false

Review of trigonometric functions, trigonometric identities and trigonometric limits. Functions, limits, continuity. Derivatives, rules of differentiation and implicit differentiation, related rates, higher derivatives, logarithms, exponentials. Trigonometric and inverse trigonometric functions, linear approximations. Mean value theorem, graphing, min-max problems, l‚ÄôH√¥pital‚Äôs rule; anti- derivatives. Examples from life science and physical science applications.

More
Less
Get Access

Available 24 hours after each lecture

Current Study Guide

24HR

Premium

130 views

79 Pages

Fall 2018

Current Lecture

24HR

Premium

MAT135 - Lecture 39 - Antiderivatives For todays Lecture Prepara...

71 views

4 Pages

Fall 2018

MAT135H1: Calculus 1(A)

University of Toronto Fall 2018

The calculus was the ﬁrst achievement of modern mathematics and it is diﬃcult

to overestimate its importance. I think it deﬁnes more unequivocally than anything

else the inception of modern mathematics. – John von Neumann

In the 17th century, two mathematicians – German Gottfried Leibniz and Englishman

Isaac Newton – simultaneously discovered an intimate connection between two seemingly

unrelated problems: measuring changing quantities and ﬁnding areas of curved shapes. This

discovery formed the basis of calculus, a subject which stands as one of the most important

ﬁelds of mathematics today.

Calculus has earned its reputation because it provides us with tools that can be applied

to solve problems in every branch of science that would be impossible to answer without it.

For example, calculus allows us to easily ﬁnd the greatest possible proﬁt or land size under

given conditions, to accurately model how a population grows or a disease spreads, and to

compute quantities like work and centre of mass with ease. Calculus is not only important

for its applications: it is signiﬁcant because it allows us to come to grips with the inﬁnite.

In this class, we will study diﬀerential calculus, the branch of calculus that is motivated

by the problem of measuring how quantities change. We will focus on understanding why the

tools of calculus make sense and how to apply them to the social, biological, and physical

sciences.

Contents

General Course Information 1

What you will learn in MAT135H1 3

Is MAT135H1 the right calculus course for you? 4

Assessment 5

Course Activities 9

Instructors and Teaching Assistants 12

How to Succeed in MAT135 12

Additional Questions & Answers 16

General Course Information

As long as you’re alive, you can always have a new start. I’m not really diﬀer-

ent from anyone else except for my willingness to keep trying. – Carla Cotwright-

Williams

1

Key Dates

Last day to add or make section changes September 19

Thanksgiving (no classes) October 8

Term Test October 17 6:00-8:00 PM

Last day to cancel courses without academic penalty or

change credit / no credit option

November 5

Derivative Computation Quiz November 1–14 (in tutorial)

Fall Reading Week (No classes) November 5-9

Last Day of Classes December 5

Makeup Monday (for missed Thanksgiving classes) December 6

Also see for weeks when the Applied Communication Tasks will be due in tutorials.

Website and Email

The course website is located on Quercus, at q.utoronto.ca. It will contain information and

course resources, including oﬃce hours, tutorial information, homework, assessments, test

review packages, and important announcements.1You are responsible for checking it

daily. We will also send important announcements via Quercus, and recommend that you

update your notiﬁcation settings so that all announcements are emailed to you.

The University has a policy requiring that students have a U of T email address and that

you check it regularly. Instructors and TAs will only respond to emails sent from your oﬃcial

U of T email address, so be sure to use it when communicating with them.

Textbook and Software

The required textbook for MAT135 is Calculus: Single Variable, 7th edition by Hughes-Hallett

et al; it will also be used for MAT136 in the Winter of 2019. This textbook is available in a

package at the U of T Bookstore (214 College Street) in either a physical loose-leaf or enhanced

e-text form; either form is acceptable for the course, but you must use the 7th edition.2Note

that this is a diﬀerent text than what was used last year for MAT135/136.

Graphing will help you check your answers to homework problems and prepare your solu-

tions to the Applied Communication Tasks. The open-source software Geogebra is a good free

option, and will be used by many instructors for in-class demos. You can download it from

www.geogebra.org/download for free. The desktop application ‘GeoGebra Classic’ is the

most versatile option, but there is also a graphing calculator app for mobile devices available.

Your instructor might ask you to bring a laptop of phone with the app to class.

Finally, all lecture sections will be using the classroom response system Top Hat to record

votes to in-class questions. If you are taking MAT136 next semester or other courses that

use Top Hat, you should sign-up for a year-long subscription as it is more cost eﬀective than

purchasing it term-by-term. For sign-up instructions and codes, see the Top Hat instructions

posted on the course website.

1Quercus is the UofT name for Canvas; if you need help with a topic related to Quercus, you should do a

search for Canvas.

2We recommend the physical, loose-leaf copy but know that many students prefer to have an electronic

copy.

2

What you will learn in MAT135H1

There is a diﬀerence between not knowing and not knowing yet. –Sheila Tobias

Learning Goals

By the end of the course, you should be able to:

•understand, use, and translate between multiple representations of functions, limits, and

derivatives

•solve complex and novel problems using tools from calculus

•build a mental framework of calculus that serves as a foundation for future learning

•see yourself as a conﬁdent and capable user and communicator of mathematics

•possess skills and habits for eﬀectively learning math

More speciﬁc Learning Objectives are included on each homework set and tutorial assign-

ment.

Essential Questions

In this course we will address the following questions.

•Why should we represent a single relationship in diﬀerent ways?

•What is inﬁnity? What is an inﬁnitesimal?

•How do we model the real-world with mathematics?

•What is speed, and how do you measure it? What are rates, and how do you measure

them?

•How can you solve novel problems that are unlike any youve encountered before?

•What do good readers and writers of math do?

Course Units

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

below.

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

§1.1–1.6

2. Limits: How do we work with the inﬁnitely small and the inﬁnitely large? §2.1; §1.7–1.9

3. The Derivative: In what diﬀerent ways can rates of change be represented? How are

rates of change described and used? §2.2–2.6

3

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

5. Using the Derivative: How can we use the derivative to solve complex problems from

the sciences? §3.9; §4.1–4.4; §4.6–4.7

6. The Area Problem: How is the rate of change problem related to the area problem?

§5.1–5.3

Is MAT135H1 the right calculus course for you?

Math is a human activity that every sort of people, at one time or another in

history, has engaged in. – Fern Hunt

Are you prepared for MAT135H1?

Research has shown that 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 calculus.3Recent research shows that “success in calculus... comes from having a

strong foundation.”4Algebra and functions are two important tools that you will use every

day in calculus, and being able to work with them accurately and eﬃciently will make it much

easier to tackle calculus.

The prerequisite for MAT135H1 is high school level Calculus. This prerequisite is intended

to ensure that you have a strong knowledge of algebra and functions prior to the course. You

do not need to know calculus topics (such as limits, derivatives, and integrals) prior to the

course. To determine if you are ready to take MAT135, it is important for you to review

algebra and functions.

To assess whether you are ready for MAT135, complete the following self-assessments on

the Preparing for Calculus website at http://www.math.toronto.edu/preparing-for-calculus/:

•Algebra

•Inequalities & Absolute Values

•Functions, Inverses, Exponentials, & Log-

arithms

•Polynomials and Factoring

•Graphing

•Geometry

•Trigonometry

This website also contains tutorials and examples related to these topics.

It will be very diﬃcult to work on the review material throughout the semester. If you have

not yet mastered the content on the Preparing for Calculus website, we strongly recommend

that you speak with your advisor about taking calculus after you have had the opportunity

to master precalculus.

3For example, see Algebra and Precalculus Skills and Performance in First-Semester Calculus by Agustin

and Agustin and Teaching Calculus Students How to Study by Boelkins and Pfaﬀ.

4https://news.harvard.edu/gazette/story/2018/07/masters-of-calculus-come-prepared-harvard-study-

shows/

4

Alternative Calculus Courses

MAT135H1 is the ﬁrst in the sequence of calculus courses for students intending to major in

science, and is the prerequisite for MAT136H1. Other calculus courses oﬀered by the Faculty

of Arts & Sciences include MAT133Y1, MAT137Y1, and MAT157Y1.

•MAT133Y1 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 MAT137Y1 and MAT157Y1 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.

