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. Pay special attention to the grading information.
• Watch the video Hands-On Start to Mathematica by Wolfram.
• Read the Introduction through page 10 of Computational Mathematics, Chapter 1.
• Complete the Intro Mathematica practice 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 problem, and upload your solution to Moodle.
• Read through page 22 in Computational Mathematics, Chapter 1.
• 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: John Urschel-NFL Math Whiz

• 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 solution to Moodle.
• Read Section 1.4 (pages 26–29) in Computational Mathematics, Chapter 1.

• Complete the Inverse Tangent Formulas practice problem and upload your solution to Moodle.
• Read Section 1.5 (pages 29–32) in Computational Mathematics, Chapter 1. Do Exercise 1.26 (not to turn in).

• Complete the Iterative Methods for \(\pi\) practice problems and upload your solutions to Moodle.
• Begin work on the \(\pi\) Project (due next Friday).
• Read Section 1.6 (pages 32–38) in Computational Mathematics, Chapter 1.

Bonus video: Eugenia Cheng on The Late Show

• Complete the Dart Board \(\pi\) practice problem and upload your solution to Moodle.
• Read the following pages about the Wolfram language: Ways to Apply Functions, Pure Anonymous Functions, and Tests and Conditionals
• Work on the \(\pi\) Project (due Friday).

• Finish the \(\pi\) Project. Upload your notebook to the \(\pi\) Project link on Moodle
• Watch The magic of Fibonacci numbers, a 6-minute TED talk by Arthur Benjamin.
• Read Sections 2.1 and 2.2 (pages 45–55) in Computational Mathematics, Chapter 2.

• Complete the Fibonacci implementations practice problem and upload your solution to Moodle.
• Read Section 2.3 (pages 55–67) in Computational Mathematics, Chapter 2.

Bonus: video How Not to Be Wrong: The Power of Mathematical Thinking - with Jordan Ellenberg

• Complete the Fibonacci Identities practice problems and upload your solutions to Moodle.
• Begin revising your solution to the \(\pi\) Project. Revisions are due Monday, March 7.
• Re-read Section 2.3 (pages 55–67) in Computational Mathematics, Chapter 2. Focus on the process of discovering Cassini's identity. Also note the various methods presented for verifying the identity for lots of indexes \(n\).

• Read pages 67–71 in Section 2.4 of Computational Mathematics, Chapter 2.
• Complete the Polynomial Identities practice problem and upload your solution to Moodle.
• Work on revising your solution to the \(\pi\) Project. Revisions are due Monday, March 7.

• Finish reading Section 2.4 in Computational Mathematics, Chapter 2. Note the algorithms corresponding to what we did in class today. Also take a look at the generalizations of the Fibonacci sequence in Section 2.5.
• Complete the Fibonacci and Lucas practice problems and upload your solution to Moodle.
• Finish revising your solution to the \(\pi\) Project, if necessary. Revisions are due Monday, March 7.
• Read the Generalized Fibonacci Project. Optionally, start experimenting with generalized Fibonacci sequences.

Bonus video: Hannah Fry — Beautiful equations: how insects walk on water and galaxies form

MSCS Colloquium: Monday 3:30–4:30pm in RNS 310

• Complete the Fibonacci and Lucas II practice problems and upload your solution to Moodle.
• Begin the Generalized Fibonacci Project. Experiment with generalized Fibonacci sequences.

• Work on the Generalized Fibonacci Project. Experiment with generalized Fibonacci sequences.
• Optionally, work on a Challenge Problem.

• Read pages 83–91 in Computational Mathematics, Chapter 3. Pay special attention to the algorithms and pseudocode.
• Work on the Generalized Fibonacci Project. Experiment with generalized Fibonacci sequences. Upload your project to the Generalized Fibonacci Project assignment on Moodle.

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

• Read the rest of Section 3.1 (pages 91–97) in Computational Mathematics, Chapter 3.
• Complete the Collatz Heights practice problems and upload your solutions to Moodle.

• Complete the Collatz Stopping Times practice problems and upload your solutions to Moodle.
• Read Section 3.2 (pages 97–103) in Computational Mathematics, Chapter 3.
• Watch The Simplest Math Problem No One Can Solve - Collatz Conjecture by Veritasium.

• Begin the Iterated Functions Project (due next Friday).
• Read pages 103–117 in Section 3.3 of Computational Mathematics, Chapter 3.

Bonus video: Moon Duchin: "Political Geometry"

• Complete the Logistic Map Practice Problems and upload your solutions to Moodle.
• Read Section 3.3 (pages 103–124) in Computational Mathematics, Chapter 3.
• Work on the Iterated Functions Project (due Friday).

