Matthew L. Wright
Associate Professor, St. Olaf College

## MATH 384 ⋅ Spring 2024

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Today
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In the Wild 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.
Thursday
February 8
Course introduction; Markov chains
Do the following before next class:
• Complete the Introductory Survey, if you haven't done so already.
• Read Section 6.1 (pages 263–272) of Computational Mathematics.
• Complete the Exercises 6.6 and 6.7 on page 271 of Computational Mathematics. Prepare your solutions in a computational notebook (Mathematica, or a different language if you prefer). Make sure your work is complete and clearly explained. Submit your notebook to the Markov Chains assignment on Moodle.
Tuesday
February 13
Markov chain Monte Carlo (MCMC) sampling
Do the following before next class:
• Read Section 6.2 (pages 272–283) of Computational Mathematics.
• Complete the Exercises 6.12 and 6.13 on page 281 of Computational Mathematics. Prepare your solutions in a computational notebook (Mathematica, or a different language if you prefer). Make sure your work is complete and clearly explained. Submit your notebook to the Markov Chain Sampling assignment on Moodle.
Thursday
February 15
MCMC sampling from large state spaces
Do the following before next class:
• Read Section 6.3 (pages 283–293) of Computational Mathematics.
• Complete Practice 6.16 and Exercise 6.17 (pages 291-292) in Computational Mathematics. Prepare your solutions in a computational notebook (Mathematica, or a different language if you prefer). Make sure your work is complete and clearly explained. Submit your notebook to the MCMC sampling from large state spaces assignment on Moodle.
• Look back over Sections 6.1–6.3 in the Computational Mathematics text. What makes sense in these sections? What do you find to be confusing? What questions do you have? Bring some thoughts to share in class on Tuesday.
Tuesday
February 20
MCMC Optimization and Simulated Annealing
Do the following before next class:
• From Computational Mathematics, read Section 6.4 (pages 293–299) and the following portions of Section 6.5: from the start of the section on page 299 to the Bin Packing heading on page 303; skip the Bin Packing subsection; then read from the start of the Magic Squares subsection on page 305 through Practice 6.30.
• Complete Exercise 6.27 and Practice 6.30 in Computational Mathematics. Prepare your solutions in a computational notebook (Mathematica, or a different language if you prefer). Make sure your work is complete and clearly explained. Submit your notebook to the MCMC simulated annealing assignment on Moodle.
Thursday
February 22
Simulated annealing
Do the following before next class:
• Read the "Magic Squares" subsection on pages 305–307 of Computational Mathematics.
• Complete the following two practice problems:
• Exercise 6.33 in Computational Mathematics. For this, you may modify code from class.
• Compare at least two different objective functions for finding magic squares ($$4 \times 4$$ or larger). You may use objective functions listed on page 306 in the text, or other functions of your choice. On average, how many iterations are required to find a magic square with each function?
Submit your work to the Magic squares assignment on Moodle.
• Read the requirements for the Bin Packing Project. Make a plan for using simulated annealing to solve the bin packing problem. Begin implementing your algorithm and exploring its effectiveness.
Tuesday
February 27
Computational complexity
Do the following before next class:
Thursday
February 29
Computational graph theory

STEM Alumni Panel: UNSCRIPTED, Friday, March 1, 5–7pm, Buntrock 142

Do the following before next class:
Tuesday
March 5
Computational graph theory; Computational complexity
Do the following before next class:
Thursday
March 7
Computational complexity; Traveling salesperson problem

Physics & Math Colloquium: Colin Scheibner '17, Spiking at the Edge: Excitability at interfaces in reaction-diffusion systems" Friday, March 8, 3:30–4:30pm in RNS 210

MSCS Colloquium: Lara Pudwell, "Patterns in Permutations," Monday, March 11, 3:30–4:30pm in RNS 310

Do the following before next class:
Tuesday
March 12
Traveling salesperson problem
Do the following before next class:
• Read the "Traveling Salesperson" subsection on pages 310–313 of Computational Mathematics.
• Work on revising your Bin Packing Project. Revisions are due Tuesday, March 19.
• Optionally, look for articles/topics for the Computation "in the Wild" assignment.
Thursday
March 14
Traveling salesperson problem

MSCS Research Seminar: Francesca Gandini, "Invariants Three Ways," Friday, March 15, 3:30–4:30pm in RNS 210 (this talk requires Abstract Algebra)