Breadth & Distribution Requirements

This course satisﬁes 0.5 credits of the Science distribution requirement and the Physical and

Mathematical Universe Breadth requirement.

Assessment

While grades are (one) measure of progress, they are not a measure of promise.

–Francis Su

Grading

Your ﬁnal grade will be calculated according to one of the following grading schemes, depend-

ing on which one results in a higher grade

Scheme 1 Scheme 2 Assessment

5% 5% In-Class Responses (Top Hat)

10% 10% WeBWorK Homework

12% 12% Applied Communication Tasks

8% 8% Derivative Computation Quiz

25% 15% Term Test

40% 50% Final Exam

For information about how the percentage grade translates into letter grades and grade

point values, see the grading scale available at

http://www.artsci.utoronto.ca/newstudents/transition/academic/grading

In-Class Responses (Top Hat)

Peer Instruction is one of the activities that we will be doing during lecture. You will be

presented with a conceptual problem – often one that is known to be an area of common

confusion or misunderstanding – and asked to vote on your answer to the question individually.

5

After voting, the class will either discuss (if a clear majority of students gets the correct

answer) or will take a few minutes to discuss the answer with a partner until you arrive at a

consensus.

Research has demonstrated that this technique increases students’ conceptual understand-

ing in calculus, supports better retention of knowledge, increases course satisfaction, makes

students more likely to complete a course, and increases student engagement.

Your participation and responses to questions will be recorded using the classroom re-

sponse system Top Hat. 5% of your ﬁnal course grade will come from your responses to

questions in-class, as recorded in Top Hat. You must attend the section you are enrolled in

for your participation and responses to count; therefore you should ensure that you are

registered in a section that you can attend.

Since you may have legitimate circumstances that prevent you from attending class or

days when you forget to bring technology to class, your participation grade will be rounded

up to 100% for the purposes of your ﬁnal course grade as long as you participate in more

than 80% of classes. (If your participation is between 0% and 80%, it will remain unchanged

in the ﬁnal grade). This generous rounding is meant to account for all excused absences and

technological you may have; no other documentation will be accepted. This also applies to

students who register in the course after the start of the semester; no additional grades will

be dropped for missed classes.

WeBWorK Homework

In order to learn math, you must do math. For each lecture, you will be assigned a homework

set with pre-class reading and problems (to be completed before the lecture), and after-class

problems (to be completed as soon as possible after the lecture).

The pre-class portion of the homework problems will be completed through the online

homework system WeBWorK. It will provide you with instant feedback on how well you have

met pre-class learning goals. Here is some information about using the system:

•The WeBWorK homework problems will be available on Quercus.

•You will have an unlimited number of attempts for each problem.

•WeBWorK sets for your lecture section will be due according to deadlines set by your

instructor; see Quercus for details.

•The ﬁrst WeBWorK set is practice and will be ungraded

•To account for sickness, late course additions, technical problems, or other circumstances

that may prevent you from completing WeBWorK, 20% will be added to your WeBWorK

grade at the end of the term, to a maximum of 100%.

•See How to Enter Answers into WeBWorK, posted on the course website, for additional

information about how to type mathematics notation

•Do not click the ‘Email Instructor’ button on WeBWorK; these emails will automatically

be ﬁltered into our junk mail and not receive a reply.

6

Applied Communication Tasks

Applied Communication Tasks will give you the opportunity to develop and demonstrate

that you have achieved course learning objectives related to communication and application

of calculus. They will help you to develop skill sets that you can use to 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.

ACTs will be due in tutorials, so the exact due date will depend on when you have your

tutorial; the weeks are shown below.

ACT A Draft Sept 21–27

ACT A Final Sept 28–Oct 3

ACT B Draft Oct 11–17

ACT B Final Oct 25–31

ACT C Topic Nov 15–21

ACT C Draft Nov 22–28

ACT C Final Nov 29–Dec 5

You may be required to submit a course assignment to Turnitin.com for a review of

textual similarity and detection of possible plagiarism. In doing so, students will allow their

assignments to be included as source documents in the Turnitin.com reference database, where

they will be used solely for the purpose of detecting plagiarism. The terms that apply to the

Universitys use of the Turnitin.com service are described on the Turnitin.com web site.

Derivative Quiz

While MAT135 is focused primarily on solving problems it is also important that you develop

computational ﬂuency.

Between November 1 and 14, you will write a 30-minute computer-based derivative com-

putation quiz in your tutorial. You must bring a device with you to class that day from which

you can access WeBWorK. A link to practice quizzes will be posted on the course website

ahead of the quiz; you will be able to practice it unlimited times ahead of the in-class quiz.

Your grade will not be recorded if you write it in a section you are not enrolled in.

If you are unable to write the quiz due to sickness or other emergency, your Derivative

Quiz component of your grade will be reallocated to your Final Exam.

Term Test and Final Exam

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 ﬁnal answer: you will

need to show how you arrived at your answer by providing a complete solution. Likewise,

you may still receive partial marks even if you do not arrive at a correct ﬁnal answer but

7

demonstrate an understanding of the key ideas or progress towards the correct answer. Not

all questions will be of equal diﬃculty or be worth the same number of points. There will also

be some questions that do not require an explanation, such as true/false or multiple choice

questions. When an explanation is not required, it will be clearly marked in the problem.

The questions on the Term Test will be based on the Learning Goals and Objectives given

on each homework set. 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: as instructors, we would be delighted if the average was “high” and a

large portion of our students displayed mastery of the content! Since we are measuring your

performance against these set criteria, we will not be releasing average grades or other infor-

mation about how the class as a whole performs. According to Dr. Jay Parkes, an renowned

expert in college assessment “releasing class-level performance data is not only irrelevant but

it draws students’ focus away from their individual mastery of learning objectives to how their

mastery compares to others.”

Term Test and Exam cover sheets and sample problems will be posted prior to the test

so that you can familiarize yourself with the speciﬁc instructions and style of problems. The

sample problems posted will be more indicative of what you can expect on the Term Test

and the Exam than MAT135 exams from Fall terms prior to 2017. Further details on the

administration of these assessments will be given in lectures.

Academic Integrity

Academic integrity is fundamental to learning and scholarship at the University of Toronto

and beyond. Participating honestly, respectfully, responsibly, and fairly in this academic

community ensures that the U of T degree that you earn will be valued as a true indication of

your individual academic achievement, and will continue to receive the respect and recognition

it deserves. Violating standards of academic integrity will prevent you from learning material,

reﬁning your problem-solving skills, and developing self-suﬃciency and self-esteem.

The MAT135 instructors and TAs are strongly committed to assigning grades based on

our students’ honest eﬀorts to demonstrate learning in this course. Academic dishonesty in

any form will thus not be tolerated in this course.

Students are expected to know what constitutes academic integrity: familiarize yourself

with the information available at (http://www.artsci.utoronto.ca/osai/students). It is

the rule book for academic behaviour at the U of T. Potential oﬀences include, but are not

limited to:

•Bringing notes or hints into a term test, quiz, or exam, including notes on your hand or

on a piece of paper

•Having another student write a term test, quiz, or exam for you, or impersonating

someone else in writing one of these assessments

•Allowing someone else to complete your WeBWorK homework problems, or completing

it for someone else

•Falsifying Applied Communication Task records or taking unattributed text from some-

where else

8

•Replying to Top Hat questions remotely

•Looking at someone else’s answers on a test or exam

•Communicating with another student during a quiz, term test, or exam

•Submitting fraudulent medical notes

•Misrepresenting reasons for being late or absent for a term test, quiz, or exam

•Submitting an altered test or assignment for re-grading

•Violating test, exam, or quiz procedures

The following actions are not oﬀences in this class.

•Discussing questions from homework with classmates, building oﬀ of each others’ ideas

•Using online resources to help you understand the content of the course or homework

problems

In accordance with the University’s Code of Behaviour on Academic Matters, we will

actively investigate any suspected cheating, plagiarism, misrepresentation or other dishonest

practices. The consequences for academic misconduct can be severe, including a failure in the

course, a notation on your transcript, suspension, and expulsion.

