Fall 2022

Course Objectives

The course has four“big picture”objectives:

1. Calculus concepts. We will study various concepts in calculus (functions, limits, derivatives, diferential equa-

tions). We want you to build a mental framework of calculus that serves as a foundation for future learning.

2. Problem solving. We want to train you in the art of problem solving. In your future career, you will see problems that you haven’t seen before. We want you to be able to igure out by yourself how to adjust the methods you know to it new situations and to be conident with your solutions. You can only achieve this by understanding rather than memorizing formulas and methods.

3. Applications. We will introduce you to many diferent ways to apply calculus to understand the world around us. We want to make you comfortable to take in a situation and see it through the lens of calculus.

4. Scientifc communication. We want you to see yourself as a conident and capable user and communicator of mathematics.

Essential Questions

In this course we will address the following questions:

1. Why should we represent a single relationship in diferent ways?

2. What is ininity? What is an ininitesimal?

3. How do we model the real-world with mathematics?

4. What is speed, and how do you measure it? What are rates, and how do you measure them?

5. How can you solve novel problems that are unlike any you’ve encountered before?

6. What do good readers and writers of math do?

Course Topics

We will work through the following units in MAT135, corresponding to the textbook sections below.

1. 1.1–1.6. Modelling with Functions: How do we use mathematics to describe related quantities?

2. 2.1, 1.7–1.9. Limits: How do we work with the ininitely small and the ininitely large?

3. 2.2–2.6. The Derivative:  In what diferent ways can rates of change be represented?  How are rates of change described and used?

4. 3.1–3.7. Computing Derivatives: How are derivatives eiciently computed?

5. 3.9, 4.1–4.4, 4.6–4.7 Using the Derivative:  How can we use the derivative to solve complex problems from the sciences?

6. 11.1–11.3 Diferential Equations: How can we understand relationships described using rates of change?

Is MAT135H the right calculus course for you?

MAT135H is the irst in the sequence of calculus courses for students intending to major in science, and is the prereq- uisite for MAT136H1. Other calculus courses ofered by the Faculty of Arts & Sciences include MAT133Y, MAT137Y, and

MAT157Y.

• MAT133Y introduces students to both calculus and linear algebra and is intended for Commerce students.  It does not cover as much calculus as MAT135H1 and MAT136H1, and is not a valid prerequisite for most math and statistics courses.

•  Both MAT137Y and MAT157Y are proof-based approaches to calculus, intended for students who are planning to take further mathematics courses. These courses go further into the mathematical basis of calculus, whereas the MAT135/MAT136 sequence will focus more on applications.

Course Components

What we assume you know

Historically, students who come into a calculus course with strong knowledge of algebra and functions perform far better than students who have weaker skills.

Further, students who work to improve their pre-calculus and mathematics study skills attain greater mastery of calculus1,2 . Other recent research shows that a solid precalculus foundation is a very good predictor of success in

calculus3 .

To help you prepare for the course, the Math department prepared the website

http://uoft.me/precalc

This website contains tutorials, examples, and self-diagnostic quizzes of the topics we expect you to have learned in high school.

How to learn?

ANNOTATE textbook

MAKE connections

REVIEW what you learned

USE additional resources

Pre-class essentials

Before each class, you will spend about 30 minutes learning the elementary concepts of the material that we will work on during class.

We have created short videos to introduce you to the basics of each concept. We expect you to watch them before each class. The videos are linked from the course website.

There will be a short quiz every week to prepare you for class about on of the topics of the week.

We will also be using Perusall to establish a community where you can read the textbook, annotate it, ask questions about it, and engage in discussions with your peers. These will be assigned at the end of each week and due before your irst lecture of the week.

Classes will be designed towards students who have done the pre-class essentials. If you did not do so, you cannot expect to learn anything in class.

1.                                             20                    232-236  20              .http://wacraorg/publicdomain/ijcra%xxi_iii_pg%agustinpdf

2.      .        10.1080  10511979808965902http://dxdoiorg//

3.              .                                    2018  07                -    -                -        -                -              -          -https://newsharvardedu/gazette/story///mastersofcalculuscomepreparedharvardstudy shows/

Textbook

The textbook we will be using is Calculus: Single Variable by Deborah Hughes-Hallett, et al, 7th edition.

To get the book, you need to create an account with Perusall at https://app .perusall .com and use the course code:

GALVAO-SOUSA-GZJ82. The price for the etextbook together with Perusall is: $100 for 50 years!

Class

You will have three weekly hours of class. Classes will be a mix of the instructors introducing concepts and students working with each other.  We won’t record classes.  We will post the questions we use in class, but no solutions or anything else. The point of class is for you to actively engage with the material, not to watch or read somebody else’s solutions.

Teaching Team.

Instructors Email Section

Mathmatize assignments are your chance to get a benchmark on how well you know the concepts covered that week. They serve as a good practice for term tests and the fnal exam.  Don’t start with Mathmatize.  Finish with it.  Doing Mathmatize should be the last step in your learning process for each module. Don’t jump right to it.

Based on the classroom and tutorial experience, you will now have an idea which concepts are clear to you and which

you should work on. There are many resources at your disposal to help you study:

Suggested problems can be found on Quercus

Ed discussion board where you can ask questions to instructors and peers

Drop-in hours where you can come ask questions to instructors or TAs

Math Learning Center (MLC) in the Student Commons at 230 College St, room B120 where you can work and ask questions to instructors or TAs

Recognized Study Groups (RSG) where you can join/start a study group (https://uoft .me/RSG)

Academic Success Centre ofers a variety of services and programming to help students meet their academic             and personal goals at the University (https://www .studentlife .utoronto.ca/asc)

Each week, you will attend one tutorial, a class of about 30 students led by your own Teaching Assistant (TA). The purpose of tutorials is to improve your problem-solving and communication skills, and to provide you opportunities to collaborate with other students.