MSCS Colloquium: Janet Page, "Gorenstein rings and the Chicken McNugget Problem," Monday, March 18, 3:30–4:30pm in RNS 310

Do the following before next class:
• Read Chapter 1 of The Traveling Salesman Problem: A Computational Study by Applegate et al., Moodle link, Library link. Submit at least three interesting observations or questions from this reading to the TSP Reading assignment on Moodle.
• Work on revising your Bin Packing Project. Revisions are due Tuesday, March 19. Upload your revisions to the same Bin Packing Project assignment on Moodle.
Tuesday
March 19
Minimum spanning trees
Bin Packing
revisions due
Do the following before next class:
• Use computational investigation to answer the following two questions:
• What is the average length of the minimum spanning tree for ten points sampled uniformly at random from the square $$[0,1]\times[0,1]$$?
• Suppose $$n$$ points are sampled uniformly at random from the square $$[0,1]\times[0,1]$$. How does the average length of the minimum spanning tree depend on $$n$$? What function of $$n$$ approximates this average length?
Submit your work to the Minimum Spanning Tree assignment on Moodle.
• Optionally, work on your Computation "in the Wild" assignment.
Thursday
March 21
Linear optimization and the traveling salesperson problem

To learn more about linear optimization and the simplex method, see Linear Programming and its Applications by Eiselt and Sandblom, especially Chapter 3 — Moodle link, Library link.

To learn more about the original linear programming method for solving the traveling salesperson problem, read Chapter 3 of The Traveling Salesman Problem: A Computational Study by Applegate et al., — Moodle link, Library link.

Have a great spring break! No class March 25–April 1.
Tuesday
April 2
Simplicial complexes
Do the following before next class:
Thursday
April 4
Simplicial complexes and Euler characteristic

MSCS Research Seminar: Sunrose Shrestha, "Cylinders on the Mucube," Thursday, April 4, 11:30–12:30am in RNS 210

MSCS Recital: Thursday, April 4, 7pm, Ytterboe Lounge

Do the following before next class:
Tuesday
April 9
Simplicial complexes and Euler characteristic
Do the following before next class:
Thursday
April 11
Simplicial complexes and Euler characteristic
Do the following before next class:

Math Across the Cannon: Moon Duchin, "Design for Democracy" April 15, 7–8pm in Carleton College Olin Hall 149

Tuesday
April 16
Simplicial homology

Math Across the Cannon: Moon Duchin, The Accidental Arboretum" April 16, 3:30–4:30pm in Regents 150

Do the following before next class:
Thursday
April 18
Simplicial homology

Kleber-Gery Lecture: Aleszu Bajak, "Telling Your Story with Data," Thursday, April 18, 7–8pm in Tomson 280;

MSCS Colloquium: Aleszu Bajak, "Stats in the Newsroom," Friday, April 19, 3:30–4:30pm in RNS 310

Do the following before next class:

MSCS Colloquium: Lisa Tonder, "A Day in the Life of a Statistician at Medtronic," Monday, April 22, 3:30–4:30pm in RNS 310

Tuesday
April 23
Persistent homology
Do the following before next class:
Thursday
April 25
Persistent homology
TSP Project
revisions due

BRIDGES: Common Ground Friday, April 26, 3–5pm, RNS 356

MSCS Research Seminar: Jacob Laubacher, "Classifying Prime Character Degree Graphs," Friday, April 26, 3:30–4:30pm in RNS 210

Do the following before next class:

MSCS Colloquium: Lori Ziegelmeier, "On the Data of Images," Monday, April 29, 3:30–4:30pm in RNS 310

Tuesday
April 30
Finish persistent homology; Computer-assisted proof
Do the following before next class:
Thursday
May 2
Computer-assisted proof and artificial intelligence; Final projects

MSCS Research Seminar: Corey Brooke, "Two Vignettes on Pythagorean Triples," Friday, May 3, 3:30–4:30pm in RNS 210

Do the following before next class:
Tuesday
May 7
Computer-assisted proof and artificial intelligence; Final projects
Do the following before next class:
Thursday
May 9
Final projects
Do the following before next class:
Tuesday
May 14
Final projects
We've made it to the end of the semester! A few last things to do:
Thursday
May 16
Final Presentations 9:00–11:00am