If you have any questions about what is or is not permitted in this course, please do not

hesitate to contact your instructor or TA. Students are usually reluctant to report incidents

of academic dishonesty. As we are working together to preserve the fairness of this course, we

encourage you to let us know (anonymously, if necessary) if you observe behaviour that you

feel might be unethical. Your name will be held in conﬁdence.

Grading

We will be using the platform CrowdMark for grading in MAT135. Using this platform helps

increase fairness and eﬃciency. When an assignment has been graded you will receive a URL

via email where you can view your original assignment and the grader’s comments and grades.

All grading is done by TAs and instructors in MAT135.

Course Activities

You have to spend some energy and eﬀort to see the beauty of math. - Maryam

Mirzakhani

Preparing for Class

The homework for each class will consist of readings and several problems.

Your personal notes on the assigned readings and problems should contain enough detail

to be easily understood by you at a later time. For example, you will want to refer to these

problems when preparing for the Term Test, and the Final Exam. While you do not need to

write your solutions in complete sentences, they should be easy to follow and clear.

9

Reading

You will be assigned readings to prepare for each lecture. Lectures will help to clarify im-

portant or confusing parts of the reading, but will not recap every aspect of the reading.

Completing the reading before each lecture is important to fully beneﬁt from lectures.

Why should you read before class rather than after class or when you are studying for an

exam? It leaves room during the lecture for the most important learning activities. 36 hours

is not enough time to cover all of calculus in depth. By coming to a lecture with a basic

understanding of the material, you will be able to focus on the big questions that are diﬃcult

to learn on your own, such as how the content ﬁts into the broader narrative of calculus,

points that students typically ﬁnd confusing, and common misconceptions.

The ability to understand mathematical texts is an important skill for any future mathe-

matical study. This skill is vital for at least three reasons.

1. Future Learning. When you need to learn a mathematical concept on your own, your

main resources will be written.

2. Eﬃciency. In an ideal world we might try to discover mathematics itself, but this

would be impractical. Calculus, for example, took hundreds of years to develop and

another 200 years to gain a ﬁrm footing. The great abundance of mathematical writing

available allows us to learn from the experts.

3. Learning to Communicate. Just as reading many stories makes you a better story-

teller, reading a lot of mathematics makes you a better mathematical communicator.

Additional tips for getting the most out of reading your math textbook are posted on the

course website.

Problems

Problem solving is at the heart of mathematics, and allows us to apply our knowledge of math

to science, social science, and beyond. Developing problem solving skills is just as important

as the content that we will be covering, and can be used as you work through courses in any

major or pursue any profession. Throughout this course, you can expect to encounter many

unfamiliar problems from math and beyond, and it won’t always be clear right away how to

apply the course content to solve these problems.

The problems on homework will be of varying diﬃculty: some will be easy warm-ups to

the reading or simple computations, while others will involve complex situations and require

problem solving skills. The pre-class portion of the homework will be completed and submitted

via WeBWorK; the after-class portion of the homework will not be collected but form a vital

part of your learning. Solutions to the problems will be available on the course website

approximately one week after the assignment is completed.

Lectures

You will attend three hours of lecture each week of the course. Each lecture is taught by a

course instructor.

10

The lectures of this course will support your learning of calculus in a number of ways.

During lectures, we will motivate new material, clarify diﬃcult concepts, test your under-

standing of calculus prior to the major assessments, and give you the opportunity to meet

with fellow students. You should come prepared to not only hear about math during lectures,

but to think and engage with math. While your instructor will use some of the lecture time

to explain the material, you may also be expected to actively engage in learning by working

on problems, discussing ideas with your fellow students, and sharing your thinking with the

class.

The more you prepare for and engage in class, the more you will get out of it. The following

are basic guidelines for ensuring that you and your classmates get the most out of class.

•Be sure not to speak when someone else is speaking during class. While it might seem

as though no one notices, even one person whispering in the back of the classroom

can be a signiﬁcant distraction for the entire class, and can side-track learning. If you

have a question about the class, pose the question to the entire class - not just to your

neighbour.

•Please be on time to class. Coming in late means that you may miss important infor-

mation and it disrupts the learning of other students.

•Likewise, do not leave late at the end of class or pack up before class has ended. If you

must leave one class early for an appointment or other special commitment, sit near the

door to minimize disruptions.

•Bring pencils, paper, textbook, a scientiﬁc calculator, and a device to connect to Top

Hat to every class.

•If you use technology during class, make sure that it is always for an in-course use.

While it may seem harmless to check your email or a game update, it can be distracting

for students around you; research has demonstrated that the learning of students who

can see the laptop of another person engaging in oﬀ-task behaviour is damaged.

Tutorials

Each week, you will attend one tutorial, a class of about 30 students from across MAT135H1

lecture sections. The purpose of tutorials is to improve your problem-solving and communica-

tion skills, and to provide you opportunities to collaborate with other students. You will also

be submitting and working on components of Applied Communication Tasks during tutorials.

Also be aware that tutorials take priority over other tests, so you should not skip your tutorial

to attend a test in another course.

Each tutorial is 50 minutes, starting at 10 minutes past the hour and ending on the hour.

Tutorials will begin on Thursday, September 13. Be aware that tutorials take priority

over other tests, so you should not skip your tutorial to attend a test in another course. If you

need to miss a tutorial due to illness or another emergency, you do not need to notify your

Teaching Assistant. If you miss a tutorial where you are supposed to submit a component

of an Applied Communication Task, you must attach oﬃcial documentation verifying your

absence to your assignment submission in the next tutorial.

If you are more than 20 minutes late for a tutorial, you will not be permitted to submit

assignments due in tutorials.

11

Instructors and Teaching Assistants

Instead of looking around and worrying about how many students are ‘better’

than you, why not look around for someone you can help pull up? –Karen E. Smith

Instructors

The instructors for MAT135 are shown below. Before emailing us, be sure to check the

guidelines for asking questions at the end of this syllabus. In particular, note that instructors

and TAs will not answer questions about course content or questions that can be answered

by reading the syllabus via email; such inquiries will be deleted without response.

You are expected to treat all members of the instructional team with respect. Examples

of disrespectful behaviour are speaking over someone, using inappropriate language, leaving

a tutorial early, or arriving late.

Instructor Email Section(s)

Dr. Su LEC0601

Teaching Assistants

Teaching Assistants (‘TAs’ for short) are an important part of the teaching team for MAT135H1.

TAs are advanced undergraduate or graduate students who are experienced in calculus. They

play a number of roles, including:

•leading tutorials

•grading assessments

•answering questions in the Math Aide Centre

How to Succeed in MAT135

In math we have to look at a problem from all directions. If one approach isn’t

working, then we try another. If the problem is too hard, we ﬁnd a simpler problem

and then come back to the more diﬃcult one after we’ve solved the ﬁrst. Every

mathematician hits a wall at some point. You have to learn how to get around it,

how to keep working on challenging things. Those are all skills that transfer to

real life. –Rebekah Yates

12

Top 10 Tips for Success in MAT135

1. Work with other students and talk about calculus with them

2. Do many problems, and focus on why a solution works rather than the ﬁnal answer

3. After every lecture or tutorial, take 30 seconds to summarize what you have learned

4. Read the assigned textbook reading before coming to class and keep up on the assigned

problems

5. Instead of re-reading, test yourself on the material by solving additional problems and

by explaining it to someone else

6. Use examples as a road map: rather than focusing on the individual steps, think about

how they are connected to the overall goal of the problem

7. ‘Interleave’ your practice: mix up the types of problems, solutions, and approaches as

you review rather than only reviewing one section at a time.

8. Do not ‘cram’: complete reading and homework when they are assigned

9. Think in class: don’t be a passive listener

10. Use the free resources available to you as a student of University of Toronto (see the

Resources section of this syllabus)

How to improve your problem-solving skills

The key to improving your problem solving skills is to work through many problems. When

faced with a new problem, resist the temptation to immediately search the textbook or the

web for a similar problem. Instead, start by asking yourself what you know and identifying

what the goal of solving the problem is. Problem-solving is all about ﬁnding a path between

what you know and what you want to know, and developing strategies to build this path

is a key to success. You will be discussing speciﬁc problem solving strategies during many

tutorials.

Working with your classmates can be very valuable in getting past roadblocks and im-

proving your problem-solving skills. Simply discussing a problem with someone else can help

you better understand the problem and a solution. Remember that the process of solving the

problem is more important than the answer.

