# MAT135H1

Calculus 1(A)

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.
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### Dimitri Chouchkov

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##### MAT135H1 Study Guide - Fall 2018, Comprehensive Quiz Notes - Trigonometric Functions, Graph Of A Function, Derivative 24HRPremium

Mathematics
MAT135H1
Dimitri Chouchkov
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MAT135H1
Dimitri Chouchkov

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#### MAT135H1 Syllabus for Dimitri Chouchkov — 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
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.
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
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
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.
This course satisﬁes 0.5 credits of the Science distribution requirement and the Physical and
Assessment
While grades are (one) measure of progress, they are not a measure of promise.
–Francis Su
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
8% 8% Derivative Computation Quiz
25% 15% Term Test
40% 50% Final Exam
point values, see the grading scale available at
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
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-
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
6
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
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 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
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.
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
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
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.
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
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. Chouchkov dmitri.chouchk[email protected]to.ca LEC0101
Dr. Mayes-Tang may[email protected] LEC0201
Dr. Rajaratnam kr.ra[email protected]to.ca LEC0401
Dr. Emory [email protected]to.ca LEC0402, LEC0501
Dr. Su LEC0601
Dr. Richards larissa.ric[email protected]to.ca LEC0701
Dr. LeBlanc [email protected]to.edu LEC0801, LEC5201
Dr. Nica [email protected]to.ca LEC0901
Dr. Guo [email protected]to.ca LEC1001
Dr. Verberne yvon.verb[email protected] LEC5101
Teaching Assistants
Teaching Assistants (‘TAs’ for short) are an important part of the teaching team for MAT135H1.
play a number of roles, including:
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
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
to other students, writing a solution, or explaining a concept to the class. By approaching
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.
you do matters to others.
Creating a positive learning environment requires the participation of everyone involved.
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
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.
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
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.
The schedule for Math Aid Centre oﬃce hours will be posted online, with the other oﬃce
hours of the course.
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
asc.
Other free support services, such as English Language Learning programs and College-Speciﬁc
Resources can be found at uoft.me/freeresources.
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.
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
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
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
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

### LeBlanc E.

Current Study Guide

Mathematics
MAT135H1
LeBlanc E.
Current Lecture

Lecture 26

Mathematics
MAT135H1
LeBlanc E.

View All

#### MAT135H1 Syllabus for LeBlanc E. — 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
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.
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
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
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.
This course satisﬁes 0.5 credits of the Science distribution requirement and the Physical and
Assessment
While grades are (one) measure of progress, they are not a measure of promise.
–Francis Su
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
8% 8% Derivative Computation Quiz
25% 15% Term Test
40% 50% Final Exam
point values, see the grading scale available at
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
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-
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
6
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
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 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
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.
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
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
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.
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
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. Chouchkov dmitri.chouchk[email protected]to.ca LEC0101
Dr. Mayes-Tang may[email protected] LEC0201
Dr. Rajaratnam kr.ra[email protected]to.ca LEC0401
Dr. Emory [email protected]to.ca LEC0402, LEC0501
Dr. Su LEC0601
Dr. Richards larissa.ric[email protected]to.ca LEC0701
Dr. LeBlanc [email protected]to.edu LEC0801, LEC5201
Dr. Nica [email protected]to.ca LEC0901
Dr. Guo [email protected]to.ca LEC1001
Dr. Verberne yvon.verb[email protected] LEC5101
Teaching Assistants
Teaching Assistants (‘TAs’ for short) are an important part of the teaching team for MAT135H1.
play a number of roles, including:
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
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
to other students, writing a solution, or explaining a concept to the class. By approaching
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.
you do matters to others.
Creating a positive learning environment requires the participation of everyone involved.
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
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.
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
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.
The schedule for Math Aid Centre oﬃce hours will be posted online, with the other oﬃce
hours of the course.
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
asc.
Other free support services, such as English Language Learning programs and College-Speciﬁc
Resources can be found at uoft.me/freeresources.
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.
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
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
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
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

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