Modern Computational Math

• Complete the Introductory Survey.
• Watch the Hands-On Start to Mathematica video.
• 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 syllabus quiz.
• Read the following pages about the Wolfram Language: Fractions & Decimals, Variables & Functions, Lists, Iterators, and Assignments.
• Complete Intro Mathematica assignment. Upload your solution notebook to Moodle.

• Watch this video, which explains why the sum of reciprocals of squares converges to \(\pi^2/6\).
• Start the \(\pi\) Project (due Monday Wednesday). Implement at least one of the methods for approximating digits of \(\pi\) before Friday's class. Also look over the sample project report.
• Complete Mathematica Quiz 1 (on Moodle).
• Optional bonus: Watch this video to learn why the product formula from the Intro Mathematica assignment converges to \(\pi\).

• Read How to Create Lists and How to Get Elements of Lists from the Wolfram language documentation.
• Work on the \(\pi\) Project. It's now due Wednesday, but try to make as much progress as you can this weekend, and ask questions on Monday. Prepare a Mathematica notebook that contains your code and discussion. Pay attention to the grading rubric in the assignment file and refer to the sample project report.
• Watch The magic of Fibonacci numbers, a 6-minute TED talk by Arthur Benjamin.

• Finish the \(\pi\) Project. Pay attention to the grading rubric in the assignment file and refer to the sample project report. Submit your notebook to the Pi Project on Moodle.
• Investigate \( F_n^2 - F_{n+1}F_{n-1} \), where \( F_n \) is the \(n\)th Fibonacci number. Evaluate this quantity for lots of values of \(n\). What pattern do you observe?

• Catalan's identity says \(F_n^2 - F_{n+r}F_{n-r} = (-1)^{n-r}F_r^2 \). Verify this for at least three values of \(r > 2 \). For each value of \( r \), check at least 100 values of \( n \).
• Vajda's identity says \(F_{n+i}F_{n+j} - F_nF_{n+i+j} = (-1)^n F_i F_j \). Verify this for at least six pairs \(i,j\). For each pair \(i,j\), check at least 100 values of \(n\).
• Submit a Mathematica notebook containing your verifications of Catalan's and Vajda's identities to the Fibonacci Assignment on Moodle. Please put your name at the top of your notebook. (Note that this is an Assignment, not a Project.)

• Complete Mathematica Quiz 2 (on Moodle). This quiz covers lists, indexed variables, functions, and Modules.
• Take a look at this paper, which proves various identities involving the Pell numbers. Read through the Introduction, which gives some background about the Pell numbers. Note that Proposition 1 corresponds to our observations in class. Take a quick look at the other propositions and theorems that the authors prove.
• Begin the Pell Project, due Wednesday, March 3.

• Finish the Pell Project (due Wednesday). Upload your notebook to Moodle.
• Continue your investigation of sequences that arise when iterating the Collatz function or some other function. Bring observations and questions to class on Wednesday.

Extra credit opportunity: Attend either of Dr. Trachette Jackson's lectures on March 2 or 3 and answer these two questions on Moodle to earn two extra-credit points.

• Read Mathematician Proves Huge Result on 'Dangerous' Problem and answer three questions on Moodle before class on Friday.
• Continue your computational exploration of Collatz sequences and the logistic function. Take a look at the Iterated Functions Project and think about what you want to investigate.

Bonus video: Steven Strogatz — The science of sync

• Watch This equation will change how you see the world by Veritasium. Observe how the bifurcation diagram of the logistic map relates to the Mandelbrot set. There are even applications to fluid convection, neuron firing, and more. Wow!
• Work on the Iterated Functions Project, due Wednesday.

• Finish the Iterated Functions Project. Upload your notebook to Moodle.
• Reading to be announced...