How to get the most from lectures

During classes, you may be asked to participate in tasks like thinking about problems, talking

to other students, writing a solution, or explaining a concept to the class. By approaching

these activities with enthusiasm and doing your best, you will not only help your own learning

but also the learning of those around you. In a large class, it is easy to feel as though you

are just one in a crowd and that what you do is not noticed by anyone else. However, if you

change perspectives and think about how you have been inﬂuenced by others in large groups

you’ll see this isn’t true: you notice your neighbour browsing the internet on their laptops,

13

are distracted by loud coughing ﬁt or cellphone reminder, wonder what a whispering group

of people across the room is talking about, or look over when you hear someone packing their

bags up. You’ve probably also experienced the eﬀect of small behaviours spreading in a crowd.

When you return to thinking about your own behaviour, you should be able to see why what

you do matters to others.

Creating a positive learning environment requires the participation of everyone involved.

Your instructor will set a structure and activities to help you learn calculus well. By actively

engaging in course activities and working with your classmates, you will not only help your

own learning but theirs’ as well.

How to use assessments for learning

The Term Test and the Final Exam will help to accomplish the Learning Goals of this course

in several ways. For example, they will:

•Encourage you to push yourself to understand diﬃcult concepts and to complete many

challenging problems

•Help you identify areas where your knowledge and problem solving skills are already

strong, and where you still have room to grow

•Work with others to deepen your understanding

•Ensure that you have the necessary foundation for building on your knowledge in

MAT135, MAT136, and in courses that require calculus as a prerequisite

There are 3 important phases of the test-learning cycle. They apply to any assessment.

1. Preparation:All learning activities that you engage in prior to the assessment fall

into this category, including reading, completing problems, preparing for and attending

lectures and tutorials, working with other students, and reviewing past assessments. It

also includes ways of preparing yourself to take a test, such as getting a good night’s

sleep, scheduling meals and snacks so that you aren’t hungry during the test, and exer-

cising so that you have the energy that you need.

2. Performance: This is what comes to mind when we think of ‘taking a test’ or ‘complet-

ing an assignment’. Make sure that you think about what the test-taking environment

will be like and incorporate that into your practice. For example, if you usually study

while lying down or with music in the background try to do some practice in a silent

environment in a chair similar to that you will be in during the test.

3. Reﬂection: An assessment isn’t over when you hand it in! Write some quick notes to

yourself about what went well, what didn’t go well, and what topics you need to review.

Once you receive your test back, review your solutions along with the feedback you

received and sample solutions and develop a strategy for better learning the material.

There is always room for improvement.

Where to ﬁnd support

There are several free sources of support available to help you learn calculus.

14

Working with Peers

One of the best ways to learn math is to work with other students. This will give you the

opportunity to explain and talk about mathematical concepts, check your own understanding

and avoid overconﬁdence, and get diﬀerent perspectives on the course material. To make

group study sessions eﬀective, be sure that you discuss how problems are solved or why a

solution makes sense, rather than just trading ﬁnal answers.

It is useful to develop a network of diﬀerent students to work with: don’t be afraid to

introduce yourself to others in your class or tutorial sessions and ask if you can trade contact

information. It might take several tries to ﬁnd a study group that works for you, and you

might ﬁnd a variety of study groups successful.

Recognized Study Groups

The Recognized Study Groups Program can help you join or start a study group. It provides

a regular study time, gives you the opportunity to meet people from across the University,

and you can even receive a co-curricular credit for participating.

Instructor Oﬃce Hours

An ‘oﬃce hour’ refers to a period of time (usually 50 minutes or one hour) that an instructor

is available to discuss course content and answer questions. In MAT135, these will be ‘drop-in

hours’.

You may attend the oﬃce hours of any instructor in the course. If they are speaking with

another student, feel free to come in and listen. You do not need to make an appointment,

but please come to oﬃce hours prepared with questions, your notes, textbook, and any other

materials you might need.

See the course website for oﬃce hour locations and times.

Math Aid Centres

The main Math Aid Centre is located in the Physical Geography building (PG), Room 101.

During times listed on the Oﬃce Hour Calendar, TAs for MAT135 will hold oﬃce hours there.

We encourage you to also use the Math Aid Centre to work with other students in the course

and to meet new classmates. When you come to the Math Aid Centre, please bring speciﬁc

questions, your textbook, homework assignments, and any other material you may want to

refer to. If the TA is speaking with another student, please join them at the table and listen

to the discussion.

College-speciﬁc Math Aid centres are also available at several Colleges. See http://www.

math.utoronto.ca/cms/math-aid-centres/ for more information.

The schedule for Math Aid Centre oﬃce hours will be posted online, with the other oﬃce

hours of the course.

Academic Success Centre

The Academic Success Centre oﬀers a wide variety of services and programming to help

students meet their academic and personal goals at the University. Individualized learning

skills consultations are available by appointment, or on a ﬁrst-come, ﬁrst-served basis for

15

drop-in visitors. You can reserve private study space, attend workshops and lectures related to

academic success, or consult their library of helpful publications about best learning practices.

More information can be found on their website, https://www.studentlife.utoronto.ca/

asc.

Additional Support Services

Other free support services, such as English Language Learning programs and College-Speciﬁc

Resources can be found at uoft.me/freeresources.

Additional Questions & Answers

If you want to know, you ask the question. There’s no such thing as a dumb

question. It’s dumb if you don’t ask it. –Katherine Johnson

What should I do if I require an academic accommodation?

The University provides academic accommodations for students with disabilities in accordance

with the terms of the Ontario 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 Universitys courses and programs.

If you have a learning need requiring an accommodation, immediately register at Accessi-

bility Services at http://www.accessibility.utoronto.ca/Home.htm. You can also register

online at https://www.studentlife.utoronto.ca/as/new-registration.

Can I record the lectures that I attend or share course materials?

Course materials are provided for the use of enrolled students only and that registered students

are not allowed to post, share, or sell course materials without written permission of both the

Instructor and the Course Coordinator.

If a student wishes to tape-record, photograph, video-record, take pictures of, or oth-

erwise reproduce lecture presentations, course notes or other similar materials provided by

instructors, he or she must obtain the instructor’s written consent beforehand. Otherwise all

such reproduction is an infringement of copyright and is absolutely prohibited. In the case

of private use by students with disabilities, the instructors consent will not be unreasonably

withheld.

For more information on copyright and the University of Toronto, please visit the copyright

page at https://onesearch.library.utoronto.ca/copyright/copyright.

What if I have a scheduling conﬂict with the Term Test, or I get sick?

Instructions will be posted on the course website prior to the Term Test; do not inquire before

these are posted.

16

If I have a question about the course, who should I ask?

First, make sure that your question has not been answered in this syllabus, on the course

website, or in class. You should start by asking your classmates to ensure that your question

has not yet been answered. Instructors and TAs will not answer questions about the

content of the course (‘math questions’) via email. If you have a math question for an

instructor or TA, you should attend an oﬃce hour, or take advantage of other resources for

learning on campus.

If you send an email about the course, you must use your U of T email address, as your

instructors will not communicate information about the course to other addresses.

•Questions speciﬁc to your section should be sent to your instructor.

•Questions related to MAT135 as a whole (including tutorials and assessments) may be

directed to [email protected]to.edu. This address will be checked 2-3 times a week,

and inquiries directed to it will be forwarded to the appropriate contact. Note that:

–Inquiries about registration in lecture sections or tutorial sections cannot be an-

swered by the MAT135 instructional team (registration is done centrally through

the Registrar’s Oﬃce).

–Initial regrading requests for the midterm must be submitted through the process

announced following the Term Test; appeals of regrading decisions may be sent to

the administrative email.

–We will not answer questions addressed in the Syllabus or on the course website.

•Teaching Assistants do not answer any inquiries via email.

You do not need to email your TA or instructor if you miss a tutorial or lecture.

Remember that you should always be respectful in your speaking and actions. When

in doubt about how you should speak, write, or act, always err on the side of formality.

You will never oﬀend or annoy someone by being overly formal or polite. The University is

a professional environment, and that when you send emails you must be professional. For

example, you must be polite and use proper grammar and should begin an email with “Dear

Professor ” rather than “Hi”.

