Matthew L. Wright
Assistant Professor, St. Olaf College

# Modern Computational Math

## Math 242 ⋅ Spring 2020

Prof. Wright's office hours:
In the classroom RNS 160R: Mon., Wed., and Fri. 12:50–1:50pm (between sections of Math 242)
In office RMS 405: Wed. 10:00–11:00am, Thurs. 10:30–11:30am, by appointment, and whenever the door is open

Help sessions: Tues. and Thurs. 7:00–8:00pm in RNS 316

Friday
February 7
Introduction; Mathematica basics
Do the following before next class:
Monday
February 10
Computing the digits of $$\pi$$
Do the following before next class:
• Start the $$\pi$$ Project (due Friday). Implement at least one of the methods for approximating digits of $$\pi$$. Look over the sample project report.
• For an explanation of why the sum of reciprocals of squares converges to $$\pi^2/6$$, watch this video. For an explanation of why the product formula from last time converges to $$\pi$$, watch this video.
Wednesday
February 12
Fibonacci numbers
Do the following before next class:
• Finish the $$\pi$$ Project. 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. 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?
Friday
February 14
Fibonacci identities No class—Prof. Wright is ill
Do the following before next class:
• 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?
Monday
February 17
Fibonacci identities
Do the following before next class:
• 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.)
Wednesday
February 19
Pell numbers
Do the following before next class:
• 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. Look at the other propositions and theorems that the authors prove.
• Begin the Pell Project, which is due Monday.
Friday
February 21
Iterated functions: Collatz conjecture
Do the following before next class:
• Finish the Pell Project, which is due Monday.
• Formulate some obserations and questions about the Collatz function...more details to be posted soon.
Monday
February 24
Iterated functions: logistic map and chaos
Do the following before next class:
Wednesday
February 26
Iterated functions and fractals
Do the following before next class:
Friday
February 28
Mean-median map
Do the following before next class:
Monday
March 2
Mean-median map
Do the following before next class:
Wednesday
March 4
Primes
Do the following before next class:
Friday
March 6
Primes sieves
Do the following before next class:
Monday
March 9
Prime sieves
Do the following before next class:
Wednesday
March 11
Prime powers
Do the following before next class:
Friday
March 13
Mathematics of RSA cryptography
Do the following before next class:
Monday
March 16
Encrypting text with RSA cryptography
Do the following before next class:
Wednesday
March 18
Counting primes
Do the following before next class:
Friday
March 20
Prime patterns and the Riemann zeta function
Have a great spring break! No class March 23 – 27.
Do the following before next class:
Monday
March 30
Introduction to Python
Do the following before next class:
Wednesday
April 1
Yahtzee in Mathematica and Python
Do the following before next class:
Friday
April 3
Yahtzee in Python, and plotting with Matplotlib
Do the following before next class:
Monday
April 6
Trouble simulation
Do the following before next class:
Wednesday
April 8
One-Dimensional Random Walks
Do the following before next class:
Friday
April 10
Two-Dimensional Random walks
Do the following before next class:
Monday
April 13
Random Walks
Do the following before next class:
Wednesday
April 15
Percolation
Do the following before next class:
Friday
April 17
Percolation
Do the following before next class:
Monday
April 20
Finish percolation; begin Markov chains
Do the following before next class:
Wednesday
April 22
Markov chain inverse problem
Do the following before next class:
Friday
April 24
Markov Chain Monte Carlo (MCMC)
Do the following before next class:
Monday
April 27
MCMC function minimization: simulated annealing
Do the following before next class:
Wednesday
April 29
Combinatorial optimization via simulated annealing
Do the following before next class:
Friday
May 1
Magic squares
Do the following before next class:
Monday
May 4
Traveling salesperson problem
Do the following before next class:
Wednesday
May 6
Traveling salesperson problem
Do the following before next class:
Friday
May 8
Introduction to computational geometry
Final projects
Do the following before next class:
Monday
May 11
Introduction to computational algebra
Final projects
Do the following before next class:
Wednesday
May 13
Introduction to computational graph theory
Final projects
Do the following before the final exam period.
Tuesday
May 19
2–4pm: Final presentations for Math 242 B
Wednesday
May 20
2–4pm: Final presentations for Math 242 A