/j/86267750882 Passcode: 353054).
6.4 Piazza
We encourage you to ask questions about course content on Piazza. The instructional team will be regularly responding
to and moderating the content.
6.5 Crowdmark
Assignments and the take-home midterm will be submitted on Crowdmark. It is your responsibility to ensure you are
able to access Crowdmark and are familiar with the assignment submission process before the assignment deadline.
7 Evaluation
There will be 6 assignments, due roughly every two weeks. They must be submitted on Crowdmark by the due dates.
Your assignment with the lowest grade will be dropped. You may choose to submit scanned handwritten work, work
typeset on Latex, or handwritten work on a tablet, as long as your solution is clearly legible.
There will be a take-home midterm. You will have 24 hours solve the problems and submit your solution to Crowdmark.
It will be scheduled by LSM during the June examination period (June 22-27). Solutions submitted after
the deadline will not be accepted.
There will be an in-person final exam to be held during the final exam period in August. We will announce the date and
time when it is scheduled by the faculty of Arts and Science.
For digital submissions please ensure your pages are clearly legible and in the correct orientation in the
correct order. For all submissions, if your work is not clearly legible you will not get the mark for it. Late
submissions will not be accepted.
Assessment Weight
Assignments (6 total, lowest grade is dropped) 50%
Midterm (24 hour take-home test) 15%
Final (in-person) 35%
8 Code of Conduct
You are expected to treat your classmates, TAs, and instructors with respect and professional behaviour. Students who
commit offences against others (e.g. harassment) will be disciplined according to university policy.
You can find the U of T Code of Student Conduct at the following link:
https://governingcouncil.utoronto.ca/secretariat/policies/code-student-conduct-december-13-2019
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9 Academic Integrity
All suspected cases of academic dishonesty will be investigated following procedures outlined in the Code of Behaviour
on Academic Matters. If you have questions or concerns about what constitutes appropriate academic behaviour, please
reach out to your course instructor.
The university takes academic offences seriously. Here are some guidelines on how you can avoid academic offences:
• Do not post assignment/term test questions to online forums and homework help sites. We know these sites too,
and it’s very obvious to us when you copy their solution.
• Do not solicit help on assignments/term tests from external tutoring services. Many of these services are not very
good and it’s easy to spot and penalize students who turned in a solution from a tutoring service.
• If you work with others in the class, it is generally fine to discuss the assignment questions, but you must not copy
down or take photos of other people’s solutions. You should be able to explain any solution you submit in your own
words without looking at other people’s work.
• Do not share photos of your solution with other students. If we flag both solutions because they are similar, both
students will be penalized for violation of academic integrity.
• You can ask about questions you are stuck on on Piazza and during office hours. If you are concerned other students
will see your work, we will make a private room for you if this is over Zoom, and you can post a private question on
Piazza that only the instructors and TAs will see.
You can find the U of T Code of Behaviour on Academic Matters at the following link:
https://governingcouncil.utoronto.ca/secretariat/policies/code-behaviour-academic-matters-july-1-2019
10 Technical Requirements
It is recommended that students have a high speed broadband connection (LAN, Cable, or DSL) with a minimum
download speed of 5 Mbps. In order to participate in this course, students will be required to have reliable internet access
and a computer satisfying the minimum technical requirements (see https://www.viceprovoststudents.utoronto.ca/covid-
19/tech-requirements-online-learning/ ). If you are facing financial hardship, you are encouraged to contact your college
or divisional registrar https://future.utoronto.ca/ current-students/ registrars/ to apply for an emergency bursary. Free
scanners are available at some on-campus libraries (https://onesearch.library.utoronto.ca/copy-scanners).
11 Policy on Missed Work
As flexibility for missed or late course assignments have been built into the marking scheme, late and missed assignments
will not be accepted for any reason.
Please note that Verification of Illness forms (also known as a “doctor’s note”) are temporarily not required. Students
who are absent from class for any reason (e.g., COVID, cold, flu and other illness or injury, family situation) and who
require consideration for missed academic work should report their absence through the online absence declaration. The
declaration is available on ACORN under the Profile and Settings menu.
If you miss a term test or the final assessment, then you must inform your course instructor within 72 hours of the test.
No exceptions. If your request is approved, you may receive an accommodation in the form of an oral exam, written
make-up test, or a re-weighting of your assessments.
Please note that the online declaration of absence does not notify your instructors of your illness nor the
work you missed, you are still required to contact us to discuss alternative assessment options.
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12 Accessibility
The University provides academic accommodations for students with disabilities in accordance with the terms of the On-
tario Human Rights Code. This occurs through a collaborative process that acknowledges a collective obligation to develop
an accessible learning environment that both meets the needs of students and preserves the essential academic requirements
of the University’s courses and programs. Students with diverse learning styles and needs are welcome in this course. If
you have a disability that may require accommodations, please feel free to approach your Course Instructor and/or the
Accessibility Services office as soon as possible. https://studentlife.utoronto.ca/department/accessibility-services/ The
sooner you let us know your needs the quicker we can assist you in achieving your learning goals in this course.
13 Equity, Diversity, and Inclusiveness
The University of Toronto is committed to equity, human rights and respect for diversity. All members of the learning
environment in this course should strive to create an atmosphere of mutual respect where all members of our community can
express themselves, engage with each other, and respect one another’s differences. U of T does not condone discrimination
or harassment against any persons or communities.
14 Copyright
Lectures for the online section of this course will be recorded on video and will be available to students in the course for
viewing remotely and after each session. Course videos and materials belong to your instructor, the University, and/or
other sources depending on the specific facts of each situation and are protected by copyright. Do not download, copy, or
share any course or student materials or videos without the explicit permission of the instructor. For questions about the
recording and use of videos in which you appear, please contact your instructor.
15 Tentative Schedule
This is a tentative schedule of topics for the term.
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Topic Chapters Week of Description
Strings and Sets Chapter 2.1-2.3 May 9 Introduction to enumeration of strings
of letters or numbers with restrictions,
as well as permutations and combina-
tions. Lectures and office hours be-
gin on May 9.
Binomial Coefficients Chapter 2.4-2.6 May 16 Combinatorial proofs and the binomial
theorem. Tutorials start May 16.
Recurrence and Induction Chapter 3 May 23 Our first look at recurrence relations,
motivating the formal proof system of
induction. No classes on May 23.
Pigeonhole Principle and Graph Basics Chapter 4, 5.1-5.2 May 30 A famous existence theorem; and an in-
troduction to graphs.
Graph Theory Chapter 5.3-5.5 June 6 Properties and enumerations of graphs.
Trees and Posets Chapter 5.6, 6.1-6.5 June 13 A closer look at certain types of graphs.
Take Home Midterm Jun 20 Content covers the first 6 weeks of the
course. Last day of classes on June
20.
Break June 27 No classes/office hours.
Inclusion-Exclusion and Derangements Chapter 7.1-7.5 July 4 A counting principle that applies to col-
lections of intersecting sets. Classes
begin on July 4.
Generating Function Basics Chapter 8.1-8.3 July 11 A bookkeeping method to store infor-
mation about sequences in a useful way.
Generating Functions Chapter 8.4-8.6 July 18 Applying generating functions to count
complicated scenarios.
Recurrences Chapter 9 July 25 Revisiting recurrences with new tools.
Combinatorial Game Theory August 1 No classes on August 1.
Combinatorial Game Theory August 8
Exam Review August 15 Last day of class on August 15.
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