This is not the end or the beginning of the end, but it is the end of the beginning.

–Winston Churchill

17

Current Study Guide

24HR

Premium

132 views

67 Pages

Fall 2018

Current Lecture

24HR

Premium

Lecture 26

58 views

11 Pages

Fall 2018

MAT135H1: Calculus 1(A)

University of Toronto Fall 2018

The calculus was the ﬁrst achievement of modern mathematics and it is diﬃcult

to overestimate its importance. I think it deﬁnes more unequivocally than anything

else the inception of modern mathematics. – John von Neumann

In the 17th century, two mathematicians – German Gottfried Leibniz and Englishman

Isaac Newton – simultaneously discovered an intimate connection between two seemingly

unrelated problems: measuring changing quantities and ﬁnding areas of curved shapes. This

discovery formed the basis of calculus, a subject which stands as one of the most important

ﬁelds of mathematics today.

Calculus has earned its reputation because it provides us with tools that can be applied

to solve problems in every branch of science that would be impossible to answer without it.

For example, calculus allows us to easily ﬁnd the greatest possible proﬁt or land size under

given conditions, to accurately model how a population grows or a disease spreads, and to

compute quantities like work and centre of mass with ease. Calculus is not only important

for its applications: it is signiﬁcant because it allows us to come to grips with the inﬁnite.

In this class, we will study diﬀerential calculus, the branch of calculus that is motivated

by the problem of measuring how quantities change. We will focus on understanding why the

tools of calculus make sense and how to apply them to the social, biological, and physical

sciences.

Contents

General Course Information 1

What you will learn in MAT135H1 3

Is MAT135H1 the right calculus course for you? 4

Assessment 5

Course Activities 9

Instructors and Teaching Assistants 12

How to Succeed in MAT135 12

Additional Questions & Answers 16

General Course Information

As long as you’re alive, you can always have a new start. I’m not really diﬀer-

ent from anyone else except for my willingness to keep trying. – Carla Cotwright-

Williams

1

Key Dates

Last day to add or make section changes September 19

Thanksgiving (no classes) October 8

Term Test October 17 6:00-8:00 PM

Last day to cancel courses without academic penalty or

change credit / no credit option

November 5

Derivative Computation Quiz November 1–14 (in tutorial)

Fall Reading Week (No classes) November 5-9

Last Day of Classes December 5

Makeup Monday (for missed Thanksgiving classes) December 6

Also see for weeks when the Applied Communication Tasks will be due in tutorials.

Website and Email

The course website is located on Quercus, at q.utoronto.ca. It will contain information and

course resources, including oﬃce hours, tutorial information, homework, assessments, test

review packages, and important announcements.1You are responsible for checking it

daily. We will also send important announcements via Quercus, and recommend that you

update your notiﬁcation settings so that all announcements are emailed to you.

The University has a policy requiring that students have a U of T email address and that

you check it regularly. Instructors and TAs will only respond to emails sent from your oﬃcial

U of T email address, so be sure to use it when communicating with them.

Textbook and Software

The required textbook for MAT135 is Calculus: Single Variable, 7th edition by Hughes-Hallett

et al; it will also be used for MAT136 in the Winter of 2019. This textbook is available in a

package at the U of T Bookstore (214 College Street) in either a physical loose-leaf or enhanced

e-text form; either form is acceptable for the course, but you must use the 7th edition.2Note

that this is a diﬀerent text than what was used last year for MAT135/136.

Graphing will help you check your answers to homework problems and prepare your solu-

tions to the Applied Communication Tasks. The open-source software Geogebra is a good free

option, and will be used by many instructors for in-class demos. You can download it from

www.geogebra.org/download for free. The desktop application ‘GeoGebra Classic’ is the

most versatile option, but there is also a graphing calculator app for mobile devices available.

Your instructor might ask you to bring a laptop of phone with the app to class.

Finally, all lecture sections will be using the classroom response system Top Hat to record

votes to in-class questions. If you are taking MAT136 next semester or other courses that

use Top Hat, you should sign-up for a year-long subscription as it is more cost eﬀective than

purchasing it term-by-term. For sign-up instructions and codes, see the Top Hat instructions

posted on the course website.

1Quercus is the UofT name for Canvas; if you need help with a topic related to Quercus, you should do a

search for Canvas.

2We recommend the physical, loose-leaf copy but know that many students prefer to have an electronic

copy.

2

What you will learn in MAT135H1

There is a diﬀerence between not knowing and not knowing yet. –Sheila Tobias

Learning Goals

By the end of the course, you should be able to:

•understand, use, and translate between multiple representations of functions, limits, and

derivatives

•solve complex and novel problems using tools from calculus

•build a mental framework of calculus that serves as a foundation for future learning

•see yourself as a conﬁdent and capable user and communicator of mathematics

•possess skills and habits for eﬀectively learning math

More speciﬁc Learning Objectives are included on each homework set and tutorial assign-

ment.

Essential Questions

In this course we will address the following questions.

•Why should we represent a single relationship in diﬀerent ways?

•What is inﬁnity? What is an inﬁnitesimal?

•How do we model the real-world with mathematics?

•What is speed, and how do you measure it? What are rates, and how do you measure

them?

•How can you solve novel problems that are unlike any youve encountered before?

•What do good readers and writers of math do?

Course Units

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

below.

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

§1.1–1.6

2. Limits: How do we work with the inﬁnitely small and the inﬁnitely large? §2.1; §1.7–1.9

3. The Derivative: In what diﬀerent ways can rates of change be represented? How are

rates of change described and used? §2.2–2.6

3

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

5. Using the Derivative: How can we use the derivative to solve complex problems from

the sciences? §3.9; §4.1–4.4; §4.6–4.7

6. The Area Problem: How is the rate of change problem related to the area problem?

§5.1–5.3

Is MAT135H1 the right calculus course for you?

Math is a human activity that every sort of people, at one time or another in

history, has engaged in. – Fern Hunt

Are you prepared for MAT135H1?

Research has shown that 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 calculus.3Recent research shows that “success in calculus... comes from having a

strong foundation.”4Algebra and functions are two important tools that you will use every

day in calculus, and being able to work with them accurately and eﬃciently will make it much

easier to tackle calculus.

The prerequisite for MAT135H1 is high school level Calculus. This prerequisite is intended

to ensure that you have a strong knowledge of algebra and functions prior to the course. You

do not need to know calculus topics (such as limits, derivatives, and integrals) prior to the

course. To determine if you are ready to take MAT135, it is important for you to review

algebra and functions.

To assess whether you are ready for MAT135, complete the following self-assessments on

the Preparing for Calculus website at http://www.math.toronto.edu/preparing-for-calculus/:

•Algebra

•Inequalities & Absolute Values

•Functions, Inverses, Exponentials, & Log-

arithms

•Polynomials and Factoring

•Graphing

•Geometry

•Trigonometry

This website also contains tutorials and examples related to these topics.

It will be very diﬃcult to work on the review material throughout the semester. If you have

not yet mastered the content on the Preparing for Calculus website, we strongly recommend

that you speak with your advisor about taking calculus after you have had the opportunity

to master precalculus.

3For example, see Algebra and Precalculus Skills and Performance in First-Semester Calculus by Agustin

and Agustin and Teaching Calculus Students How to Study by Boelkins and Pfaﬀ.

4https://news.harvard.edu/gazette/story/2018/07/masters-of-calculus-come-prepared-harvard-study-

shows/

4

Alternative Calculus Courses

MAT135H1 is the ﬁrst in the sequence of calculus courses for students intending to major in

science, and is the prerequisite for MAT136H1. Other calculus courses oﬀered by the Faculty

of Arts & Sciences include MAT133Y1, MAT137Y1, and MAT157Y1.

•MAT133Y1 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 MAT137Y1 and MAT157Y1 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.

Breadth & Distribution Requirements

This course satisﬁes 0.5 credits of the Science distribution requirement and the Physical and

Mathematical Universe Breadth requirement.

Assessment

While grades are (one) measure of progress, they are not a measure of promise.

