Welcome to Modern Computational Math! For course info and policies, please see the syllabus. For grades, log into Moodle. If you need help, contact Prof. Wright.

**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

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Friday

February 7

February 7

Introduction; Mathematica basics

Do the following before next class:

- Complete the syllabus quiz.
- Watch the Hands-on Start to Mathematica video. Then look through the resources in the Fast Introduction for Math Students.
- Complete the assignment at the end of the Introduction to Mathematica notebook. Upload your solutions to the three problem to Intro Mathematica assignment on Moodle.

Monday

February 10

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

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

February 14

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

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

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

February 21

Iterated functions: Collatz conjecture

Do the following before next class:

- Finish the Pell Project, which is due Monday.
- Continue your investigation of sequences that arise when iterating the Collatz function or some other function. Make at least three observations and formulate at least three questions about iterated functions. Submit your observations and questions to Collatz observations and questions on Moodle.

Monday

February 24

February 24

Iterated functions: logistic map and chaos

Do the following before next class:

- Read Mathematician Proves Huge Result on 'Dangerous' Problem and answer three questions on Moodle.
- Begin the Iterated Functions Project, due Friday.

Wednesday

February 26

February 26

Iterated functions and fractals

Do the following before next class:

- Read this blog post about periodic points of iterated functions. How does this relate to the logistic map?
- For more information about the Mandelbrot Set, see this Numberphile video with an explanation by Holly Krieger.
- Finish the Iterated Functions Project, due Friday (Moodle upload link).

Friday

February 28

February 28

Mean-median map

Do the following before next class:

Monday

March 2

March 2

Mean-median map

Do the following before next class:

Wednesday

March 4

March 4

Primes

Do the following before next class:

Friday

March 6

March 6

Primes sieves

Do the following before next class:

Monday

March 9

March 9

Prime sieves

Do the following before next class:

Wednesday

March 11

March 11

Prime powers

Do the following before next class:

Friday

March 13

March 13

Mathematics of RSA cryptography

Do the following before next class:

Monday

March 16

March 16

Encrypting text with RSA cryptography

Do the following before next class:

Wednesday

March 18

March 18

Counting primes

Do the following before next class:

Friday

March 20

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

March 30

Introduction to Python

Do the following before next class:

Wednesday

April 1

April 1

Yahtzee in Mathematica and Python

Do the following before next class:

Friday

April 3

April 3

Yahtzee in Python, and plotting with Matplotlib

Do the following before next class:

Monday

April 6

April 6

Trouble simulation

Do the following before next class:

Wednesday

April 8

April 8

One-Dimensional Random Walks

Do the following before next class:

Friday

April 10

April 10

Two-Dimensional Random walks

Do the following before next class:

Monday

April 13

April 13

Random Walks

Do the following before next class:

Wednesday

April 15

April 15

Percolation

Do the following before next class:

Friday

April 17

April 17

Percolation

Do the following before next class:

Monday

April 20

April 20

Finish percolation; begin Markov chains

Do the following before next class:

Wednesday

April 22

April 22

Markov chain inverse problem

Do the following before next class:

Friday

April 24

April 24

Markov Chain Monte Carlo (MCMC)

Do the following before next class:

Monday

April 27

April 27

MCMC function minimization: simulated annealing

Do the following before next class:

Wednesday

April 29

April 29

Combinatorial optimization via simulated annealing

Do the following before next class:

Friday

May 1

May 1

Magic squares

Do the following before next class:

Monday

May 4

May 4

Traveling salesperson problem

Do the following before next class:

Wednesday

May 6

May 6

Traveling salesperson problem

Do the following before next class:

Friday

May 8

May 8

Introduction to computational geometry

Final projects

Final projects

Do the following before next class:

Monday

May 11

May 11

Introduction to computational algebra

Final projects

Final projects

Do the following before next class:

Wednesday

May 13

May 13

Introduction to computational graph theory

Final projects

Final projects

Do the following before the final exam period.

Tuesday

May 19

May 19

**2–4pm**: Final presentations for Math 242

**B**

Wednesday

May 20

May 20

**2–4pm**: Final presentations for Math 242

**A**