Category: Assignment Instructions (Page 4 of 5)

Comment due Sunday, March 3

Background

Gracie’s questions

Gracie Cunningham was a student who went viral on Twitter a few years ago when someone tweeted her Tik Tok and said, “this is the dumbest video ive ever seen.” (That person’s Twitter account was soon suspended btw.)

After catching a lot of hate on Twitter, Gracie made a follow-up video and tweeted it herself. (I like both videos but I think I prefer the first one tbh.)

Alongside all the critical comments calling her dumb, Gracie got a huge outpouring of support from mathematicians, physicists, philosophers, and teachers, who loved her videos. Like, really, really loved them.

Dr. Cheng’s answers

Eugenia Cheng is a mathematician who is very good at explaining math to non-mathematicians. She’s published a few popular books about math for a general audience and is very active on social media. She’s even appeared on the Late Show with Stephen Colbert!

Gracie’s questions are mostly about the history and philosophy of math (which is a real academic discipline that people can study and get PhD’s in!). Some of her questions have concrete answers and some of her questions just lead to more questions. When Dr. Cheng saw Gracie’s videos and the critical comments on them, she tried answering Gracie’s questions one-by-one on her blog.

Assignment instructions

None of us are experts in the history of math or in the philosophy of math (unless there’s something you’re not telling us in your OpenLab introduction post from last week!). But we all have studied math and encountered math in some form in our day-to-day lives…which means that we’ve all spent time thinking about math, so we can ask questions about it.

For this week’s assignment, think about math in the big picture of the human experience, not just the math you see in your math classes.

1. Watch both of Gracie’s videos above and read Eugenia Cheng’s blog post.
2. Choose one of the following prompts:
   1. What are you curious about? Have you ever had any questions like “Is math real?” or like Gracie’s questions that you’ve thought about before? What is one of your questions and what have your thoughts been about it? Was there something in particular that made you have question? Was there something that changed your mind about how you think about it? Do you have any possible answers for your question, even if they contradict each other?
   2. Which of Dr. Cheng’s answers is the most interesting to you? Why? Did you agree with everything she said or do you have a different idea? How would you have answered this question?
   3. Imagine Gracie is your friend. What would your answers to her questions be? Which of her questions would you ask her more questions about? What would you ask her? How would you engage with her ideas in a supportive way?
   4. What’s something mathematical that you have encountered in your life that had nothing to do with the math you learned in school? Was there a problem you had to solve on your own? Did you have to look up how to solve it or did you figure out a way to solve it yourself? Did you use algebra without realizing you used algebra? How do you know what you did counts as math instead of as something that’s not math?
   5. Look up the history of a mathematical fact, formula, or idea. What problem were people trying to solve when they discovered it? How did it solve the problem for them? How did they know they were right and how did they use it? What is the story of this fact, formula, or idea? (I’m not sure how reliable it is, but the website the Story of Mathematics might be a good place to start).
   6. Make your own video (on Tik Tok or anywhere else that’s public) asking your own questions about the history and philosophy of math.
3. In a comment below, respond to the prompt you chose in at least 5 sentences. Make sure to tell us which prompt you chose so we know what you’re responding to! If you are making your own video, include a link to it in your comment.

You will receive participation credit for your comment.

Comment due Sunday, February 18

You may have heard that matrices are extremely useful tools in several different fields. Our class does not focus on real-world applications of linear algebra, but it might help you slog through some of these long calculations if you have an idea of their potential uses.

Instructions

For this assignment, you will learn a little bit about an application of matrices/linear algebra to a discipline or problem that is interesting to you and/or your major. You don’t have to become an expert (do not worry about being 100% correct here, this is very informal), but you should do your best to answer these questions:

1. What is a description of the real-world problem that is being solved using matrices? Can you describe simply it to a non-expert?
2. Are there variables? What are the variables called and what real-world quantities do they represent?
3. Are there equations relating the variables? Where do the equations come from?
4. Are the entries in the matrices coefficients of some variables or do they represent something else?
5. Why was this particular application interesting to you?

Summarize your findings as a comment on this post. Your comment should be about 8 to 10 sentences long. Cite your sources and include links to the resources you used. As always, your writing should be your own.

Your comment should be written in a way so that if your classmate is also interested in the same topic, they’ll come away with a bit more of an understanding of how linear algebra is used, together with a link to resources they can check out if they want more information.

Resources

The internet has lots of resources about the application of matrices/linear algebra to different problems/disciplines; some are good and some are not so good, so you will have to use your own judgment. You can always try searching for “applications of linear algebra to [your topic of choice].” Here are a few other suggestions:

• Your textbook describes some applications at the end of section 1.2:
  • Balancing Chemical Reactions (chemistry),
  • Dimensionless Variables (physics/mechanical engineering),
  • Resistor Network (electrical engineering).
• This medium post introduces a few applications of linear algebra to computer science/computer programming, as well as links to resources with more details.
• Linear algebra is an important tool for data science; this article outlines a few uses. Data science and analytics have many applications to problems or disciplines you may be interested in.

Your comment will earn you one participation point.