Dusty Wilson

Written Assignment 0

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 number of quarters at Highline
2.) Pandemic questions: Are you and your family safe (COVID/health)? Are you stable economically? How are you feeling about the racial unrest in America?
3.) Class/school: What (if anything) is the best/worst part about school moving fully online? What (if anything) may I do as your instructor to support you at this time?
4.) Tech Questions: Do you have good and consistent internet access? Do you have consistent access to a computer that you can use for this class?
a.) Canvas: When is the assignment, "1.1 HW - Systems of Linear Equations" due?
b.) MyLab: How many questions are in assignment, "1.1 HW - Systems of Linear Equations"
c.) Gradescope: Upload your responses as a pdf into Gradescope.
d.) Webpage: There is a picture of me catching a boomerang on the "About Me" page of my website.  What is in the background?
e.) Zoom: What color shirt was Dusty wearing in class?
f.) YouTube: Dusty is not (yet) a famous YouTuber.  Which of his videos has the most views?
g.) Slack: (a.) What is the meme posted under #random?  And, (b.) what is the description of the channel #linear-algebra-winter-21?

 

Written Assignment 1

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 randomly selected 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.

1.) Please read (at least) three randomly assigned letters from my former students.
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. 

Written Assignment 2

Overview: The purpose of this assignment is to provide a quick overview of some of the applications of linear algebra.  While we may not talk about the details in the class, I want you to come away with a sense for how these skills can be extended to solve questions in the world around us.  Answer the following and upload your results as a pdf into Gradescope.

1.) Watch the two very short videos with Tim Chartier (here and here).  I heard Tim speak at a conference and was impressed by how he was able to bring linear algebra to life which is probably why he has won national teaching awards.
2.) What is a MOOC?  Tim uses this phrase repeatedly. What do you learn from his repeated use about communication?
3.) Tim talks about three main applications.  What are they and can you provide an example of how each might be useful?
4.) Tim says we could use linear algebra to predict how a person would rank a movie.  How might this idea be monitized (that is, why is prediction of preference such a valuable thing today)?
5.) Tim has a very unusual side hobby outside of mathematics and computer science.  What is it (there are some cool videos if you want to search)?  What is something unusual about you outside of mathematics and science?

 

Written Assignment 3

Overview: Google's 2019 revenue was about $160 billion.  That is a lot of money and so we might wonder how it all started?  It's origin was as a really effective search engine founded on an algorithm (process) originally called PageRank.  As a $160,000,000,000/year question, it seems work understanding a bit of how that works, but that is going to take us a couple of lessons.  There is no linear algebra in this lesson, but it will come once we now a little more.

1.) What is your name?  What does it mean?  (mine is Dustin which means valient fighter)
2.) In order to understand PageRank, we first must learn something about Markov Chains.  What is a Markov Chain?
3.) Watch this video that uses chess to illustrate Markov Chains.  Have you ever played chess?  How/what do you know about chess?
4.) According to the video, a Markov Chain is made up of two things __________ and ___________.  What is a stationary distribution?
5.) At the end of the video, you are asked to determine the average number of moves before a rook returns to the corner.  What is the answer?
6.) Do you like learning about applications of mathematics?  Why or why not?  What applications are the most interesting to you?

 

Written Assignment 4

Overview: This is the first of two assignments on the historical development of linear algebra.  The focus is on content and timeline.  To begin, please read this article.

0.) What is your name?  Do you have a nickname?  (Other than my nickname Dusty, I was also called Chewie and Encyclopedia)
1.) When and where did linear algebra begin? By way of comparison, when/where/by whom was the calculus discovered/invented?
2.) What mathematicians play a prominent role in the history of linear algebra (their name is mentioned at least three times)?
3.) What percent of the article is about determinants? What percent of our course is about determinants? Why do you think there is such a difference?
4.) What is the difference between proofs by Cayley, Hamilton, Kronecker, and Weierstrass and what we are learning as exemplified by Frobenius?
5.) How have applications of linear algebra changed?  (This will require you to refer to things taught in class and not in the article).
6.) What are insights you have into mathematics and education after reading this history?

 

Written Assignment 5

Overview: Long video overviewing matrix applications.  This video addresses familiar topics, but does so at greater depth.  To begin, please watch this 25 minute video.

0.) What is your name?  How many of your family members have attended College and how (if at all) does this influence you?
1.) How does linear algebra help us in a Zombie apolocylpes?
2.) How can linear algebra be used in law enforcement? 
3.) How can linear algebra be helpful on Valentine's Day?
4.) Like many YouTubers, Zach Star ends by giving an advertisement.  But this one is interesting in that he connects it to what application of linear algebra?

 

Written Assignment 6

Overview: This is the second of two assignments on the historical development of linear algebra.  The focus is on its illogical development.  To begin, please read this article which is excerpted from an excellent overview of mathematical history and philosophy by Morris Kline called, "Mathematics and the Loss of Certainty."

0.) What is your name?  What are sources of information do you trust?  What sources don't your trust?  Optional: What is your new CTCLink ID number?  
1.) How have the ideas/methods of proof changed?  Does this give you more/less confidence in mathematics?
2.) Why is communativity (the property that ab=ba) so important in the development of mathematics?
3.) What leads to our confidence in arithmetic?  Does 1+1 always equal 2? 
4.) How do these stories encourage/discourage your studies of mathematics?
This reading focuses on the time period from about 1800-1870.  A lot has happened since.  For a fun novelized glimpse at the next 80 years, I highly recommend the graphic novel "Logicomix: An epic search for truth."

 

Written Assignment 7

Overview: This assignment asks you to consider connections between ethics and mathematics.  Ethics are the moral principles that govern a person's behavior or the conducting of an activity.

0.) What is your name?  What is an ethical choice you have faced since the start of the pandemic?
1.) Google "Ethics in mathematics" or something similar.  Find an article of at least 500 words to read.  What is the article (and link)?
2.) Summarize the article.
3.) Give an argument for why ethics does not apply within mathematics.
4.) Give an argument for why ethics applies in mathematics.
5.) What role do you believe that ethics plays in mathematics and why?

 

Written Assignment 8

Overview: This is a detailed introduction to Google's PageRank algorithm.  To begin, please watch this 9 minute video.

0.) What is your name?  What do you find when you Google your name?  (Most of the top hits are me, but it looks like there is a muscian, costume designer, and playwright that all share my name).
1.) PageRank is similar to the chess question (week 3) and the zombie apocolypse (week 5) in that it is an example of what kind of math (hint: MC) and uses what concept from linear algebra?
2.) What does it mean to solve a problem iteratively?
3.) The approach outlined could be simplified by using the diagonalization method.  But that won't work.  Why?
4.) What is the power method and what are the two reasons it is effective?
5.) What is damping factor?  How often do you go to a webpage by directly typing a URL vs clicking a link (or button)
6.) Why is the efficiency of algorithms important?
7.) How has Google helped you?  How has Google hurt you?

 

Written Assignment 9

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?

 

Written Assignment 10

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 COVID class taught by Dusty?
4.) Please end your letter with something to encourage the reader.