–Francis Su

Grading

Your ﬁnal grade will be calculated according to one of the following grading schemes, depend-

ing on which one results in a higher grade

Scheme 1 Scheme 2 Assessment

5% 5% In-Class Responses (Top Hat)

10% 10% WeBWorK Homework

12% 12% Applied Communication Tasks

8% 8% Derivative Computation Quiz

25% 15% Term Test

40% 50% Final Exam

For information about how the percentage grade translates into letter grades and grade

point values, see the grading scale available at

http://www.artsci.utoronto.ca/newstudents/transition/academic/grading

In-Class Responses (Top Hat)

Peer Instruction is one of the activities that we will be doing during lecture. You will be

presented with a conceptual problem – often one that is known to be an area of common

confusion or misunderstanding – and asked to vote on your answer to the question individually.

5

After voting, the class will either discuss (if a clear majority of students gets the correct

answer) or will take a few minutes to discuss the answer with a partner until you arrive at a

consensus.

Research has demonstrated that this technique increases students’ conceptual understand-

ing in calculus, supports better retention of knowledge, increases course satisfaction, makes

students more likely to complete a course, and increases student engagement.

Your participation and responses to questions will be recorded using the classroom re-

sponse system Top Hat. 5% of your ﬁnal course grade will come from your responses to

questions in-class, as recorded in Top Hat. You must attend the section you are enrolled in

for your participation and responses to count; therefore you should ensure that you are

registered in a section that you can attend.

Since you may have legitimate circumstances that prevent you from attending class or

days when you forget to bring technology to class, your participation grade will be rounded

up to 100% for the purposes of your ﬁnal course grade as long as you participate in more

than 80% of classes. (If your participation is between 0% and 80%, it will remain unchanged

in the ﬁnal grade). This generous rounding is meant to account for all excused absences and

technological you may have; no other documentation will be accepted. This also applies to

students who register in the course after the start of the semester; no additional grades will

be dropped for missed classes.

WeBWorK Homework

In order to learn math, you must do math. For each lecture, you will be assigned a homework

set with pre-class reading and problems (to be completed before the lecture), and after-class

problems (to be completed as soon as possible after the lecture).

The pre-class portion of the homework problems will be completed through the online

homework system WeBWorK. It will provide you with instant feedback on how well you have

met pre-class learning goals. Here is some information about using the system:

•The WeBWorK homework problems will be available on Quercus.

•You will have an unlimited number of attempts for each problem.

•WeBWorK sets for your lecture section will be due according to deadlines set by your

instructor; see Quercus for details.

•The ﬁrst WeBWorK set is practice and will be ungraded

•To account for sickness, late course additions, technical problems, or other circumstances

that may prevent you from completing WeBWorK, 20% will be added to your WeBWorK

grade at the end of the term, to a maximum of 100%.

•See How to Enter Answers into WeBWorK, posted on the course website, for additional

information about how to type mathematics notation

•Do not click the ‘Email Instructor’ button on WeBWorK; these emails will automatically

be ﬁltered into our junk mail and not receive a reply.

6

Applied Communication Tasks

Applied Communication Tasks will give you the opportunity to develop and demonstrate

that you have achieved course learning objectives related to communication and application

of calculus. They will help you to develop skill sets that you can use to 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.

ACTs will be due in tutorials, so the exact due date will depend on when you have your

tutorial; the weeks are shown below.

ACT A Draft Sept 21–27

ACT A Final Sept 28–Oct 3

ACT B Draft Oct 11–17

ACT B Final Oct 25–31

ACT C Topic Nov 15–21

ACT C Draft Nov 22–28

ACT C Final Nov 29–Dec 5

You may be required to submit a course assignment to Turnitin.com for a review of

textual similarity and detection of possible plagiarism. In doing so, students will allow their

assignments to be included as source documents in the Turnitin.com reference database, where

they will be used solely for the purpose of detecting plagiarism. The terms that apply to the

Universitys use of the Turnitin.com service are described on the Turnitin.com web site.

Derivative Quiz

While MAT135 is focused primarily on solving problems it is also important that you develop

computational ﬂuency.

Between November 1 and 14, you will write a 30-minute computer-based derivative com-

putation quiz in your tutorial. You must bring a device with you to class that day from which

you can access WeBWorK. A link to practice quizzes will be posted on the course website

ahead of the quiz; you will be able to practice it unlimited times ahead of the in-class quiz.

Your grade will not be recorded if you write it in a section you are not enrolled in.

If you are unable to write the quiz due to sickness or other emergency, your Derivative

Quiz component of your grade will be reallocated to your Final Exam.

Term Test and Final Exam

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 ﬁnal answer: you will

need to show how you arrived at your answer by providing a complete solution. Likewise,

you may still receive partial marks even if you do not arrive at a correct ﬁnal answer but

7

demonstrate an understanding of the key ideas or progress towards the correct answer. Not

all questions will be of equal diﬃculty or be worth the same number of points. There will also

be some questions that do not require an explanation, such as true/false or multiple choice

questions. When an explanation is not required, it will be clearly marked in the problem.

The questions on the Term Test will be based on the Learning Goals and Objectives given

on each homework set. 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: as instructors, we would be delighted if the average was “high” and a

large portion of our students displayed mastery of the content! Since we are measuring your

performance against these set criteria, we will not be releasing average grades or other infor-

mation about how the class as a whole performs. According to Dr. Jay Parkes, an renowned

expert in college assessment “releasing class-level performance data is not only irrelevant but

it draws students’ focus away from their individual mastery of learning objectives to how their

mastery compares to others.”

Term Test and Exam cover sheets and sample problems will be posted prior to the test

so that you can familiarize yourself with the speciﬁc instructions and style of problems. The

sample problems posted will be more indicative of what you can expect on the Term Test

and the Exam than MAT135 exams from Fall terms prior to 2017. Further details on the

administration of these assessments will be given in lectures.

Academic Integrity

Academic integrity is fundamental to learning and scholarship at the University of Toronto

and beyond. Participating honestly, respectfully, responsibly, and fairly in this academic

community ensures that the U of T degree that you earn will be valued as a true indication of

your individual academic achievement, and will continue to receive the respect and recognition

it deserves. Violating standards of academic integrity will prevent you from learning material,

reﬁning your problem-solving skills, and developing self-suﬃciency and self-esteem.

The MAT135 instructors and TAs are strongly committed to assigning grades based on

our students’ honest eﬀorts to demonstrate learning in this course. Academic dishonesty in

any form will thus not be tolerated in this course.

Students are expected to know what constitutes academic integrity: familiarize yourself

with the information available at (http://www.artsci.utoronto.ca/osai/students). It is

the rule book for academic behaviour at the U of T. Potential oﬀences include, but are not

limited to:

•Bringing notes or hints into a term test, quiz, or exam, including notes on your hand or

on a piece of paper

•Having another student write a term test, quiz, or exam for you, or impersonating

someone else in writing one of these assessments

•Allowing someone else to complete your WeBWorK homework problems, or completing

it for someone else

•Falsifying Applied Communication Task records or taking unattributed text from some-

where else

8

•Replying to Top Hat questions remotely

•Looking at someone else’s answers on a test or exam

•Communicating with another student during a quiz, term test, or exam

•Submitting fraudulent medical notes

•Misrepresenting reasons for being late or absent for a term test, quiz, or exam

•Submitting an altered test or assignment for re-grading

•Violating test, exam, or quiz procedures

The following actions are not oﬀences in this class.

•Discussing questions from homework with classmates, building oﬀ of each others’ ideas

•Using online resources to help you understand the content of the course or homework

problems

In accordance with the University’s Code of Behaviour on Academic Matters, we will

actively investigate any suspected cheating, plagiarism, misrepresentation or other dishonest

practices. The consequences for academic misconduct can be severe, including a failure in the

course, a notation on your transcript, suspension, and expulsion.

If you have any questions about what is or is not permitted in this course, please do not

hesitate to contact your instructor or TA. Students are usually reluctant to report incidents

of academic dishonesty. As we are working together to preserve the fairness of this course, we

encourage you to let us know (anonymously, if necessary) if you observe behaviour that you

feel might be unethical. Your name will be held in conﬁdence.

Grading

We will be using the platform CrowdMark for grading in MAT135. Using this platform helps

increase fairness and eﬃciency. When an assignment has been graded you will receive a URL

via email where you can view your original assignment and the grader’s comments and grades.

