Matthew L. Wright
Assistant Professor, St. Olaf College

Modern Computational Math

Math 242 ⋅ Spring 2022

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Today
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Challenge Problems
Do the following before the first class:
  • Complete the Introductory Survey.
  • Install Mathematica on your computer. If you've already installed Mathematica, open it up and check that your license key is still active. You might be prompted to upgrade to the most recent version. For assistance, see this IT Help Desk page.
Wednesday
February 9
Introduction; Mathematica basics
Do the following before next class:
Friday
February 11
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Monday
February 14
Madhava series for \(\pi\)

Bonus video: John Urschel-NFL Math Whiz

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Wednesday
February 16
Inverse tangent formulas for \(\pi\)
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Friday
February 18
Formulas for \(\pi\) by Ramanujan and others
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Monday
February 21
Probabilistic approaches for \(\pi\)

Bonus video: Eugenia Cheng on The Late Show

Do the following before next class:
Wednesday
February 23
Fibonacci numbers
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Friday
February 25
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Monday
February 28

Bonus: video How Not to Be Wrong: The Power of Mathematical Thinking - with Jordan Ellenberg

Do the following before next class:
  • Complete the Fibonacci Identities practice problems and upload your solutions to Moodle.
  • Begin revising your solution to the \(\pi\) Project. Revisions are due Monday, March 7.
  • Re-read Section 2.3 (pages 55–67) in Computational Mathematics, Chapter 2. Focus on the process of discovering Cassini's identity. Also note the various methods presented for verifying the identity for lots of indexes \(n\).
Wednesday
March 2
Fibonacci polynomial identities
Do the following before next class:
Do the following before next class:
  • Finish reading Section 2.4 in Computational Mathematics, Chapter 2. Note the algorithms corresponding to what we did in class today. Also take a look at the generalizations of the Fibonacci sequence in Section 2.5.
  • Complete the Fibonacci and Lucas practice problems and upload your solution to Moodle.
  • Finish revising your solution to the \(\pi\) Project, if necessary. Revisions are due Monday, March 7.
  • Read the Generalized Fibonacci Project. Optionally, start experimenting with generalized Fibonacci sequences.
Monday
March 7
\(\pi\) Project
revisions due

Bonus video: Hannah Fry — Beautiful equations: how insects walk on water and galaxies form

MSCS Colloquium: Monday 3:30–4:30pm in RNS 310

Do the following before next class:
Wednesday
March 9
Generalized Fibonacci numbers
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Friday
March 11
Iterated Functions
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Bonus videos: Satyan Devadoss — Blue Collar Mathematics and Mage Merlin's Unsolved Mathematical Mysteries

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Do the following before next class:
Friday
March 18
Do the following before next class:

Bonus video: Moon Duchin: "Political Geometry"

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Wednesday
March 23
Logistic map bifurcation diagrams
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Friday
March 25
The Feigenbaum Constant
Have a great spring break! No class March 28 – April 1.
Monday
April 4
Introduction to Python

Bonus video: Francis Su — Mathematics for Human Flourishing

Do the following before next class:
Wednesday
April 6
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Friday
April 8
Prime numbers: Sieve of Eratosthenes
Do the following before next class:
  • Finish implementing the sieve of Eratosthenes, if you haven't done so already. Consider the efficiency of your implementation, and think about how you might make it more efficient.
  • Optionally, work on revising your Iterated Functions Project.
  • Optionally, work on a challenge problem.
Monday
April 11
Prime numbers: Sieve of Eratosthenes

Bonus video Interview with Karen Uhlenbeck and article Karen Uhlenbeck, Uniter of Geometry and Analysis, Wins Abel Prize

MSCS Colloquium: Monday 3:30–4:30pm in RNS 310

Do the following before next class:
Wednesday
April 13
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Monday
April 18
Counting Primes and the Riemann Zeta Function

Bonus video: Yitang Zhang: An Unlikely Math Star Rises

Do the following before next class:
Wednesday
April 20
Counting Primes and the Riemann Zeta Function
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Friday
April 22
Probabilistic simulation: Random Walks
Do the following before next class:
  • Finish the Primes Project, if you haven't done so already.
  • Continue the exploration of 1-D random walks from class. In particular, how does the average diameter depend on the number of steps? You don't have to turn in anything for this exploration.
Monday
April 25

Bonus video: MEET a Mathematician! - Trachette Jackson

Do the following before next class:
Wednesday
April 27
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Friday
April 29
Probabilistic simulation: Random Walks
Do the following before next class:
  • Work on the Random Walk Project, due next Friday.
  • Take a look at the Final Project Information. Think about which topics interest you and who you would like to work with.
  • Optionally, finish revising your Primes Project. To submit a revised project, update your Moodle submission to indicate revisions, even if the notebook link is unchanged.
  • Optionally, work on a problem from the (updated) list of challenge problems.

Bonus: Why is Mathematics Useful — Robert Ghrist, and Applied Dynamical Systems Vol. 1

Do the following before next class:
Wednesday
May 4
Probabilistic simulation: Percolation Theory
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Friday
May 6
Probabilistic simulation: Percolation Theory
Do the following before next class:
  • Finish the percolation investigation from class (not to be collected).
  • Optionally, work on a challenge problem.
Monday
May 9
Final projects

Bonus: Susan D'Agostino book and interview

Do the following before next class:
  • Work on your final project. Identify what mathematical questions you would like to investigate. Start planning and writing code.
  • Optionally, revise your random walk project.
Wednesday
May 11
Final projects
Do the following before next class:
  • Work on your final project.
  • Optionally, revise your random walk project.
Friday
May 13
Final projects
Do the following before next class:
  • Work on your final project.
Monday
May 16
Final projects

Bonus: Living Proof: Stories of Resilience Along the Mathematical Journey

We've made it to the end of the semester! A few last things to do:
  • Finish your final project. Organize your computations and results into a notebook that demonstrates what you have accomplished in this project. Prepare your presentation.
  • Submit your final project files/links to the Final Project assignment on Moodle.
  • Recommended: schedule a practice presentation with the professor (see Google calendar appointment link in your email).
Monday
May 23
Math 242B: Final Presentations 2:00–4:00pm
Tuesday
May 24
Math 242A: Final Presentations 2:00–4:00pm