Matthew L. Wright
Assistant Professor, St. Olaf College

# Modern Computational Math

## Math 242 ⋅ Spring 2018

Prof. Wright's office hours in RMS 405: Mon. 8:00–8:55 & 2:15–3:15, Wed. 2:30–3:30, Thurs 9:30–10:30, Fri. 10:30–11:30, whenever the door is open, or by appointment

Help sessions: Thursdays 7–8pm in RNS 206

Friday
February 9
Introduction
Mathematica basics — Programming in Mathematica notebook
Do the following before next class:
Monday
February 12
Fibonacci numbers
Do the following before next class:
• Make sure you understand the code in the Mathematica notebook from class today. If you are confused about something, ask a question on Piazza!
• Cassini's Identity says $$F_n^2 - F_{n+1}F_{n-1} = (-1)^{n-1}$$. Use Mathematica to verify this for the first 1000 (or so) Fibonacci numbers. Bring your best attempt at this to class on Wednesday.
• Read Keith Devlin's blog post How today’s pros solve math problems: Part 1 and answer the questions on the reading guide. Bring your completed reading guide to class on Wednesday.
Wednesday
February 14
Fibonacci numbers
Mathematica notebook: day3_Fibonacci_properties.nb
Do the following before next class:
• Work on the Fibonacci Project. It's due on Monday, but do as much as you can by Friday, so that you can ask questions if you get confused or stuck. When you finish, upload your notebook to Moodle.
Friday
February 16
Pell numbers
Mathematica notebooks: day4_Pell_starter.nb, Section A, Section B
Do the following before next class:
• Finish the Fibonacci Project and upload your notebook to Moodle.
• Take a look at this paper, which gives various identities for the Pell numbers. Try to generate several other polynomial identities similar to those described in Proposition 1. For example, can you directly conjecture and verify the identity for $$n=11$$?
Monday
February 19
Pell numbers
Mathematica notebooks from class: Section A, Section B
Do the following before next class:
• Begin the Pell Project. It's due Friday, but don't wait until Thursday to start!
Wednesday
February 21
Pell numbers
Mathematica notebooks from class: Section A, Section B
Do the following before next class:
Friday
February 23
Iterated functions: Collatz conjecture
Mathematica notebooks from class: Section A, Section B
Do the following before next class:
• Begin the Collatz Project. It's due Wednesday, but it would be wise to start over the weekend.
Monday
February 26
Mean-median map
Do the following before next class:
Wednesday
February 28
Mean-median map
Mathematica notebook: day9_MeanMedian.nb
Do the following before next class:
Friday
March 2
Mean-median map
Do the following before next class:
Monday
March 5
Collatz Fractals
Starter notebook, in class: Section A, Section B
Do the following before next class:
• Think about the question "If someone gives you a positive integer $$n$$, how would you determine whether $$n$$ is prime?"
• Write down a simple algorithm to answer the previous question. Bring your algorithm to class on Wednesday.
• Finish the Mean-Median Project and upload your notebook to Moodle.
Wednesday
March 7
Do the following before next class:
Friday
March 9
Do the following before next class:
Monday
March 12
Prime sieves
Do the following before next class:
Wednesday
March 14
Digits of π
For fun: How pi was almost 6.283185...; in class: Section A, Section B
Do the following before next class:
Friday
March 16
Prime Powers
Starter notebook; in class: Section A, Section B
Do the following before next class:
Monday
March 19
Mathematics of RSA cryptography
Starter notebook
Do the following before next class:
• Complete the notebook from today's class. Use it to encrypt and decrypt numbers.
• Post your public key to the RSA Forum on Moodle, so that others can send you secure messages.
• Watch this video introduction to RSA encryption, if you haven't done so already.
Wednesday
March 21
RSA cryptography: encrypting text
Starter notebook; in class: Section A, Section B
Do the following before next class:
Friday
March 23
Prime patterns and the Riemann zeta function
Mathematica notebook
If you want to learn more about the Riemann zeta function, watch these two videos by 3Blue1Brown: Visualizing the Riemann zeta function and analytic continuation and Pi hiding in prime regularities.
Have a great spring break! No class March 26 – April 2.
Do the following before next class:
Wednesday
April 4
Do the following before next class:
Friday
April 6
Yahtzee in Mathematica and R
R scripts: Probability in R, Yahtzee starter; Yahtzee Mathematica notebook
Do the following before next class:
Monday
April 9
Yahtzee simulation and ggplot2
starter script file, scripts from class
Do the following before next class:
Wednesday
April 11
Do the following before next class:
Friday
April 13
RMarkdown and Markov Chains
Files: Sample Markdown file, Intro to Markov chains
Do the following before next class:
Monday
April 16
Do the following before next class:
• Finish the first two exercises in the R Markdown file from class.
• Finish the Trouble Project and upload your Mathematica notebook or HTML or PDF file (knit from R Markdown) to Moodle.
Wednesday
April 18
Monopoly
Solutions from last time; Mini Monopololy: R Markdown and HTML
Do the following before next class:
Friday
April 20
Do the following before next class:
Monday
April 23
Monopoly
Do the following before next class:
Wednesday
April 25
Do the following before next class:
Friday
April 27
Markov Chain Monte Carlo (MCMC)
Files: Files: MCMC R Markdown, MCMC PDF
Do the following before next class:
Monday
April 30
MCMC Function Minimization
Files: Minimize Function R Markdown, Minimize Function HTML
Do the following before next class:
Wednesday
May 2
Combinatorial Optimization: Simulated Annealing
Files: Optimization R Markdown, Optimization HTML
Do the following before next class:
• Make sure you are caught up with the MCMC function minimization.
• Work on the exercise and assignment in the Optimization file. (The Magic Square assigment is due Monday.)
• Think about a topic and (optionally) a group for the Final Project.
Friday
May 4
Magic Squares
Do the following before next class:
• Finish the Magic Square assignment (in the Optimization file) and submit your solution to Moodle.
• Think about a topic and (optionally) a group for the Final Project.
Monday
May 7
Traveling Salesperson Problem (TSP)
TSP PDF file
Do the following before next class:
Wednesday
May 9
Traveling Salesperson Problem (TSP)
TSP PDF file
Do the following before next class:
Friday
May 11
Work on final project
Do the following before next class:
Monday
May 14
Work on final project
Do the following before next class:
• Work on your Final Project.
• Prepare in 1–2 paragraphs describing what you have accomplished on your project, what remains to do, and what questions you have.
Wednesday
May 16
Work on final project
Finish your Final Project. Upload your Mathematica Notebook or HTML/PDF file (knit from R Markdown) to Moodle. Prepare your presentation for the final exam time period.
Tuesday
May 22
2–4pm: Final projects due, presentation time for Math 242 B
Wednesday
May 23
2–4pm: Final projects due, presentation time for Math 242 A