• Watch This equation will change how you see the world (the logistic map) by Veritasium.
• Finish the Iterated Functions Project.

Bonus video: Francis Su — Mathematics for Human Flourishing

• Read the following pages from the Python Land tutorial: Variables, Strings, Functions, Booleans, and Loops.
• Work on any four of the six exercises in the Intro to Python notebook. If you get stuck, send questions to the professor or bring questions to class on Wednesday. By Friday, submit your work by copying the sharable link to your notebook and pasting it in the text field of the Intro Python assignment on Moodle.
• Optionally, work on revising your Generalized Fibonacci Project. Submit your revisions to the same Moodle assignment link as for the original project.

• Read pages 133–137 in Computational Mathematics, Chapter 4.
• Finish four of the six exercises in the Intro to Python notebook and submit your notebook link to the Intro Python assignment on Moodle.
• Optionally, finish revising your Generalized Fibonacci Project. Submit your revisions to the same Moodle assignment link as for the original project.

• Finish implementing the sieve of Eratosthenes, if you haven't done so already. Consider the efficiency of your implementation, and think about how you might make it more efficient.
• Optionally, work on revising your Iterated Functions Project.
• Optionally, work on a challenge problem.

Bonus video Interview with Karen Uhlenbeck and article Karen Uhlenbeck, Uniter of Geometry and Analysis, Wins Abel Prize

MSCS Colloquium: Monday 3:30–4:30pm in RNS 310

• Complete the Primes I practice problems and submit your solutions to Moodle.
• Optionally, work on revising your Iterated Functions Project.

• Complete the Primes II practice problem and submit your solution to Moodle.
• Optionally, finish on revising your Iterated Functions Project.
• Take a look at the Primes Project, due next Friday.

• Read Section 4.3 (pages 142–147) in Computational Mathematics, Chapter 4.
• Complete the Primes III practice problems and submit your solution to Moodle.
• Work on the Primes Project, due next Friday.

Bonus video: Yitang Zhang: An Unlikely Math Star Rises

• Complete the Primes IV practice problems and submit your solution to Moodle.
• Work on the Primes Project, due Friday.

• Finish the Primes Project, due Friday.
• Optional: For another look at the Riemann zeta function, watch Visualizing the Riemann zeta function and analytic continuation by 3Blue1Brown.

• Finish the Primes Project, if you haven't done so already.
• Continue the exploration of 1-D random walks from class. In particular, how does the average diameter depend on the number of steps? You don't have to turn in anything for this exploration.

Bonus video: MEET a Mathematician! - Trachette Jackson

• Watch the 1D Random Walk Proof to learn how often a simple symmetric 1-D random walk returns to the origin.
• Complete the 1D Random Walk Practice Problems.
• Read through this NumPy quickstart guide.

• Complete the 2D Random Walk Practice Problem, and submit your link to Moodle.
• Take a look at the Random Walk Project, due next Friday.
• Optionally, revise your Primes Project. To submit a revised project, update your Moodle submission to indicate revisions, even if the notebook link is unchanged.

• Work on the Random Walk Project, due next Friday.
• Take a look at the Final Project Information. Think about which topics interest you and who you would like to work with.
• Optionally, finish revising your Primes Project. To submit a revised project, update your Moodle submission to indicate revisions, even if the notebook link is unchanged.
• Optionally, work on a problem from the (updated) list of challenge problems.

Bonus: Why is Mathematics Useful — Robert Ghrist, and Applied Dynamical Systems Vol. 1

• Complete the Percolation Practice Problems and submit your link to Moodle.
• Work on the Random Walk Project, due Friday.
• Take a look at the Final Project Information. Think about which topics interest you and who you would like to work with.
• Optionally, work on a challenge problem.

• Complete the Final Project Planning Survey regarding your topic and group preferences for the final project.
• Finish the Random Walk Project, due Friday.

• Finish the percolation investigation from class (not to be collected).
• Optionally, work on a challenge problem.

Bonus: Susan D'Agostino book and interview

• Work on your final project. Identify what mathematical questions you would like to investigate. Start planning and writing code.
• Optionally, revise your random walk project.

• Work on your final project.
• Optionally, revise your random walk project.

• Work on your final project.

Bonus: Living Proof: Stories of Resilience Along the Mathematical Journey

• Finish your final project. Organize your computations and results into a notebook that demonstrates what you have accomplished in this project. Prepare your presentation.
• Submit your final project files/links to the Final Project assignment on Moodle.
• Recommended: schedule a practice presentation with the professor (see Google calendar appointment link in your email).