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MAT 137Y: Calculus with proofs

Fall 2021– Winter 2022

Syllabus


Introduction

Welcome to MAT137! This course has four objectives:

1. Calculus concepts: We want you to become fluent in various concepts in calculus (limits, deriva-tives, integrals, sequences, and series) and their applications to math and science. This includes learning to compute with them, and learning the most important theorems that deal with them,

2. Mathematical rigour: We will introduce you to mathematical logic. We want to make you com-fortable with reading and understanding mathematical statements and precise definitions, and with reading, critiquing, and writing rigorous proofs.

3. Problem solving: In your future career, we would like you to be able to attack new problems that you have never seen before, to figure out by yourself how to adjust old methods to new situations, and to learn how to be confident with your answers. You will achieve this not by memorizing a lot of formulas and methods, but by understanding why they work and by coming up with them by yourself.

4. Academic Integrity: University life requires respecting academic integrity. This includes being honest and fair, honouring the trust that is placed on you, taking responsibility for your actions, and never using other’s work as your own. You will uphold these values in this course.

We are creating many learning opportunities in this course: office hours, videos, lectures, tutorials, practice problems, Piazza, problem sets, and tests. Take advantage of all of them! We wish you a pro-ductive and rewarding year.

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.


Mask Policy for in-person lectures

Masks are an inexpensive and effective measure that limits the spread of COVID and will facilitate the return to normal life as quickly as possible. Failure to wear a mask properly entails unnecessary risks to public health and may disrupt learning by creating unwelcome distractions. It is the policy of the Math Department that in-person instruction cannot take place unless all students are wearing a mask that covers both mouth and nose, with exceptions only for students who have received documented exemptions.

As with other accommodations, any student who has an official exemption from wearing a mask is expected inform the instructor BEFORE classes begin, providing documentation.


Course sites

● Quercus. You are responsible for checking it regularly. We will post on it all official announce-ments, grades and course materials, including office hours, problem sets, and test information. By default, you should get an email every time an announcement is posted, as long as your utoronto email address is correct on Quercus. You can also always read old announcements by logging in.

● Piazza. This online forum is a resource for students to meet other MAT137 students, ask questions, discuss problems, make study groups, and in general help each other.

● GradeScope. This is the place you will submit your problem sets. Your TAs will also mark all your problems sets and exams here. Check more details about GradeScope FAQ under ” Start Here” module of the course page on Quercus.


Textbook

We don’t require a textbook in this course. The videos and practice problems are enough. Nevertheless, those who prefer a traditional textbook, and those who want more examples or a bigger collection of practice problems. You can use:

● “Calculus in One Dimension” by Tyler Holden. Volume 1. 2018 updated edition.

● “Calculus in One Dimension” by Tyler Holden. Volume 2. 2018 edition. (errata)

Volume 1 2018 updated edition contains many corrections compared to the original edition. You can still use the original one and use the list of errata to check any potential errors.

The book is a set of lecture notes written by a former MAT137 instructor. It is much cheaper than a regularly published textbook, and it is better suited for us. You may buy it at the UofT bookstore.

Notice that the textbook sometimes may go in more depth, or provide more examples, or emphasize different concepts, so it is a great source to complement videos and lectures when you are confused.


Topics

Unit 1: Logic, sets, notation, definitions, and proofs

Unit 2: Limits and continuity

Unit 3: Derivatives

Unit 4: Transcendental functions

Unit 5: The Mean Value Theorem and its applications

Unit 6: Applications of limits and derivatives

Unit 7: The definition of integral

Unit 8: The Fundamental Theorem of Calculus

Unit 9: Integration methods

Unit 10: Applications of the integral

Unit 11: Sequences

Unit 12: Improper integrals

Unit 13: Series

Unit 14: Power series and Taylor series


Week-by-week Schedule

For our week-by-week course schedule, including list of topics, which videos to watch each week, tu-torial dates, problem sets due dates, and more, see the ”Modules” under course page on Quercus. This will likely change during the terms.


