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Math 264: Multivariable Calculus

Spring 2020

Contents [Top]

Participate handouts and videos  [Top Contents]

Due 4/6: Intro Survey

Due 4/10: Covid, exponential growth, and logistic growth (video questions)

Due 4/17: Mathematical modeling (video, questions)

Due 4/24: none

Due 5/1: Historical excerpt on Newton and series (article questions)

Due 5/8: Why convergence/divergence matters (article questions)

Due 5/15: none

Due 5/22: Musa on success (video questions optional article)

Due 5/29: Plato's Allegory of the Cave (video article questions)

Due 6/5: The Unreasonable Effectiveness of Mathematics in the Natural Sciences (video article questions)

Online Resources [Top Contents]

MIT Open Courseware videos (here)

Khan Academy videos (here)

Wolfram Demonstration Project (here) with the CDF viewer

Discussion Questions [Top Contents]

Questions for 4/10:

1.) What are the two models discussed in the video?
2.) According to the video, will there be any places unimpacted by COVID?  Please explain.
3.) According to the video, what number/stat should we be watching to know if things might be getting better?

Questions for 4/17:

1.) According to the talk, what are the three components of a mathematical model?
2.) According to the talk, how do we test models and what do we adjust if/when the models break down?
3.) The talk focused on cancer research, but what are COVID related questions for which we would like to find mathematical models? 

Questions for 4/24:

None, we are taking a week break ... everyone is welcome to join the COVID conversation after class.

Questions for 5/1:

1.) What was so powerful about Newton's contribution to the binomial theorem?
2.) What basic concept of calculus was Newton unable to define?  How long would it take for this to become clear?
3.) What happened to Newton's manuscript "On the Analysis of Infinite Series"?

Questions for 5/8:

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?
4.) Did you complete the survey about the textbook:-) (survey here) 

Questions for 5/15:

None, we are taking a week break ... everyone is welcome to join the COVID conversation after class.

Questions for 5/22:

1.) Musa says that we must know who we are (not let others define us).  Who are you?
2.) 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?
3.) What do you need (from yourself and others) to finish this quarter strong?

Questions for 5/29:

The most famous film based upon the Allegory is The Matrix.

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.

Questions for 6/5:

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?