Math 163: Calculus III
Fall 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: How concerned are you for your
health (COVID, mental health)? Are you stable economically? How
are you feeling about being a college student at this point in
time in American history? If you could change one thing
about your Highline education, what would it be?
3.) Class/school: 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 "Check your understanding questions" are in,
"12.1: 3D Coordinates"? How will these questions impact
you in this class?
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?
- Note: His daughter Melissa just moved back east to become an
actress (@melissaruth4961
on YouTube and @wildlissaw2 on Instagram)
e.) Slack: There are four channels we will use on Slack.
Please add a picture to your profile.
- # 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?) Please post an
audio clip of you pronouncing your name.
- # checkunderstanding: This is where you will
post questions and answers to "check your understanding questions"
- # studygroups: 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: The Seven Baby Steps
Overview:
Later this quarter, we will learn some of the math about
annuities (saving money) and amortization (borrowing money).
With an eye toward that future topic, this is the first in a
series of Discussion Seminars aimed at personal finance.
Instructions:
I'm a big fan of radio guru Dave Ramsey because he offers a
simple plan to build wealth and live/give like nobody else.
Read about Dave's Seven Baby Steps to financial success or
(if you prefer) watch a
video with the same content.
0.) What is your name and what is the best job you have ever had?
1.) Do you believe that you can be a millionaire? If so,
what is your plan to get there?
2.) Baby Step 1 is to save
$1000 (or $500 if you are a broke college student). Why is
it important to have a little money in the bank?
3.) Dave is
pretty hard on all forms of debt (car, credit cards, student
loans, and even home loans). He believes that we can all
be financially debt free? Do you believe this is possible
for you? Why or why not?
4.) What is the most
helpful/exciting thing about Dave's plan? What is the most
ridiculous/scary part?
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: Saving for the Future
Overview: In the Baby Step seminar, Dave recommended saving 15% of your wages for retirement. In this seminar we look at a form of saving for retirement called an "Annuity."
Instructions: Please watch this short and kinda boring video on the future value of an annuity. Then answer the following.
0.) What is your name? Would you rather
that no-one knew your name or that everyone knew you because of
something embarrassing that you had done? Why?
1.) What
is an "Annuity"? (Ask Google)
2.) What is the average
return of the stock market over the last 30 years? (Ask
Google)
3.) Suppose you save $200/mo in the stock market
earning 8% interest beginning at age 20. How much will you
have when you retire 45 years later at age 65? How much
total money will you have saved? How much interest will
you have earned?
4.) Suppose you retire with $1,000,000 (PV)
invested at 8% and then withdraw an equal amount each month for
the next 25 years until you have $0 (FV) left. How much
should you withdraw each month? How much total did you
withdraw? How much interest will you have earned?
5.)
These results in (3.) and (4.) were possible in part because
they assumed an 8% interest rate. Is it reasonable to
predict an 8% return? Why or why not.
6.) What are the
pros and cons of beginning to save for retirement early?
How (if at all) does this impact you personally?
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+ ...?
3.) What did mathematicians
do to fill in holes created by their vagueness and lack of
proof?
Discussion Seminar VIII: Math millionaire mogul mindset moves (Borrowing Money)
Overview: In the Baby Steps, Dave outlines his plan for eliminating debt. In this seminar we look "Amortzation" which is the math behind three kinds of debt (car loans, student loans, and house loans).
Instructions: Everyone should answers questions 0, 1, 2, 4, and 5. For question 3, please choose the topic most interesting to you and answer (just) those questions.
0.) What is your name? What is a story
about how debt (or the lack thereof) has impacted you or someone
you know?
1.) Ask Google, "What is amortization in a loan."
2.) Interest rates vary based upon the the type of loan and the
purpose of the money. What is the average rate in each
category?
a.)
Car
loan
b.)
Student loan
c.)
House loan
d.)
Personal loan
e.)
Business loan
f.)
Credit card rate
g.)
Payday loans (about)
3.) Choose ONE of the categories below to focus on. I will
provide specific scenarios, but you are free to change these to
fit your situation.
Student
loans
i.) Learn a little about student loans by choosing one
of: video
by Priya the influencer,
video by
white guy professional,
article from college funding website, or
article by Dave.
ii.)
What are words used in this lesson that you did not understand?
iii.) Which is better: a federal or private loan? Why?
iv.) What is the difference between a federal loan being
deferred and subsidized.
v.) What are the
financial challenges of being an international student?
vi.)
Google "Cost to attend ____" for five (or more) schools not
named The University of Washington. Include at least one
elite private college, one religious college, and one state
school in Washington. For each university, record the (i.)
name, (ii.) average cost before aid, and the (iii.) average cost
after aid.
vii.) Suppose you graduate with $30,000 in
student loans at 5.5% which you will repay with equal payments
over the course of 10 years.
viii.) How much
will you pay over the life of the loan? How much interest
will you pay?
ix.) How do
student loans impact your DTI and other financial goals?
x.) What percent of US college students graduate from college?
What happens if you take out student loans, but do not graduate
college?
xi.) What is your plan for paying
for college?
Car loans
i.) What are the pros/cons of
buying a new car? What are the pros/cons of buying a used
car?
ii.) How many cars
under $3k are available in this area? How many cars
between $3 and 5k are available? (Note: These links
are to cars for sale by owner and not available through a
dealer).
iii.) Find a nice car on the list for about $5,000
... what is its: year, make, model, and mileage.
iv.) Find
the Kelley Blue Book value of
this car if you were to get it from a dealer vs if you were to
get it from a private party.
v.) Suppose you get a car loan
for $5,000 at
13.5% for 72
months. Use the TVM solver on your calculator to
determine the expected payment.
vi.) How much will you pay
over the life of the loan? How much interest will you pay?
vii.) Cars lose their value (this is called depreciation).
Estimate what your car will be worth when the loan is paid off.
To do this, find the Kelley Blue Book value of your same car,
but choose one that is six years older with 6*12,000=72,000 more
miles on it.
viii.) Most of us will buy a car at some point,
what is your plan for purchasing a car? How does this fit
within your other financial goals?
Home loans
i.) What
is the
average cost of a house in Des Moines, WA?
ii.) The
average down payment for first time home buyers is about 6%.
How much do you need to save for a down payment? (Note: For the
sake of simplicity, we are ignoring loan origination fees)
iii.) If you make the down payment in (ii.), how big a mortgage
(aka loan) will you need to purchase the house? Use the
TVM solver on your calculator.
iv.) What monthly payment
can you expect to pay for the house? Assume a 30 year
fixed rate mortgage at the average house loan rate you found
above. (Note: For the sake of simplicity, we are ignoring
taxes and insurance)
vi.) How much (down payment + monthly
payments) will you pay for the house over the life of the loan?
How much interest will you pay?
vi.) Traditionally, you
shouldn't spend more than 28% of your income on a mortgage.
How much would you need to make a month (and year) to be able to
afford this house?
vii.) How much does a
Software Developer make? Could they afford this house?
What if they saved up a 20% down payment? What if the
house was $100,000 cheaper? What if interest rates were
4%? What are other ideas you have for making a home
purchase affordable for you?
viii.) What is your plan for
having/finding a place to live?
4.) There is an old
proverb that says that the borrower is the slave of the lender.
How have you seen this play out (perhaps in your life or perhaps
in that of someone else you know)?
5.) Do you think it is
possible to be debt free in America? What is it worth to
you to be debt free?
Discussion Seminar IX: 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:-).
0.) PLEASE TYPE SO THE FUTURE STUDENT CAN READ WHAT YOU HAVE TO
SHARE:-)
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.