Modern 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 and complete the Syllabus Quiz on Moodle.
• Watch the video Hands-On Start to Mathematica by Wolfram.
• Read pages 1–10 of Exploring Mathematics from a Computational Perspective. Come to class prepared to summarize Archimedes's method for computing \(\pi\).
• Complete the Intro Mathematica homework problems and submit your notebook to the Intro Mathematica assignment on Moodle.

• Read the following pages about the Wolfram Language: Fractions & Decimals, Variables & Functions, Lists, Iterators, and Assignments.
• Modify the code from class to complete the Archimedes's Method practice problems, and upload your solutions to the Archimedes's Method assignment on Moodle.
• Read pages 11–23 in our Exploring Mathematics text. Come to class prepared to explain what the text means by accuracy, efficiency, and representation.
• If you're curious why the sum of reciprocals of squares converges to \(\pi^2/6\) (on the Intro Mathematica practice problem), then watch this video.

Bonus video: Paths to Math: John Urschel

• Read the following pages about the Wolfram Language: Functions and Programs, Operations on Lists, and Assigning Names to Things
• Complete the Madhava series practice problem and upload your solutions to the Madahava Series assignment on Moodle.
• Read Section 1.4 (pages 28–31) in our Exploring Mathematics text. Come to class ready to discuss how sums arising from arctangent formulas can be used to compute digits of \(\pi\).

• 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.

• Complete the Iterative Methods for \(\pi\) practice problems and upload your solutions to the Iterative Methods assignment on Moodle.
• Begin work on the \(\pi\) Project (first draft due Friday).
• Read Section 1.6 (pages 37–43) in our Exploring Mathematics text. Come to class prepared to discuss the "dart board" method for computing \(\pi\).

Bonus video: Eugenia Cheng on The Late Show

• Finish your \(\pi\) Project. Your first draft is due Wednesday (Moodle link). Remember that after the initial grading, you will have a chance to revise and resubmit for a higher grade.
• Optionally, read how Google computed 100 trillion digits of \(\pi\).
• Optionally, work on the Dart Board \(\pi\) practice problems. These are due on Monday.
• Read the following pages about the Wolfram language: Ways to Apply Functions, Pure Anonymous Functions, and Tests and Conditionals
• Read Section 2.1 (pages 49–51) in our Exploring Mathematics text. Come to class ready to say what recursive means (in the context of a recursive sequence or a recursively-defined function).

• Finish the Dart Board \(\pi\) practice problems from Wedneseday and upload your solution to the Dart Board Pi assignment on Moodle.
• Watch The magic of Fibonacci numbers, a 6-minute TED talk by Arthur Benjamin.
• Read Section 2.2 (pages 51–60) in our Exploring Mathematics text.

• 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.

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

• Complete the Fibonacci Identities practice problems and upload your solutions to the Fibonacci Identities assignment on Moodle.
• Finish reading Section 2.3 (pages 61–74) in our Exploring Mathematics text.
• Optionally, work on 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.

• Read Section 2.4 (pages 74–82) in our Exploring Mathematics text.
• Complete the Polynomial Identities practice problem and upload your solution to the Polynomial Identities assignment on Moodle. Come to class ready to discuss your observation about Fibonacci Polynomial identities.
• Optionally, finish revising your \(\pi\) Project. Talk with the professor if you have questions about how to do this. Revisions are due Friday, March 1. You may submit your revisions to the same project link on Moodle.

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

• Read Section 2.5 through page 87 in our Exploring Mathematics text.
• Complete the Lucas Identities practice problems and upload your solution to the Lucas Identities assignment on Moodle.
• Take a look at the Generalized Fibonacci Project. Optionally, start experimenting with generalized Fibonacci sequences.

Bonus: Susan D'Agostino book and interview

• Finish reading Section 2.5 in our Exploring Mathematics text.
• Complete the Pell Identities practice problems and upload your solution to the Pell Identities assignment on Moodle.
• Begin the Generalized Fibonacci Project. Experiment with generalized Fibonacci sequences.

• Read pages 91–96 in our Exploring Mathematics text.
• Finish your Generalized Fibonacci Project. Upload your project to the Generalized Fibonacci Project assignment on Moodle.

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

• Finish reading Section 3.1 (pages 97–106) in our Exploring Mathematics text.
• Watch The Simplest Math Problem No One Can Solve — Collatz Conjecture by Veritasium. Come prepared to discuss something interesting from this video at the beginning of class on Wednesday.
• Complete the Collatz Patterns practice problems and upload your solutions to the Collatz Patterns assignment on Moodle.

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

• Read Mathematician Proves Huge Result on 'Dangerous' Problem in Quanta magazine.
• Read Section 3.2 (pages 106–112) in our Exploring Mathematics text.
• Complete the Collatz Extensions practice problems and upload your solutions to the Collatz Extensions assignment on Moodle.