Math 163: Calculus III
Winter 2023
- Syllabi and Calendar
- Class notes and videos
- Assessments
- ***Discussion seminars, readings, videos, etc.
- Shared Documents
- Other resources
Discussion Seminars [Top Contents]
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Slack 0: Understanding the Tech
Overview: The purpose of this assignment
is to make sure that you know how to access the tech in this
class.
Instructions: Answer the following and upload your
results as a pdf into Gradescope (check your email for
an invite to Gradescope). Include the questions on your
document
1.) General Questions: Name (and what
you want to be called), major, and how many quarters have you
attended
Highline
2.) Life questions: Are you and your family safe
(COVID/health)? Are you stable economically? How are you feeling
about the racial unrest in America? How (if at all) are
you impacted by the war in Ukraine (or other wars/conflicts)?
3.) Class/school: What
(if anything) is the best/worst part about returning to
face-to-face college? What (if anything) may I do as your instructor to
support you at this time?
4.) Accessing the
apps/web used in this class
a.) Canvas: What is the class image?
b.)
WebAssign: How many questions are in
assignment, "12.1: 3D Coordinates"
c.) Dusty's Webpage:
- What stickers are on page two of the
completed workalong for 12.1
of the class website?
- How many completed workalongs are linked on the class website?
- How many minutes long is the 12.1 video?
d.) YouTube: Dusty is not (yet) a famous YouTuber.
Which of the video on his channel has the most views?
e.) Slack: There are four channels we will use on Slack.
- General: This is where I will make announcements and you
should ask general questions about the class (i.e., What
sections are on the Assessment?)
- Homework: This is where you will
post questions and answers to homework questions
- Study groups: This is where you can post about upcoming study
groups. Please share where and when you most often
study math.
- Random: You can post about club meetings, off campus
gatherings, and fun stuff.
f.)
Gradescope: Upload your responses as a pdf into
Gradescope under assignment "Slack 0"
Discussion Seminar I: Letters from Previous Students
Overview: The purpose of this assignment is to help you get the most from this class by having you reflect upon what former students have shared.
Instructions: Please read three letters from past students. Use your observations of the letters and reflections upon your own skills and ablities as a mathematician to answer the following. Include the questions on your document and bring a physical (paper) copy to class.
0.) What is your name? In general,
do you like to hear your name spoken? (Dale Carnegie said:
"Remember that a person's name is to that person, the sweetest
and most important sound in any language.")
1.) Please read (at least)
three
letters from my
former students. Please choose letters randomly using a
random number generator.
2.) What is one similarily you have
with these students ... one difference
3.) What are two
habits they indicate will help you be successful?
4.) What
are two questions/concerns that the letters address?
5.)
Having read the letters, you now have a sense for how this class
may foster broader math skills. What mathematical skills and
abilities would you like to develop this quarter? If you need
somewhere to start, here is an
article on 10 skills and abilities that math students
develop.
Discussion
Seminar II:
Overview: The purpose of this assignment is to reflect on how the virtue "Justice" relates to mathematics, the study of math, and math classrooms (including this one).
Instructions:
Please read the chapter on Justice (here)
from Francis Su's book Mathematics for
Human Flourishing. Then answer the discussion questions
below in writing. Include the questions on your document and
bring a physical (paper) copy to class.
Note: It is around 15 pages long,
but should be very readable. Some math topics are
referenced that you may not be familiar with. That is okay
and not required to answering the questions. For more
information on the book, a review is
here and the Francis' talk that inspired the book is
here.
0.) What is your name? Do you have a story to
share about meeting someone with your same name? (If so,
go for it! If not, that is okay too).
1.) If people
have realized that the way we teach math needs to change, why
hasn't it changed yet? Who benefits from keeping it the
same way it has always been? Explain.
2.) All of us
unwittingly harbor bias, so how can we mitigate bias in
mathematical spaces? Who is harmed by bias in mathematical
spaces, and why?
3.) What inequities do you notice in
mathematical spaces? Who is harmed by those inequities?
Think deeper than the obvious answers.
4.) What can be done
to make this class more equitable? What can you do? we do?
the teacher do?
Discussion Seminar III: Plato's Allegory of the Cave
Overview: In understanding the world, some basic philosophical concepts are important. One of these is Plato's Allegory of the cave. Here is a video outling the allegory and then you can read the full work here. Note: The most famous film based upon the Allegory is The Matrix.