Important dates

● 22 Sep 2021 – Last date to add a course, or to add or change a lecture section or tutorial section

● 21 Feb 2022 – Last date to drop the course without academic penalty.


Whom to contact?

Our emails are listed above. For office hours, see the course page on Quercus.

● For math-related questions about MAT137, you may ask any of the instructors or TAs during office hours, talk to TAs in tutorial or at the Math Learning Centre, or post on Piazza.

● For issues of academic integrity, contact Sarah Cook

● For logistical questions about MAT137, contact the course coordinator Xiaoyue Cui.

● If you require accommodations for a disability, or have any accessibility concerns about the course, the classroom, or course materials, please contact Accessibility Services.

● If you have a personal situation and are concerned about how it will affect your academic per-formance, please contact your College Registrar.


How to get help?

1. Office hours: for math-related questions, you are welcome to talk to any of us in-person; you are not restricted only to your lecturer. For our office hours and locations, please check the course page on Quercus, as they will likely change. You do not need an appointment to come during our regularly scheduled office hours. If you cannot make any of our office hours, ask us for an appointment by email or by talking to us at the end of a lecture. We are always happy to talk to students! Please include “MAT137” on the subject of any email you send to us.

2. Piazza: we also encourage the use of Piazza to ask other students for help.

3. Math Learning Center: at the MLC, you can drop-in and:

● Find space to work on problem sets.

● Collaborate with other 137 students.

● Ask math questions to any TA. Certain hours have TAs with 137 expertise.

The MLC serves many different MAT courses and has daily regular hours. It opens on September 20, 2021. Other college-specific MLCs can be found here. The MLC also holds online TA office hours in the evenings and weekends. A TA will answer your questions via video chat but you will not need to share audio or video. More details will be posted on the course site.


What we expect you to know before the course starts

One of the most common reasons for failure in calculus is a weak background in precalculus. To help you with this, our department has developed a precalculus preparation website.

This site contains a summary of the topics we expect you to have learned in high-school. There are self-diagnostic quizzes, as well as worked examples and practice problems.

We will not review this material in class. We expect you to review it by yourself and work on the prac-tice problems by the end of the second week of class. Ignoring this material or letting it go past the second week will make it very difficult to succeed in this course. You may of course ask any questions to instructors or TAs during office hours. You may also use Piazza to ask other students.


The MAT137 Learning Cycle

Preparing for Class-Videos

We have short YouTube videos that contain short summaries of the main concepts throughout the course. They are linked from the course page on Quercus. Your instructor will tell you which videos to watch before each lecture. We expect you to watch them before each class, so we can start each day doing meaningful practice. This way, we don’t have to waste time on copying down definitions or performing rote computations. If there’s something you don’t understand in the videos, you should ask about it on Piazza before class. Coming to lecture without having watched the corresponding videos will be a waste of time. It is recommended to plan ahead and put time for this into your weekly sched-ule.


Classes

You have three weekly hours of class. They are called ”Lectures” at UofT, but there won’t be a lot of actual “lecturing” on the lecture sections( that is what the videos are for!). We will expect you to have watched some short videos and take your own notes before coming. You will spend class time working on difficult, conceptual questions and discussing them with your peers. There are eight lecture sections. Each section meets for three weekly hours.


Problem Sets

The only way to learn mathematics is to practice and receive feedback. To help you with this, there will be 8 problem sets throughout the year. You may submit problem sets individually or in groups of two people. You may change your group from problem set to problem set. One of you will need to scan your completed problem sets (or take a picture) and submit them electronically via GradeScope. For details (including how to do this and when they are due), see the ”Start Here” module under the course page on Quercus. It also explains the penalty for late submission. There won’t be any exceptions. Please do not ask.

We will mark your problem sets, post the grades on Quercus, and return them to you electronically. The problem sets are worth collectively 15% of the course grade.

If you commit an academic offense on any single problem set, we may not accept your work and we may decide to give you no credit for any of them. Otherwise, for each student, we will only count the best 6 out of 8 grades. If you need to miss one problem set for any reason, justifiable or not, that will be one of the two grades that we will not count for you.


