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.
Office hours: Mon. 9–10, Tues. 10–11, Wed. 10:30–11:30, Thurs. 1–2, Fri. 9–10 (see Moodle for the Zoom link)
Help sessions: Mon., Wed., and Thurs. 8–9pm (see Moodle for the link)
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Today
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Do the following before the first class:
- 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.
Monday
February 15
February 15
Introduction; Mathematica basics
Do the following before the next class:
- 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.
Wednesday
February 17
February 17
Computing the digits of \(\pi\)
Do the following before the next class:
- Watch this video, which explains why the sum of reciprocals of squares converges to \(\pi^2/6\).
- Start the \(\pi\) Project (due
MondayWednesday). 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 \(\pi\).
Friday
February 19
February 19
Computing the digits of \(\pi\)
Do the following before the next class:
- 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.
Do the following before the next class:
- 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?
Wednesday
February 24
February 24
Fibonacci identities
Do the following before the 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.)
Friday
February 26
February 26
Pell numbers
Do the following before the next class:
- 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.
Do the following before the next class:
- 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.
Wednesday
March 3
March 3
Iterated functions: logistic map and chaos
Do the following before the next class:
- 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.
Friday
March 5
March 5
Iterated functions: fractals
Bonus video: Steven Strogatz — The science of sync
Do the following before the next class:
- 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.
Do the following before the next class:
- Finish the Iterated Functions Project. Upload your notebook to Moodle.
- Finish implementing your isPrime function, if not finished in class.
- Read "Why prime numbers still fascinate matematicians, 2,300 years later" and answer these four questions on Moodle.
Do the following before the next class:
- Finish implementing the Sieve of Eratosthenes in Mathematica.
- Read "The Sequence of Prime Numbers" (JSTOR link) and answer these questions on Moodle.
Bonus video: Yitang Zhang: An Unlikely Math Star Rises
Do the following before the next class:
- Finish implementing the Sieve of Sundaram in Mathematica.
- Take a look at the Primes Project, which is due March 22.
Monday
March 15
March 15
Primes powers
Wednesday
March 17
March 17
Rest Day — no class
Do the following before the next class:
- Work on the Primes Project.
- Watch this video introduction to RSA encryption.
Friday
March 19
March 19
Mathematics of RSA Cryptography
Do the following before the next class:
- Finish the Primes Project and submit your notebook to Moodle.
- Read RSA Encryption – Keeping the Internet Secure.
- Watch this RSA encryption video. This video gives an overview of how we will convert text to numbers that we can encrypt. It's important to watch this before Monday's class!
- Choose two (secret) prime numbers of 30 digits each. (Use your fermatPrime function!) Keep them in a safe place for the next week.
Monday
March 22
March 22
Encrypting text with RSA cryptography
Do the following before the next class:
- Use your secret primes to compute your public key \( (e,n) \). Post your public key to the RSA Forum on Moodle. Then use the forum to send encrypted messages to Prof. Wright and at least two other people. (This is the RSA Assignment.)
- Watch How Quantum Computers Break Encryption.
Wednesday
March 24
March 24
Counting primes
Do the following before the next class:
- RSA Assignment: Send and receive secure messages with at least two other people using the RSA Forum. Use your Mathematica code to encrypt and decrypt the messages.
- Complete Exercises 1–6 in the Counting Primes Mathematica notebook. Upload your answers to the Counting Primes Assignment on Moodle.
- Read The Riemann Hypothesis, explained. Answer these reading questions on Moodle.
Friday
March 26
March 26
Prime patterns and the Riemann zeta function
Do the following before the next class:
- Complete the five exercises in the Primes and the Zeta Function Mathematica notebook. Upload your solutions to the Riemann Zeta Assignment on Moodle.
- For one more take on the Riemann Hypothesis, watch this video by Quanta Magazine.
Monday
March 29
March 29
Introduction to Python
Do the following before the next class:
- 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.
- Read the following pages from the Python Land tutorial: Variables, Strings, Functions, Booleans, and Loops.
Wednesday
March 31
March 31
Yahtzee in Mathematica and Python
Do the following before the next class:
- Finish four of the six exercises in the Intro to Python notebook and submit your notebook link to the Intro Python assignment on Moodle.
- Finish implementing the Yahtzee simulation in Python. You don't have to submit it for a grade, but we will use it for further investigation in Friday's class.
- Please complete the Mid-Semester Survey. Answers are voluntary and anonymous.
Friday
April 2
April 2
Yahtzee investigation and plotting with Matplotlib
Do the following before the next class:
- Complete Python Quiz 1 (topics are variables, lists, if statements, and functions).
- Use simulation and make plots to answer the three questions in the Yahtzee Investigation notebook. Give this your best shot before class on Monday, and bring questions to class.
Monday
April 5
April 5
Trouble simulation
Wednesday
April 7
April 7
Rest Day — no class
Do the following before the next class:
- Finish the Yahtzee Investigation, if you haven't done so already, and submit a link to your notebook to the Yahtzee Investigation assignment on Moodle.
- Work on the Trouble Investigation. Bring questions to class on Friday.
Friday
April 9
April 9
Trouble Investigation; Intro to Random Walks
Do the following before the next class:
- Finish the Trouble Investigation and submit a link to your notebook to Moodle.
- Investigate the questions in the Random Walk Notebook.
Monday
April 12
April 12
1D and 2D Random Walks
Do the following before the next class:
Wednesday
April 14
April 14
2D Random walks
Do the following before the next class:
Friday
April 16
April 16
2D and 3D Random Walks
Do the following before the next class:
Monday
April 19
April 19
Percolation
Do the following before the next class:
Wednesday
April 21
April 21
Percolation
Do the following before the next class:
Friday
April 23
April 23
Percolation
Do the following before the next class:
Monday
April 26
April 26
Markov chain inverse problem
Do the following before the next class:
Wednesday
April 28
April 28
Markov Chain Monte Carlo (MCMC)
Do the following before the next class:
Friday
April 30
April 30
MCMC optimization: simulated annealing
Do the following before the next class:
Monday
May 3
May 3
Magic squares
Do the following before the next class:
Wednesday
May 5
May 5
Magic squares
Do the following before the next class:
Friday
May 7
May 7
Traveling salesperson problem
Do the following before the next class:
Monday
May 10
May 10
Traveling salesperson problem
Do the following before the next class:
Wednesday
May 12
May 12
To be announced
Do the following before the next class:
Friday
May 14
May 14
Final projects
Do the following before the next class:
Monday
May 17
May 17
Final projects
Do the following before the final exam period:
Thursday
May 20
May 20
2–4pm: Final presentations for Math 242 B
Saturday
May 22
May 22
2–4pm: Final presentations for Math 242 A