The course has two main layers:
- Understand ideas: Address the question “What is mathematics?”
- Obtain skills: Be able to construct and evaluate mathematical proofs
Course logistics, communication and feedback
- Quercus: The course will be run through Quercus. All course materials, announcements, and grades will be posted there. Quercus announcements are considered to be the main source of important announcements. Quizzes and reflections will be posted on Quercus.
- Crowdmark: We will use Crowdmark for processing midterms and finals.
- Piazza: We will use Piazza for discussions, questions, and answers. Please use Piazza for all course-related questions. If you have a question, it is likely that someone else has the same question. Piazza is the best way to ask questions and get answers.
- Google feedback form: We will use a general feedback form for any individual anonymous feedback. Feedback form link.
- Padlet feedback board: We will use a Padlet board for general feedback and suggestions. Padlet board link
Textbooks
An Introduction to Proof via Inquiry-Based Learning by Dana Ernst. Available for free at this link. Please check the website of the book for other accessible formats (.html, paperback, etc.).
Discrete Mathematics. An Open Introduction, 4th edition by Oscar Levin. The book is available in .html and .pdf for free at this link.
Additional Text (not required)
A Readable Introduction to Real Mathematics by Daniel Rosenthal, David Rosenthal, and Peter Rosenthal. Undergraduate Texts in Mathematics. Springer International Publishing, 2018. https://doi.org/10.1007/978-3-030-00632-7.
Any required or useful additional material will be provided on Canvas with prior notice.
Course material
The course will cover most material from chapters
Class material schedule
(subject to change following the course pace)
| Week | Topic | Readings |
|---|---|---|
| MODULE 1: Logic, sets, functions and relations | ||
| Week 1 | Course Introduction | |
| Propositional and predicate logic | IP ch. 2 | |
| Week 2 | What are proofs? | DM ch. 1 |
| Sets: definitions and operations on sets | IP ch. 3 | |
| Week 3 | Sets: power sets, cartesian products | IP ch. 3 |
| Maps and functions | IP ch. 8 | |
| Week 4 | Induction | IP ch. 4 |
| Midterm I | Feb 4th 9-11 am | |
| MODULE 2: Number theory, number systems and polynomials | ||
| Week 5 | Relations, partitions and equivalence relations | IP ch. 7 |
| Number theory: divisibility | IP ch. 2 section 1 | |
| Week 6 | Number theory: moduli arithmetics | |
| Reading week | ||
| Week 7 | Number systems | |
| Numbers: from natural to complex | Additional materials | |
| Week 8 | Complex numbers | Additional materials |
| Midterm II | March 10th (subject to change) | |
| MODULE 3: Cardinalities, graph theory and higher algebra | ||
| Week 9 | Cardinalities of sets | IP ch. 9 |
| Week 10 | Graph theory: connections to relations and properties of graphs | DM ch. 2 |
| Week 11 | Introduction to higher algebra and maps between structures | Additional materials |
| Week 12 | Review week | Additional materials |
| Final exam | April 9-30th (precise date to be specified later) |
Assignments
- Weekly reflections on pre-class reading and course organization.
- Two midterms.
- Weekly Quercus quizzes on lecture material.
- Weekly Quercus quizzes on tutorial material.
- Final exam.
- Practice problems (ungraded).
Grading
| Assignment | Weight | Notes |
|---|---|---|
| Midterms I and II | 40% | (0.75 * higher score + 0.25 * lower score) |
| Weekly quizzes | 10% | (drop lowest 2 scores) |
| Tutorial quizzes | 10% | (drop lowest 2 scores) |
| Reflections | 5% | (drop lowest 2 scores) |
| Final Exam | 35% |
Extra credit
Extra credit will be attributed for contributing to the peer-to-peer interactions in the course. Up to 4% extra credit can be obtained for Piazza Q&A participation. (This will be assessed three times: 1% for every 4 weeks of the course, and 1% for the entirety of the course) Up to 4% extra credit can be obtained for Piazza solution posting participation. (This will be assessed three times: 1% for every 4 weeks of the course, and 1% for the entirety of the course)
Communication
Instructor e-mail: denis.gorodkov+mat246@utoronto.ca. Please only use for emergencies or out of privacy concerns. For all administrative requests, please use private messages on Piazza.
This term we will be using Piazza for class discussion. The system is highly catered to getting you help fast and efficiently from classmates, the TA, and myself. Rather than emailing questions to the teaching staff, I encourage you to post your questions on Piazza. If you have any problems or feedback for the developers, email team@piazza.com.
You will be automatically invited to Piazza if you are a member of the course in Quercus. If you have not received an invitation, please let me know.