Practice problems

In addition to the problem sets that you will turn in, we will also post practice problems. We encourage you to work through them as we cover the sections in class. You can always visit us during office hour or use Piazza for help. These practice problems won’t be turned in.


On computations

We will not be including routine computational questions on your problem sets, since you do not need our feedback to become good at these. We will include them in the practice problems, in some tuto-rials, and certainly in tests. You are responsible for getting enough practice so you can quickly solve such questions on tests without error.


Tutorial

In addition to lectures, you will have one hour of tutorial per week, on Tuesday or Wednesday. Each week we will select a topic that is particularly important or that we know students struggle with, and you will have the opportunity during tutorial to get very useful practice and to get help from a TA in a small setting.

Notice that you need to enrol (through ACORN or through your register) both on a lecture section and on a tutorial section separately by September 22. If you need to make changes to your tutorial after this date, there will be easy instructions on the course page on Quercus on how to do the change. Please do not attend a different tutorial section without changing your tutorial section first. Tutorials begin the week of September 20th.


Studying

After class, you should spend time organizing your notes and coming up with questions you still need answered. Your classmates, TAs, and instructors will be available on Piazza to discuss these problems with you. Also you can use office hours and MLC to get help.We also recommend putting time for study-ing into your weekly schedule.


Midterms and Final Assessment

There will be four term tests. The dates and times are still tentative:

● Test #1: Thursday 21 October 2021, 4:10-6pm( alternate time: 6:30pm to 8:20pm).

● Test #2: Friday 3 December 2021, 4:10-6pm( alternate time: 6:30pm to 8:20pm).

● Test #3: Thursday 3 February 2022, 4:10-6pm( alternate time: 6:30pm to 8:20pm).

● Test #4: Thursday 17 March 2022, 4:10-6pm( alternate time: 6:30pm to 8:20pm).

We will confirm the dates on the course website once they are definite. We will also post detailed in-formation on each test on the course site three weeks before it takes place.

If you have an academic conflict for one of the tests (for example, a tutorial or a lab for a different course), then we will offer you an alternative time. For this, you will need to let us know at least one week before the date of the test. We will post more information on the course page on Quercus.

If you are unable to write any of the term tests for a legitimate reason (e.g. severe illness), we will accommodate you, but you must notify us as soon as it is possible (if at all possible in the next 24 hours after the test, but certainly no more than a week after the test), and you will have to provide us with appropriate documentation. We will post more information on the course page. For some tests, the accommodation consists of a make-up test; for others, the weight of the test is distributed among the other three term tests. You do not get to choose. We will inform you of the details once you are approved.

There will be a three-hour cumulative final exam during the April 2022 exam period. The exact date and time will be posted by the Faculty of Arts and Science.

We do not permit the use of any type of calculator during term tests or the final exam.


Surveys

We will share various surveys throughout the year. Some will count towards your final grade. We will make it clear when that happens.


Marking Breakdown

Your course mark will be

If one Term Test is held online, then 20% of its weight will be shifted evenly to problem sets.

If the final exam is held online then 30% of its weight will be shifted evenly to problem sets.


Adjustments and curving

We understand that sometimes things happen (you may have a bad day, your may have multiple tests in a row, perhaps a particular test is a bit easier or a bit harder). That is why we have a generous grading scheme with automatic “adjustment” procedures built into it: we drop the lowest two problem set scores and the lowest midterm score. This is a way to soften any blow and allow you to recuperate easily from a bad day.

We try to evaluate you in absolute, not relative standards. Your grade should reflect the quality of your work against the learning objectives of the course, not how well you do relative to your peers. If you all do well, there will be a lot more As than usual. If you all do poorly, there will be a lot more Fs than usual. When appropriate, we will round up to nearby letter grades but that is all. A passing grade in MAT137 should mean that you have a chance of completing MAT237, not that you are in a certain per-centile of the class. We will not adjust grades just because students do well or bad. So do not ask for any additional adjustments: there will be none.