All grading is done by TAs and instructors in MAT135.

Course Activities

You have to spend some energy and eﬀort to see the beauty of math. - Maryam

Mirzakhani

Preparing for Class

The homework for each class will consist of readings and several problems.

Your personal notes on the assigned readings and problems should contain enough detail

to be easily understood by you at a later time. For example, you will want to refer to these

problems when preparing for the Term Test, and the Final Exam. While you do not need to

write your solutions in complete sentences, they should be easy to follow and clear.

9

Reading

You will be assigned readings to prepare for each lecture. Lectures will help to clarify im-

portant or confusing parts of the reading, but will not recap every aspect of the reading.

Completing the reading before each lecture is important to fully beneﬁt from lectures.

Why should you read before class rather than after class or when you are studying for an

exam? It leaves room during the lecture for the most important learning activities. 36 hours

is not enough time to cover all of calculus in depth. By coming to a lecture with a basic

understanding of the material, you will be able to focus on the big questions that are diﬃcult

to learn on your own, such as how the content ﬁts into the broader narrative of calculus,

points that students typically ﬁnd confusing, and common misconceptions.

The ability to understand mathematical texts is an important skill for any future mathe-

matical study. This skill is vital for at least three reasons.

1. Future Learning. When you need to learn a mathematical concept on your own, your

main resources will be written.

2. Eﬃciency. In an ideal world we might try to discover mathematics itself, but this

would be impractical. Calculus, for example, took hundreds of years to develop and

another 200 years to gain a ﬁrm footing. The great abundance of mathematical writing

available allows us to learn from the experts.

3. Learning to Communicate. Just as reading many stories makes you a better story-

teller, reading a lot of mathematics makes you a better mathematical communicator.

Additional tips for getting the most out of reading your math textbook are posted on the

course website.

Problems

Problem solving is at the heart of mathematics, and allows us to apply our knowledge of math

to science, social science, and beyond. Developing problem solving skills is just as important

as the content that we will be covering, and can be used as you work through courses in any

major or pursue any profession. Throughout this course, you can expect to encounter many

unfamiliar problems from math and beyond, and it won’t always be clear right away how to

apply the course content to solve these problems.

The problems on homework will be of varying diﬃculty: some will be easy warm-ups to

the reading or simple computations, while others will involve complex situations and require

problem solving skills. The pre-class portion of the homework will be completed and submitted

via WeBWorK; the after-class portion of the homework will not be collected but form a vital

part of your learning. Solutions to the problems will be available on the course website

approximately one week after the assignment is completed.

Lectures

You will attend three hours of lecture each week of the course. Each lecture is taught by a

course instructor.

10

The lectures of this course will support your learning of calculus in a number of ways.

During lectures, we will motivate new material, clarify diﬃcult concepts, test your under-

standing of calculus prior to the major assessments, and give you the opportunity to meet

with fellow students. You should come prepared to not only hear about math during lectures,

but to think and engage with math. While your instructor will use some of the lecture time

to explain the material, you may also be expected to actively engage in learning by working

on problems, discussing ideas with your fellow students, and sharing your thinking with the

class.

The more you prepare for and engage in class, the more you will get out of it. The following

are basic guidelines for ensuring that you and your classmates get the most out of class.

•Be sure not to speak when someone else is speaking during class. While it might seem

as though no one notices, even one person whispering in the back of the classroom

can be a signiﬁcant distraction for the entire class, and can side-track learning. If you

have a question about the class, pose the question to the entire class - not just to your

neighbour.

•Please be on time to class. Coming in late means that you may miss important infor-

mation and it disrupts the learning of other students.

•Likewise, do not leave late at the end of class or pack up before class has ended. If you

must leave one class early for an appointment or other special commitment, sit near the

door to minimize disruptions.

•Bring pencils, paper, textbook, a scientiﬁc calculator, and a device to connect to Top

Hat to every class.

•If you use technology during class, make sure that it is always for an in-course use.

While it may seem harmless to check your email or a game update, it can be distracting

for students around you; research has demonstrated that the learning of students who

can see the laptop of another person engaging in oﬀ-task behaviour is damaged.

Tutorials

Each week, you will attend one tutorial, a class of about 30 students from across MAT135H1

lecture sections. The purpose of tutorials is to improve your problem-solving and communica-

tion skills, and to provide you opportunities to collaborate with other students. You will also

be submitting and working on components of Applied Communication Tasks during tutorials.

Also be aware that tutorials take priority over other tests, so you should not skip your tutorial

to attend a test in another course.

Each tutorial is 50 minutes, starting at 10 minutes past the hour and ending on the hour.

Tutorials will begin on Thursday, September 13. Be aware that tutorials take priority

over other tests, so you should not skip your tutorial to attend a test in another course. If you

need to miss a tutorial due to illness or another emergency, you do not need to notify your

Teaching Assistant. If you miss a tutorial where you are supposed to submit a component

of an Applied Communication Task, you must attach oﬃcial documentation verifying your

absence to your assignment submission in the next tutorial.

If you are more than 20 minutes late for a tutorial, you will not be permitted to submit

assignments due in tutorials.

11

Instructors and Teaching Assistants

Instead of looking around and worrying about how many students are ‘better’

than you, why not look around for someone you can help pull up? –Karen E. Smith

Instructors

The instructors for MAT135 are shown below. Before emailing us, be sure to check the

guidelines for asking questions at the end of this syllabus. In particular, note that instructors

and TAs will not answer questions about course content or questions that can be answered

by reading the syllabus via email; such inquiries will be deleted without response.

You are expected to treat all members of the instructional team with respect. Examples

of disrespectful behaviour are speaking over someone, using inappropriate language, leaving

a tutorial early, or arriving late.

Instructor Email Section(s)

Dr. Su LEC0601

Teaching Assistants

Teaching Assistants (‘TAs’ for short) are an important part of the teaching team for MAT135H1.

TAs are advanced undergraduate or graduate students who are experienced in calculus. They

play a number of roles, including:

•leading tutorials

•grading assessments

•answering questions in the Math Aide Centre

How to Succeed in MAT135

In math we have to look at a problem from all directions. If one approach isn’t

working, then we try another. If the problem is too hard, we ﬁnd a simpler problem

and then come back to the more diﬃcult one after we’ve solved the ﬁrst. Every

mathematician hits a wall at some point. You have to learn how to get around it,

how to keep working on challenging things. Those are all skills that transfer to

real life. –Rebekah Yates

12

Top 10 Tips for Success in MAT135

1. Work with other students and talk about calculus with them

2. Do many problems, and focus on why a solution works rather than the ﬁnal answer

3. After every lecture or tutorial, take 30 seconds to summarize what you have learned

4. Read the assigned textbook reading before coming to class and keep up on the assigned

problems

5. Instead of re-reading, test yourself on the material by solving additional problems and

by explaining it to someone else

6. Use examples as a road map: rather than focusing on the individual steps, think about

how they are connected to the overall goal of the problem

7. ‘Interleave’ your practice: mix up the types of problems, solutions, and approaches as

you review rather than only reviewing one section at a time.

8. Do not ‘cram’: complete reading and homework when they are assigned

9. Think in class: don’t be a passive listener

10. Use the free resources available to you as a student of University of Toronto (see the

Resources section of this syllabus)

How to improve your problem-solving skills

The key to improving your problem solving skills is to work through many problems. When

faced with a new problem, resist the temptation to immediately search the textbook or the

web for a similar problem. Instead, start by asking yourself what you know and identifying

what the goal of solving the problem is. Problem-solving is all about ﬁnding a path between

what you know and what you want to know, and developing strategies to build this path

is a key to success. You will be discussing speciﬁc problem solving strategies during many

tutorials.

Working with your classmates can be very valuable in getting past roadblocks and im-

proving your problem-solving skills. Simply discussing a problem with someone else can help

you better understand the problem and a solution. Remember that the process of solving the

problem is more important than the answer.

