Matthew L. Wright
Associate Professor, St. Olaf College

Modern Computational Math

Math 242 ⋅ Fall 2024

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Challenge Problems Earn a Token
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.
Do the following before next class:
Monday
September 9
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Wednesday
September 11
Madhava series for \(\pi\)

Bonus video: Paths to Math: John Urschel

Do the following before next class:
Friday
September 13
Inverse tangent formulas for \(\pi\)
Do the following before next class:
  • Complete the Inverse Tangent Formulas practice problems and upload your solutions to the Inverse Tangent Formulas assignment on Moodle.
  • Read Section 1.5 (pages 32–36) in our Exploring Mathematics text. Do Exercise 1.27 (not to turn in). How are the methods in this section different from what we have seen so far?
  • Take a look at the \(\pi\) Project, due next Friday. You don't need to write any code for this yet, but start thinking about the problem and planning the methodology you will use for this project.
Monday
September 16
Formulas for \(\pi\) by Ramanujan and others
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Wednesday
September 18
Probabilistic approaches for \(\pi\)

Bonus video: Eugenia Cheng on The Late Show

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Do the following before next class:
Monday
September 23
Fibonacci implementations
Do the following before next class:
  • Read Section 2.3 up to the "Further Generalizations" heading on page 70 in our Exploring Mathematics text. Focus on the process of discovering Cassini's identity and the methods presented for verifying the identity for lots of indexes \(n\).
  • Complete the Computing Fibonacci practice problems and upload your solutions to the Computing Fibonacci assignment on Moodle.
  • Optionally, begin revising your \(\pi\) Project. Talk with the professor if you have questions about how to do this. Revisions are due Monday, September 30. You may submit your revisions to the same project link on Moodle.
Wednesday
September 25

Bonus: video How Not to Be Wrong: The Power of Mathematical Thinking - with Jordan Ellenberg and article The Psychology of Statistics by Jordan Ellenberg

MSCS Showcase Thursday, September 26, 4:30pm, Tomson 280

Do the following before next class:
Friday
September 27
Fibonacci polynomial identities
Do the following before next class:
Monday
September 30
Generalized Fibonacci numbers
\(\pi\) Project
revisions due

MSCS Colloquium: How many ways are there to juggle? Monday, September 30, 3:30–4:30pm in RNS 210

Northfield Undergraduate Mathematics Symposium Tuesday, October 1, 3:15–6:45pm at Carleton

Do the following before next class:
Wednesday
October 2
Generalized Fibonacci numbers

Bonus: Susan D'Agostino book and interview

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Friday
October 4
Iterated functions; Collatz trajectories
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MSCS Colloquium: Carlos Chavez, "Which is better, one or two? Three...or four? Viewing Educational Measurement Through Multiple Lenses," Monday, October 7, 3:30–4:30pm in RNS 210

Do the following before next class:
Wednesday
October 9
More Collatz trajectories

Bonus video: Terence Tao: "The Potential for AI in Science and Mathematics"

MSCS Research Seminar: Craig Kaplan, "Computing Tiling Properties of Polyforms," Thursday, October 10, 11:30am–12:30pm in RNS 203

Do the following before next class:
Friday
October 11
The logistic map
Have a great fall break! No class October 14
Do the following before next class:
Wednesday
October 16

Bonus video: Moon Duchin: "Political Geometry" and DistrictR

Do the following before next class:
Friday
October 18
Logistic map bifurcation diagrams

MSCS Research Seminar: Prof. Dave Walmsley: "Recent Advances in Linear Dynamics" Friday, October 18, 3:30–4:30pm in RNS 210

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Monday
October 21
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Wednesday
October 23
Intro to Sage and CoCalc
Do the following before next class:
  • Read the following pages from the Python Land tutorial: Variables, Functions, Booleans, Loops, and Strings.
  • Read pages 145–148 in our Exploring Mathematics text. Take note of how the Sieve of Eratosthenes is able to efficiently find all the prime numbers up to some maximum value.
  • Complete the four practice problems in the Intro Primes practice problems notebook on CoCalc. For help, talk with the professor or with classmates, or visit the help session on Sunday evening. Simply complete the problems in the file on CoCalc and they will be automatically turned in for grading.
Monday
October 28
Prime numbers: sieve of Eratosthenes

MSCS & Biology Research Seminar: Prof. Martha Zillig: "Counting Creatures: The Statistical Science Behind Wildlife Ecology" Monday, October 28, 4:00–5:00pm in RNS 410

Do the following before next class:
Wednesday
October 30
Properties of prime numbers

Bonus: "In Music and Math, Lillian Pierce Builds Landscapes" from Quanta Magazine

Do the following before next class:
  • Read Section 4.2 in our Exploring Mathematics text.
  • Complete the Prime Sieves and Prime Pairs practice problems that you will find in the Assignments folder on CoCalc. Simply complete the problems on CoCalc and they will be automatically turned in for grading. These practice problems are due Friday at 5pm.
  • Optionally, work on revising your Iterated Functions Project. Revisions are due next Monday, November 4.
  • Take a look at the Primes Project, due next Friday, November 8.
Friday
November 1
Counting primes
Do the following before next class:
  • Read Section 4.3, pages 156–159 in our Exploring Mathematics text.
  • Complete the Counting Primes practice problems that you will find in the Assignments folder on CoCalc. Simply complete the problems on CoCalc and they will be automatically turned in for grading. These practice problems are due Monday at 5pm.
  • Optionally, finish revising your Iterated Functions Project. Revisions are due next Monday, November 4. You may submit your revisions to the Iterated Functions Project assignment on Moodle.
  • Begin the Primes Project, due next Friday, November 8.
Monday
November 4
Counting primes and the Riemann zeta function