Instructions: Please read Plato's Allegory of the Cave and watch this TED ed video. Then answer the following. Include the questions on your document and bring a physical (paper) copy to class.
0.) What is your name? What is something
you thought you understood, but were wrong?
1.) In the
context of mathematics, who is the prisoner who escapes the
cave? Explain.
2.) Interpreting the allegory as a
mathematician, what are examples of the shadows inside the cave?
What are the ideal objects outside the cave?
3.) How can we
free ourselves as mathematicians and scientists to see the real
world? Explain.
4.) How do/can we know that we are the ones
who are truly free?
Discussion Seminar IV: History of Calculus
Overview: The Calculus we learn today has some similarities and many differences to early calculus. The purpose of this assignment is to better understand the history of the derivative (including its connection to limits).
Instructions: Please read The Changing Concept of Change: The Derivative from Fermat to Weierstrass by Judith Grabiner. This is a little long and some more technical sections of the article have been marked and you may skip them if so inclined. As you read, please answer the following. Include the questions on your document and bring a physical (paper) copy to class.
0.) What is your name? What is a
holiday that
coincides with your birthday? (My birthday is on the
Independence Day of the Dominican Republic).
1.) What are the
three things Newton and Leibniz did that were enough for them to
be credited with inventing calculus?
2.) According to Dr.
Grabiner (the author), what is the difference between the stages
of discovery and invention?
3.) What did Newton seem to have
in mind by the word, "limit."
4.) Why were eighteenth-century
mathematicians more accustomed to computing than thinking?
5.) Who invented the delta-epsilon definition for the limit?
Is this something you have seen before? If so, what did/do
you think of it?
6.) How many years after Newton/Leibniz did
it take for calculus to be considered a rigourous subject?
7.) How does the history of calculus differ from the order
in which calculus is introduced in math classes? How do
you think the current method is good/bad?
Discussion Seminar V: The Seven Baby Steps
Overview: We had a brief discussion about Dave Ramsey's Seven Baby Steps to financial success.
Discussion Seminar VI: Where Math Comes From?
Overview: This assignment asks you to take on one of the great mysteries of mathematics. Have you ever wondered where math comes from? Is mathematics discovered or invented? At a simple level, this comes down to two facts that are in tension. First, every mathematician we have ever heard of is human. On the other hand, there is something that is seemingly transcendent about math: Why do pi, e, and the golden ratio keep appearing in our work and in nature? Phrased another way, why aren't there citations in a math book?
Instructions: Please watch these short videos (Where Math Comes From? (video and video)) and then answer the following.
0.) What is your name? How many of
your family members have attended College and how (if at all)
does this influence you?
1.) Why might some mathematicians
believe math is invented?
2.) Why might other mathematicians
believe math is discovered?
3.) Do you believe math is
invented or discovered? Why?
4.) How confident are you
in your response?
Discussion Seminar VII: Divergent Series and the Loss of Certainty
Overview: While Power Series may be the "Swiss Army Knife" of function families, they have an Achilles heel. They do not converge (work) everywhere and these trouble spots have caused confusion and questions in some of the most amazing mathematicians of the ages.
Instructions: Please read Divergent Series and the Loss of Certainty. Then answer the following. Include the questions on your document and bring a physical (paper) copy to class.
0.) What is your name? What is an
ethical choice you have faced since the start of the pandemic?
1.)
What was the original intent behind the creation/discovery of
infinite series?
2.) What misunderstanding(s) led to the
belief that 1/2 = 1+1-1+1-1+ ...?
3.) What did mathematicians
do to fill in holes created by their vagueness and lack of
proof?
Discussion Seminar VIII: Letter to a Future Student
Overview: This week you have a chance to reflect, direct, and encourage a future student.
Instructions: Please write a 1+ page letter to my future students. Include the parts listed below, but you do NOT need to include these headings ... I mean, this is supposed to be a letter so make it look like one:-).
1.) Introduce yourself, what you are majoring in, and a bit
about your background.
2.) What were some of the challenges
you faced this quarter (personally or as a student) and how did
you make it through?
3.) What advice do you have for being
successful in a class taught by Dusty?
4.) What are the good parts of the flipped class model?
What made it challenging for you?
5.) Please end your
letter with something to encourage the reader.