How to get the most from lectures

During classes, you may be asked to participate in tasks like thinking about problems, talking

to other students, writing a solution, or explaining a concept to the class. By approaching

these activities with enthusiasm and doing your best, you will not only help your own learning

but also the learning of those around you. In a large class, it is easy to feel as though you

are just one in a crowd and that what you do is not noticed by anyone else. However, if you

change perspectives and think about how you have been inﬂuenced by others in large groups

you’ll see this isn’t true: you notice your neighbour browsing the internet on their laptops,

13

are distracted by loud coughing ﬁt or cellphone reminder, wonder what a whispering group

of people across the room is talking about, or look over when you hear someone packing their

bags up. You’ve probably also experienced the eﬀect of small behaviours spreading in a crowd.

When you return to thinking about your own behaviour, you should be able to see why what

you do matters to others.

Creating a positive learning environment requires the participation of everyone involved.

Your instructor will set a structure and activities to help you learn calculus well. By actively

engaging in course activities and working with your classmates, you will not only help your

own learning but theirs’ as well.

How to use assessments for learning

The Term Test and the Final Exam will help to accomplish the Learning Goals of this course

in several ways. For example, they will:

•Encourage you to push yourself to understand diﬃcult concepts and to complete many

challenging problems

•Help you identify areas where your knowledge and problem solving skills are already

strong, and where you still have room to grow

•Work with others to deepen your understanding

•Ensure that you have the necessary foundation for building on your knowledge in

MAT135, MAT136, and in courses that require calculus as a prerequisite

There are 3 important phases of the test-learning cycle. They apply to any assessment.

1. Preparation:All learning activities that you engage in prior to the assessment fall

into this category, including reading, completing problems, preparing for and attending

lectures and tutorials, working with other students, and reviewing past assessments. It

also includes ways of preparing yourself to take a test, such as getting a good night’s

sleep, scheduling meals and snacks so that you aren’t hungry during the test, and exer-

cising so that you have the energy that you need.

2. Performance: This is what comes to mind when we think of ‘taking a test’ or ‘complet-

ing an assignment’. Make sure that you think about what the test-taking environment

will be like and incorporate that into your practice. For example, if you usually study

while lying down or with music in the background try to do some practice in a silent

environment in a chair similar to that you will be in during the test.

3. Reﬂection: An assessment isn’t over when you hand it in! Write some quick notes to

yourself about what went well, what didn’t go well, and what topics you need to review.

Once you receive your test back, review your solutions along with the feedback you

received and sample solutions and develop a strategy for better learning the material.

There is always room for improvement.

Where to ﬁnd support

There are several free sources of support available to help you learn calculus.

14

Working with Peers

One of the best ways to learn math is to work with other students. This will give you the

opportunity to explain and talk about mathematical concepts, check your own understanding

and avoid overconﬁdence, and get diﬀerent perspectives on the course material. To make

group study sessions eﬀective, be sure that you discuss how problems are solved or why a

solution makes sense, rather than just trading ﬁnal answers.

It is useful to develop a network of diﬀerent students to work with: don’t be afraid to

introduce yourself to others in your class or tutorial sessions and ask if you can trade contact

information. It might take several tries to ﬁnd a study group that works for you, and you

might ﬁnd a variety of study groups successful.

Recognized Study Groups

The Recognized Study Groups Program can help you join or start a study group. It provides

a regular study time, gives you the opportunity to meet people from across the University,

and you can even receive a co-curricular credit for participating.

Instructor Oﬃce Hours

An ‘oﬃce hour’ refers to a period of time (usually 50 minutes or one hour) that an instructor

is available to discuss course content and answer questions. In MAT135, these will be ‘drop-in

hours’.

You may attend the oﬃce hours of any instructor in the course. If they are speaking with

another student, feel free to come in and listen. You do not need to make an appointment,

but please come to oﬃce hours prepared with questions, your notes, textbook, and any other

materials you might need.

See the course website for oﬃce hour locations and times.

Math Aid Centres

The main Math Aid Centre is located in the Physical Geography building (PG), Room 101.

During times listed on the Oﬃce Hour Calendar, TAs for MAT135 will hold oﬃce hours there.

We encourage you to also use the Math Aid Centre to work with other students in the course

and to meet new classmates. When you come to the Math Aid Centre, please bring speciﬁc

questions, your textbook, homework assignments, and any other material you may want to

refer to. If the TA is speaking with another student, please join them at the table and listen

to the discussion.

College-speciﬁc Math Aid centres are also available at several Colleges. See http://www.

math.utoronto.ca/cms/math-aid-centres/ for more information.

The schedule for Math Aid Centre oﬃce hours will be posted online, with the other oﬃce

hours of the course.

Academic Success Centre

The Academic Success Centre oﬀers a wide variety of services and programming to help

students meet their academic and personal goals at the University. Individualized learning

skills consultations are available by appointment, or on a ﬁrst-come, ﬁrst-served basis for

15

drop-in visitors. You can reserve private study space, attend workshops and lectures related to

academic success, or consult their library of helpful publications about best learning practices.

More information can be found on their website, https://www.studentlife.utoronto.ca/

asc.

Additional Support Services

Other free support services, such as English Language Learning programs and College-Speciﬁc

Resources can be found at uoft.me/freeresources.

Additional Questions & Answers

If you want to know, you ask the question. There’s no such thing as a dumb

question. It’s dumb if you don’t ask it. –Katherine Johnson

What should I do if I require an academic accommodation?

The University provides academic accommodations for students with disabilities in accordance

with the terms of the Ontario 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 Universitys courses and programs.

If you have a learning need requiring an accommodation, immediately register at Accessi-

bility Services at http://www.accessibility.utoronto.ca/Home.htm. You can also register

online at https://www.studentlife.utoronto.ca/as/new-registration.

Can I record the lectures that I attend or share course materials?

Course materials are provided for the use of enrolled students only and that registered students

are not allowed to post, share, or sell course materials without written permission of both the

Instructor and the Course Coordinator.

If a student wishes to tape-record, photograph, video-record, take pictures of, or oth-

erwise reproduce lecture presentations, course notes or other similar materials provided by

instructors, he or she must obtain the instructor’s written consent beforehand. Otherwise all

such reproduction is an infringement of copyright and is absolutely prohibited. In the case

of private use by students with disabilities, the instructors consent will not be unreasonably

withheld.

For more information on copyright and the University of Toronto, please visit the copyright

page at https://onesearch.library.utoronto.ca/copyright/copyright.

What if I have a scheduling conﬂict with the Term Test, or I get sick?

Instructions will be posted on the course website prior to the Term Test; do not inquire before

these are posted.

16

If I have a question about the course, who should I ask?

First, make sure that your question has not been answered in this syllabus, on the course

website, or in class. You should start by asking your classmates to ensure that your question

has not yet been answered. Instructors and TAs will not answer questions about the

content of the course (‘math questions’) via email. If you have a math question for an

instructor or TA, you should attend an oﬃce hour, or take advantage of other resources for

learning on campus.

If you send an email about the course, you must use your U of T email address, as your

instructors will not communicate information about the course to other addresses.

•Questions speciﬁc to your section should be sent to your instructor.

•Questions related to MAT135 as a whole (including tutorials and assessments) may be

directed to [email protected]to.edu. This address will be checked 2-3 times a week,

and inquiries directed to it will be forwarded to the appropriate contact. Note that:

–Inquiries about registration in lecture sections or tutorial sections cannot be an-

swered by the MAT135 instructional team (registration is done centrally through

the Registrar’s Oﬃce).

–Initial regrading requests for the midterm must be submitted through the process

announced following the Term Test; appeals of regrading decisions may be sent to

the administrative email.

–We will not answer questions addressed in the Syllabus or on the course website.

•Teaching Assistants do not answer any inquiries via email.

You do not need to email your TA or instructor if you miss a tutorial or lecture.

Remember that you should always be respectful in your speaking and actions. When

in doubt about how you should speak, write, or act, always err on the side of formality.

You will never oﬀend or annoy someone by being overly formal or polite. The University is

a professional environment, and that when you send emails you must be professional. For

example, you must be polite and use proper grammar and should begin an email with “Dear

Professor ” rather than “Hi”.

This is not the end or the beginning of the end, but it is the end of the beginning.

–Winston Churchill

17

Join OneClass

Access over 10 million pages of study

documents for 1.3 million courses.

Sign up

Join to view

Continue

Continue
OR

By registering, I agree to the
Terms
and
Privacy Policies

Already have an account?
Log in

Just a few more details

So we can recommend you notes for your school.