Make-up Policy
Weekly quizzes, tutorial quizzes, and reflections have a “drop the 2 lowest scores” policy. In case you miss more than 2 quizzes/reflections for a legitimate reason, prepare the documentation and let me know as early as possible about your absence. In case you have to miss a midterm or the final, let me know as early as possible. Admissible documentation in case of absence includes:
- Absence declaration via ACORN (see below for important information on eligibility);
- U of T Verification of Illness or Injury Form (VOI);
- College Registrar’s letter;
- Letter of Academic Accommodation from Accessibility Services.
Please consult the following Faculty of Arts & Science page https://www.artsci.utoronto.ca/current/academics/student-absences for further details.
No make-up midterms or quizzes will be available in the course. In case your absence reason is considered legitimate by A & S guidelines, your grade will be reweighted. Depending on the situation, grades dropped otherwise can be used in the reweighting at the discretion of the instructor.
Academic Integrity
Please refer to https://www.academicintegrity.utoronto.ca/ for U of T’s Code of Behaviour on Academic Matters.
As specified under Grading Scheme, for some of the course components, the two lowest marks are dropped. This does not apply for an assessment in which an academic offense was committed and a sanction of “zero on the assessment” was imposed. Potential offenses include, but are not limited to:
- Posting assessment questions on any kind of website/online forum to solicit help.
- Using someone else’s ideas or words without appropriate acknowledgement.
- Looking at someone else’s answers during an exam or test.
- Misrepresenting your identity.
- Obtaining or providing unauthorized assistance on any assignment.
- Falsifying or altering any documentation required by the University, including (but not limited to) forms related to a petition.
It is an Academic Offense both to receive or to provide unauthorized assistance. It does not matter whether you “helped” or “were helped.” The University of Toronto treats cases of academic misconduct very seriously. All suspected cases of academic dishonesty will be investigated following the procedures outlined in the Code. The consequences for academic misconduct can be severe, including a failure in the course and a notation on your transcript. Every year, students get expelled from the University of Toronto for academic offenses. Remember that you enrolled in University to learn.
Generative AI Usage
It is forbidden to use Generative AI (including, but not limited to, LLMs like ChatGPT or Claude) while working on any assignments in the course. Generative AI usage in the Piazza course forum is also forbidden: one of the purposes of the discussion forum is to learn to formulate individual thoughts completely and precisely, as well as reflect on others’ writing. Usage of generative AI in Piazza would invalidate the sincerity of the discussion. Although I highly value the usefulness of Generative AI in learning, there is currently no admissible mechanism that would allow separating productive use from direct copying.
Diversity and Inclusivity Statement
As MAT 246 heavily relies on a community learning experience, I am particularly committed to fostering a diverse and inclusive environment in the course. There are several feedback mechanisms (feedback board, anonymous feedback form) in place to ensure that the course is accessible to all students. If you consider that some components of the course are excluding you or your peers from the learning process, please do not hesitate to reach out to me. The earlier you do so, the more likely we can address the issues, and the better are our chances at removing the barriers hindering your learning before catching up with the course becomes a barrier of its own. In case it becomes apparent that there are some systemic accessibility issues in our community that we have to address, we will try to decide on a community agreement (Community Agreements).
In terms of course participation, although peer-to-peer communication is probably the most efficient way to learn, I understand that there are various reasons why students might not be able to participate in this aspect of the course fully. For this reason, one-on-one meetings with me will be available upon request. They are mainly dedicated to discussing your progression through the course and discussing any course-related concerns. The format of the meetings will be decided on a case-by-case basis.
Accommodations for Students with Disabilities
Accommodation for students who have a disability or ongoing health issue is available through Accessibility Services. If you believe that you require accommodations, please feel free to approach me and/or Accessibility Services. You can find more information on the process of registering with Accessibility Services at Accessibility Services .
In case you request accommodations for any aspect of the course, please make sure to include your accessibility advisor in the conversation.
Mental Health and Wellness
As a university student, you may experience a range of issues regarding, for example, your physical or mental health, your financial situation, or your friends and family. These may result in significant barriers to achieving your personal and academic goals. The University of Toronto offers a wide range of free and confidential services and programs that may be able to assist you. We encourage you to seek out these resources early and often. You can find resources at Student Life Health & Wellness.
If, at some point during the year, you find yourself in need of immediate support, visit the Feeling Distressed Webpage for more campus resources. Immediate help is available 24/7 through U of T’s My Student Support Program in 35 languages. You can call via phone or WiFi or even chat using the app. Details can be found at My SSP.
Land Acknowledgment
We wish to acknowledge this land on which the University of Toronto operates. For thousands of years, it has been the traditional land of the Huron-Wendat, the Seneca, and most recently, the Mississaugas of the Credit. Today, this meeting place is still the home to many Indigenous people from across Turtle Island, and we are grateful to have the opportunity to work on this land.