Check your tutorial assignment. You must attend the tutorial that you are assigned to according to ACORN. Tutorials start on Thursday, September 22.

Head TAs. Fabiola Cruz Li, Gavin Hurd, Mason Lorch

TAs. Aidan, Akira, Alice, Amane, Amber, Aram, Ava, Behraz, Brandon, Charles, Charlie, Chayim, Craig, Curtis, Erik, Ethan, Fatemeh, Felix, Heyang, Isaiah, Ishaan, Ishika, Jacqueline, Kai, Kate, Kunaal, Lora, Matias, Mo, Mohammad, Muhammad, Nicholas, Osama, Pavel, Robert, Sara, Sirui, Warren, William, Yihan, Yiming, Zhongyuan.

Applied Communication Tasks (ACTs) will give you the opportunity to develop and apply your knowledge of calculus in other situations, and learn additional quantitative material on your own.

There will be three Applied Communication Tasks introduced in tutorials throughout the term. You will work on them both in tutorials and at home, and submit them in tutorial.  Your grade in this component of the course will be calculated according to the number of learning objectives that you demonstrate through the completion of the tasks throughout the term. You can fnd the learning objectives in the course Quercus page.

ACTs will be due in tutorials, so the exact due date will depend on when you have your tutorial; the weeks are shown below.

Tentative due dates for ACTs:

Draft PAR Final

ACT C    November 17 @ 9am    Tutorial 8    November 24 @ 9am

The course is collaborating with a research team to study students’learning habits and beliefs about their academic performance. There will be three surveys, approved by the Research Ethics Board, throughout the term. Each complete survey is awarded 0.5% of the course mark.  Personally identifable information will only be held until the course concludes in order to assign marks. Your responses to the surveys will remain anonymous and are not part of the evaluation of your course performance, in any shape or form.  No identifying information will be used in the study itself.

The following assessments are designed for an in-person class. If the class has to be moved online, the assessment structure and the grading scheme will change. There will be an announcement on Quercus in that case.

In this course, you will be assessed based on your mastery of these learning objectives, not against other students in the class. Therefore your grades will not be‘curved’up or down. Since we are measuring your performance against these set criteria, we will not be releasing average grades or other information about how the class as a whole performs.

Test

Final Exam

This is an assignment meant for you to be acquainted with the diferent tools that we’ll be using throughout the course. It will be available for you to complete in the frst two weeks of classes.

You need to complete all steps of the Start Here assignment to get these points.

Pre-Class Essentials with Katie (3%). There will be one assignment per week to help prepare you for the topics of the week. These will consist of a video or reading and a short quiz.

• Your Pre-Class Essentials with Katie grade will be calculated from the best 9 assignments

Pre-Class Essentials with Perusall (4%) is a platform where you can access the textbook and annotate it. Students will be divided in small groups and you can see each other’s annotations. You can also ask questions to the other students in your group and you can answer questions from others.

Each week there will be an assignment to help you prepare for lectures. You will be graded on your comments and interactions:

• You need to write at least 5 comments, and each comment is graded according to its quality

• You will get a pass (1) / fail (0) for each assignment (updated after every comment/annotation)

• To get a pass, you need to write 5 quality comments/annotations

•  For the frst 3 Perusall assignments, your scores will be considered“practice”scores that will not count towards your course mark. This is so you can get used to the Perusall scoring. At the end of the term, if some of your “practice”scores are higher than your other scores, your lower scores will be replaced by the“practice”scores  (for up to 3 assignments).

There will be a homework assignment at the end of each week on Mathmatize.

• Your Mathmatize grade will be calculated from the best 9 assignments

There will be one quiz early and one late in the term. The quizzes are mandatory and done online.

During the quiz, you can use online calculators like Desmos or Geogebra, and you can access the textbook and your class notes, but you cannot consult with anybody else or use any other internet resource.

The tentative quiz dates are:

Quiz 1 (9%). Online on October 3.

Quiz 2 (5%). Online on November 28.

Missed Assessment. The petition policy for the course can be found here:

.            .           LW   9   M  0https://formsofficecom/r/pcpwu

The Term Test and the Exam are common to all sections of MAT135 and will primarily consist of problems. Your solutions to these problems will be graded for both correctness and clarity. For many problems, it will not be enough to simply produce a correct fnal answer: you will need to show how you arrived at your answer by providing a complete solution. The questions will be based on the Learning Goals and Objectives given each week.

The tentative test date is:

Term test. on Friday, November 4 at 7–9pm.

Final exam. will be 180 minutes long and will be scheduled during the exam period.

Missed Assessment. If you miss a term test or the fnal assessment, then you must submit the missed test form https://forms.office.com/r/LWpc9pwMu0within 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.

• The University has a policy requiring that students have a U of T email address and that you check it regularly.

•  If you email us from any address other than your @mail.utoronto.ca address, your email will be ignored. We would have no way to confrm your identity.

•  If you have a question about the course policies, check the syllabus. Then check the FAQ on Quercus.

•  If you send us an email, you are communicating with us in a professional context. Emails are not text messages or other social media interactions. Your email should start with a respectful greeting, have organized paragraphs and be signed with your name. We reserve the right to not consider an email that is written unprofessionally. All that said, don’t worry too much about your grammar or spelling – we really do want to help you, however you write!

•  Please do not email your TA unless they specifcally asked you to do so.