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.

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

• 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.

• Read Section 3.3, pages 112–121, in our Exploring Mathematics text.
• Optionally, start work on the next practice problems (to be posted soon), due Friday, October 17.
• Optionally, work on revising your Generalized Fibonacci Project or begin the Iterated Functions Project.

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

• Read Section 3.3 through page pages 129 in our Exploring Mathematics text.
• Complete the Logistic Map practice problems and upload your solutions to the Logistic Map assignment on Moodle.
• Optionally, work on revising your Generalized Fibonacci Project. You may resubmit your project to the Generalized Fibonacci Project assignment on Moodle.
• Begin the Iterated Functions Project, due next Friday.

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

• Read the rest of Section 3.3 in our Exploring Mathematics text.
• Watch This equation will change how you see the world (the logistic map) by Veritasium. Come to the next class prepared to discuss at least two things you learned from the video.
• Complete the Bifurcations and Chaos practice problems and upload your solutions to the Bifurcations and Chaos assignment on Moodle.
• Optionally, work on revising your Generalized Fibonacci Project. You may resubmit your project to the Generalized Fibonacci Project assignment on Moodle.
• Begin the Iterated Functions Project, due next Friday.

• Read Section 3.4 in our Exploring Mathematics text.
• To learn more about chaos theory, watch The Science of the Butterfly Effect by Veritasium.
• Complete the Feigenbaum Constant practice problems and upload your solutions to the Feigenbaum Constant assignment on Moodle.
• Work on your Iterated Functions Project, due Friday.

Bonus: Steven Strogatz "How things in nature tend to sync up" and The Joy of x podcast

• Finish your Iterated Functions Project. Upload your project to the Iterated Functions Project assignment on Moodle.
• Read the following pages in the SageMath documentation: Assignment, Equality, and Arithmetic, Getting Help, Functions, Indentation, and Counting, Basic Algebra and Calculus, and Some Common Issues with Functions.

• 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.

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

• Finish reading Section 4.1 in our Exploring Mathematics text.
• Read Why prime numbers still fascinate mathematicians, 2300 years later.
• Try to finish your sieve of Eratosthenes code from class.
• Optionally, begin revising your Iterated Functions Project. Revisions are due next Monday, November 4.

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

• 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.

• 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.

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

• 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.

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

• Read Section 4.6 (pages 189–204) in our Exploring Mathematics text.
• Read The Riemann Hypothesis, explained.
• Optionally, to better understand complex functions and the Riemann zeta function, watch Visualizing the Riemann zeta function and analytic continuation by 3Blue1Brown.
• Finish your Primes Project, due Friday. Do your work in the Primes Project assignment folder on CoCalc, and it will be automatically available for grading.

• 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.

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

• 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.

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

• 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.

• 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.

• 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.

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

• 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.

• 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.

• 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.