MSCS Colloquium: Prof. Steven McKelvey: "One Person, One Vote: The Electoral College, Gerrymandering and the Mathematics of Optimization" Monday, November 4, 3:30pm in RNS 210

Do the following before next class:
  • Finish reading Section 4.3 (pages 160–166) in our Exploring Mathematics text.
  • Complete the Primes and Zeta practice problems that you will find in the Assignments folder on CoCalc. Simply complete the problems on CoCalc and they will be automatically turned in for grading. These practice problems are due Wednesday at 5pm.
  • Watch The Riemann Hypothesis, Explained by Quanta Magazine (16 min). Bring your answers to the following two questions to class on Wednesday:
    1. What did Riemann hypothesize in his 1859 paper?
    2. According to the video, how do the zeta zeros relate to the prime numbers?
  • Work on the Primes Project, due Friday.
Wednesday
November 6
Counting primes and the Riemann zeta function

Bonus: Yitang Zhang: An Unlikely Math Star Rises and "After Primes Proof, an Unlikely Star Rises" from Quanta Magazine

Do the following before next class:
Friday
November 8
Detecting large primes
Do the following before next class:
  • Read Section 4.4 (pages 166–176) in our Exploring Mathematics text. If you want to see how large primes are used in cryptography, read Section 4.5.
  • Complete the Large Primes practice problems that you will find in the Assignments folder on CoCalc. Simply complete the problems on CoCalc and they will be automatically turned in for grading. These practice problems are due Monday at 5pm.
  • Optionally, work on project revisions or challenge problems.
Monday
November 11
Pseudorandom numbers

MSCS Colloquium: Computer Science Faculty Candidate, Monday, November 11, 3:30pm in RNS 210

Do the following before next class:
  • Read Section 5.1, (pages 207–221), in our Exploring Mathematics text.
  • Complete the Pseudorandom Numbers practice problems that you will find in the Assignments folder on CoCalc. Simply complete the problems on CoCalc and they will be automatically turned in for grading. These practice problems are due Monday Wednesday at 5pm.
  • Take a look at the Final Project Information. Begin thinking about possible topics and groups for your project.
  • Optionally, work on revising your Primes Project. Revisions are due next Monday, November 18.
Wednesday
November 13
Probabilistic simulation

Bonus video: Francis Su — Mathematics for Human Flourishing short version and long version

MSCS Colloquium: Computer Science Faculty Candidate, Wednesday, November 13, 3:30pm in RNS 290

Do the following before next class:
  • Read Section 5.3 (pages 221–237) in our Exploring Mathematics text. Also read Page 240 about the coupon collector problem.
  • Complete the Simulation practice problems that you will find in the Assignments folder on CoCalc. Simply complete the problems on CoCalc and they will be automatically turned in for grading. These practice problems are due Wednesday Friday at 5pm.
  • Take a look at the Final Project Information. Begin thinking about possible topics and groups for your project.
  • Optionally, revise your Primes Project or work on a challenge problem.
Friday
November 15
Do the following before next class:
  • Read pages 249–255 in Section 5.5 in our Exploring Mathematics text.
  • Complete the 1D Random Walks practice problems that you will find in the Assignments folder on CoCalc. Simply complete the problems on CoCalc and they will be automatically turned in for grading. These practice problems are due Friday Monday at 5pm.
  • Take a look at the Final Project Info. Start thinking about which topics interest you and who you would like to work with.
  • Optionally, revise your Primes Project or work on a challenge problem.
Monday
November 18
1D Random walks
Primes Project
revisions due
Do the following before next class:
  • Watch the 1D Random Walk Proof to learn why a simple symmetric 1-D random walk must return to the origin. Also read Aside 5.19 on page 256 in our Exploring Mathematics text.
  • Complete the 1D Return to Origin practice problems that you will find in the Assignments folder on CoCalc. Simply complete the problems on CoCalc and they will be automatically turned in for grading. These practice problems are due Wednesday at 5pm.
  • Read the Final Project Info and continue thinking about which topics interest you and who you would like to work with.
  • Optionally, work on a challenge problem.
Wednesday
November 20
2D Random walks

Bonus videos: Satyan Devadoss — Blue Collar Mathematics and Mage Merlin's Unsolved Mathematical Mysteries

Do the following before next class:
  • Complete the 2D Random Walks practice problems that you will find in the Assignments folder on CoCalc. Simply complete the problems on CoCalc and they will be automatically turned in for grading. These practice problems are due Friday at 5pm.
  • Think about which topics interest you and who you would like to work with for the Final Project. Complete the Final Project Planning Survey.
  • Begin work on the Random Walk Project, which is due Monday.
  • Optionally, work on a challenge problem.
Friday
November 22
Do the following before next class:
  • Read Section 5.5 (pages 249--264) in our Exploring Mathematics text.
  • Work on the Random Walk Project, which is due Monday. Do this project in the Assignments → Random Walks Project folder in CoCalc.
Monday
November 25
3D Random walks
There is no assignment over break. However, you could consider the following:
  • If there is a project from earlier in the semester that you have not turned in yet, you may still use a token to turn it in. Break could be a good time to work on that project.
  • Optionally, work on a challenge problem.
Have a great Thanksgiving break! No class November 27 or 29.
Monday
December 2
Artificial intelligence and computational mathematics
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Wednesday
December 4
Artificial intelligence and computational mathematics
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Friday
December 6
Final projects
Do the following before next class:
Monday
December 9
Final projects
We've made it to the end of the semester! A few last things to do:
Monday
December 16
Final Presentations 1:00–3:00pm