Advanced Computational Math

• 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.

• Complete the Introductory Survey, if you haven't done so already.
• Read the Syllabus. Pay special attention to the grading information.
• 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.

• 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.

• 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.

• 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.

• 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.

• Read Section 1.1 of Algorithms and Complexity by Herbert Wilf: Moodle link, Library link.
• Complete exercises 2, 3, and 4 on pages 17–18 of Algorithms and Complexity by Herbert Wilf. Upload your solutions to the Orders of Magnitude assignment on Moodle.
• Work on the Bin Packing Project, due next Tuesday, March 5.

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

• Read Section 1.6 Graphs of Algorithms and Complexity by Herbert Wilf: Moodle link, Library link.
• Complete exercises 2, 4, 7, and 11 on page 46 of Algorithms and Complexity by Herbert Wilf. Upload your solutions to the Graph Theory assignment on Moodle.
• Read the "Graph Coloring" subsection on pages 307–309 of Computational Mathematics.
• Finish your Bin Packing Project, due next Tuesday, March 5. Upload your solution to the Bin Packing Project assignment on Moodle.

• Watch Solving Math's Map Coloring Problem Using Graph Theory by Quanta Magazine.
• Read Section 5.1 (NP-Completeness Introduction) of Algorithms and Complexity by Herbert Wilf Moodle link, Library link.
• Optionally, look for articles/topics for the Computation "in the Wild" assignment.

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

• Watch P vs. NP: The Biggest Puzzle in Computer Science by Quanta Magazine.
• Complete exercises 1–4 on page 174 of Algorithms and Complexity by Herbert Wilf Moodle link, Library link. Upload your solution to the P and NP assignment on Moodle.
• Optionally, look for articles/topics for the Computation "in the Wild" assignment.

• 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.

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

• 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.

• 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.

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.

• Complete the Simplicial Complex practice problems and submit your work to the Simplicial Complex assignment on Moodle.
• Watch COMPLEXES: Combinatorics" by Robert Ghrist.
• Optional reading: Chapter 1 of Computational Algebraic Topology lecture notes by Vidit Nanda
• Begin work on the Traveling Salesperson Project. Decide which option you would like to do for this project. (Due next Thursday)

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

• From the Foundations of Topological Data Analysis video series by Robert Ghrist, watch Subcomplexes, Realization, and Metric Data.
• Complete the April 4 practice problems and submit your work to the April 4 assignment on Moodle.
• Work on the Traveling Salesperson Project. (Due next Thursday)
• Optionally, work on your Computation "in the Wild" assignment.

• Finish the first draft of your Traveling Salesperson Project. Submit your notebook to the TSP project link on Moodle.
• Optionally, work on your Computation "in the Wild" assignment.

• Read Section 3.1 Euler Characteristic in the Computational Algebraic Topology lecture notes by Vidit Nanda. Optionally, continue reading in Chapter 3.
• Complete the Euler Characteristic practice problems and submit your solutions to the Euler characteristic assignment on Moodle.
• Optionally, work on your Computation "in the Wild" assignment.

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

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

• For a more thorough (and algebraic) introduction to homology and Betti numbers, read Sections 3.2—4.3 in the Computational Algebraic Topology lecture notes by Vidit Nanda.
• Optionally, work on your Computation "in the Wild" assignment.
• Optionally, begin revising your Traveling Salesperson Project.

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

• Complete the Betti number practice problems and submit your solutions to the Betti number assignment on Moodle.
• Optionally, work on your Computation "in the Wild" assignment.
• Optionally, revise your Traveling Salesperson Project.

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

• Optionally, work on your Computation "in the Wild" assignment.
• Optionally, revise your Traveling Salesperson Project.

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 310

• Complete the Matrix reduction practice problems and submit your solutions to the Matrix reduction assignment on Moodle.
• Read Why Mathematical Proof Is a Social Compact" and Can Computers be Mathematicians? (both from Quanta Magazine). Submit at least three interesting things you found in the reading or questions this reading prompts you to ask to the Computers and Proofs reading assignment on Moodle.
• Optionally, work on your Computation "in the Wild" assignment.

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

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