Math 163: Calculus III
Fall 2022
- 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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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).
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.) Tech resources: Do you have
good and consistent internet access? Do you have consistent
access to a computer that you can use for this class? Are
you able to print (at home or at school)?
5.) 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 videos on his channel has the most views?
e.) Slack: What was the date when Dusty started at Highline
(posted in Slack).
f.)
Gradescope: Upload your responses as a pdf into
Gradescope.
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. Please upload your results as a pdf into Gradescope.
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. Read the letters that correlate to (1st)
your birth month, (2nd) one more than month + 12 (mod 16), and
(3rd) one more than month + 9 (mod 16). For example, if
you are born in May, you would read letters 5,
1+17mod(16)=2, and 1+14mod(16)=15
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: Musa on Overcoming Obstacles
Overview: The purpose of this assignment is to encourage and inspire while also providing an opportunity to reflect on self-perceptions and habits. Answer the following and upload your results as a pdf into Gradescope. Please bring a printed copy to class.
Instructions: Please watch this short video (Musa on Overcoming Obstacles) and then answer the following.
1.) What is your name? Do you have
any tricks for remembering your name? (For example, I
introduce myself by saying my name is Dusty, like a road.)
2.)
Musa says that we must know who we are (not let others define
us). Who are you?
3.) Musa says that we should know, but not
focus on our goals. Rather we should focus on our behaviors that
will help us reach our goals. What are behaviors on which you
should be focusing?
4.) What do you need (from yourself and
others) to finish this quarter strong?
Discussion Seminar III: Math and Religion
Overview: After a year of calculus with its many applications, it can be tempting to think math can be used for everything. But is this true? Are there questions outside of math?One area where math is sometimes seen as an allie, sometimes as enemy, and often ignored is in the area of religion. This assignment invites you to ask and wonder.
Instructions: Please read this article (Math and Religion) and then answer the following.
1.) What is your name? What does it
mean? (mine is Dustin which means valient fighter)
2.)
Some people claim that math and religion are at odds. Why
might this be?
3.) Others claim that math and religion work
together. How might they support this?
4.) What, if
any, connection do you see between mathematics and religion?
5.) How confident are you in your answer?
Discussion Seminar IV: The Unreasonable Effectiveness of Mathematics in the Natural Sciences
Overview: One of the amazing impacts of the invention/discovery of the calculus was that this "simple" tool could explain and be applied to so many applications in science. If you will, moving symbols around on paper seemed incredibly effective at describing nature. Is this just a coincidence? In this famous article, the physicist Eugene Wigner asks whether this is an unreasonable effectiveness.
Instructions: Please read this dense article (The Unreasonable Effectiveness of Mathematics in the Natural Sciences) and then answer the following.
0.) What is your name? Do you have
a nickname? (Other than my nickname Dusty, I was also
called Chewie and Encyclopedia)
1.) The author provides a
number of examples of where he believes mathematics unreasonably
effective. Pick one of these examples and explain why Wigner
believes mathematics unreasonably effective.
2.) In light of
the article, does the effectiveness of mathematics as used by
physicists and other scientists seem "unreasonable" to you?
Explain.
3.) Wigner described the usefulness and power of
mathematics as a miracle. How do you explain the existence and
usefulness of mathematics?
Discussion Seminar V: Where Math Comes From? (video and video)
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?
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 VI: Hilbert's Hotel (TED ed video)
Overview: Infinity is a mysterious concept. This illustration helps us understand how there can be an infinite infinities.
Instructions: Please watch this short video (TED ed video) and read this article (Hilbert's Hotel) prior to answering the following question.
0.) What is your name? What sources
of information do you trust? What sources don't your
trust?
1.) Explain the idea of a one-to-one correspondence
(think "Hotel Rooms.")
2.) Explain how there are the same
number of even numbers as whole numbers.
3.) Can any infinite
set fit inside Hilbert's hotel? Why or why not.
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.
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: Plato's Allegory of the Cave (TED ed video)
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.
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 IX: Letter to a Future Student
Overview: This week you have a chance to reflect, direct, and encourage a future student. Please write a 1+ page letter to my linear algebra students next quarter.
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.) Please end your
letter with something to encourage the reader.