Welcome to Modern Computational Math! For grades, log into Moodle. If you need help, contact Prof. Wright.
Prof. Wright's office hours: Mon. 1–2pm in RMS 405, Tues. 1–2pm on Zoom, Wed. 2–3pm in RMS 405, Thurs. 10–11am in RMS 405, Fri. 1–2pm in RMS 405, and other times by appointment
Help sessions: Tuesdays, Thursdays, and Sundays 7:30–8:30 in Tomson 212
Do the following before the first class:
- Complete the Introductory Survey.
- 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 6
February 6
Introduction; Mathematica basics
Do the following before next class:
- Complete the Introductory Survey, if you haven't done so already.
- Read the Syllabus. Pay special attention to the grading information.
- Watch the video Hands-On Start to Mathematica by Wolfram.
- Read pages 1–10 of Computational Mathematics. Come to class prepared to summarize Archimedes's method for computing \(\pi\).
- Complete the Intro Mathematica practice problems and submit your notebook to the Intro Mathematica assignment on Moodle.
Wednesday
February 8
February 8
Computing \(\pi\)
Do the following before next class:
- Read the following pages about the Wolfram Language: Fractions & Decimals, Variables & Functions, Lists, Iterators, and Assignments.
- Modify the code from class to complete the Archimedes's Method practice problems, and upload your solutions to the Archimedes's Method practice problems on Moodle.
- Read through page 22 in Computational Mathematics. Come to class prepared to explain what the text means by accuracy, efficiency, and representation.
- If you're curious why the sum of reciprocals of squares converges to \(\pi^2/6\) (on the Intro Mathematica practice problem), then watch this video.
Friday
February 10
February 10
Madhava series for \(\pi\)
Do the following before next class:
- Read the following pages about the Wolfram Language: Functions and Programs, Operations on Lists, and Assigning Names to Things
- Complete the Madhava series practice problem and upload your solutions to the Madahava Series assignment on Moodle.
- Read Section 1.4 (pages 26–29) in Computational Mathematics. Come to class ready to discuss how sums arising from arctangent formulas can be used to compute digits of \(\pi\).
Monday
February 13
February 13
Inverse tangent formulas for \(\pi\)
MSCS Colloquium: Summer Research in MSCS; Monday, Feb. 13, 3:30pm in RNS 310
Do the following before next class:
- Complete the Inverse Tangent Formulas practice problems and upload your solutions to the Inverse Tangent Formulas assignment on Moodle.
- Read Section 1.5 (pages 30–33) in Computational Mathematics. Do Exercise 1.25 (not to turn in). How are the methods in this section different from what we have seen so far?
- Take a look at the \(\pi\) Project, due next Wednesday. You don't need to write any code for this yet, but start thinking about the methodology you will use for this project.
Wednesday
February 15
February 15
Formulas for \(\pi\) by Ramanujan and others
Do the following before next class:
- Complete the Iterative Methods for \(\pi\) practice problems and upload your solutions to the Iterative Methods assignment on Moodle.
- Begin work on the \(\pi\) Project (due next Wednesday).
- Read Section 1.6 (pages 33–37) in Computational Mathematics, Chapter 1. Come to class prepared to discuss the "dart board" method for computing \(\pi\).
Friday
February 17
February 17
Probabilistic approaches for \(\pi\)
MSCS Research Seminar: Prof. Paula Mercurio, Network Embeddings for Potential Energy Landscapes, Feb. 17, 3:30pm in RNS 204; video
Do the following before next class:
- Complete the Dart Board \(\pi\) practice problems and upload your solution to the Dart Board Pi assignment on Moodle.
- Read the following pages about the Wolfram language: Ways to Apply Functions, Pure Anonymous Functions, and Tests and Conditionals
- Read Section 2.1 (pages 45–47) in Computational Mathematics, Chapter 2.
- Work on the \(\pi\) Project (due Wednesday).
Monday
February 20
February 20
Fibonacci numbers
MSCS Colloquium: Prof. Steve McKelvey, "Applied Mathematics and Bad Intuition: Two Examples," Monday, Feb. 20, 3:30pm in RNS 310; video
Do the following before next class:
- Finish the \(\pi\) Project. Upload your notebook to the Pi Project assignment on Moodle.
- Watch The magic of Fibonacci numbers, a 6-minute TED talk by Arthur Benjamin.
- Read Section 2.2 (pages 47–56) in Computational Mathematics, Chapter 2.
Wednesday
February 22
February 22
Fibonacci implementations
Do the following before next class:
- Read Section 2.3, up to the "Further Generalizations" heading on page 64, in Computational Mathematics. Focus on the process of discovering Cassini's identity and the methods presented for verifying the identity for lots of indexes \(n\)
- Complete the Computing Fibonacci practice problems and upload your solutions to the Computing Fibonacci assignment on Moodle.
Friday
February 24
February 24
Fibonacci identities
Do the following before next class:
- Complete the Fibonacci Identities practice problems and upload your solutions to the Fibonacci Identities assignment on Moodle.
- Finish reading Section 2.3 (pages 64–68) in Computational Mathematics, Chapter 2.
Monday
February 27
February 27
Fibonacci polynomial identities
MSCS Colloquium: Prof. Mckenzie West (U. Wisconsin Eau Claire) — cancelled, to be rescheduled
Do the following before next class:
- Read Section 2.4 (pages 68–76) of Computational Mathematics.
- Complete the Polynomial Identities practice problem and upload your solution to the Polynomial Identities assignment on Moodle. Come to class ready to discuss your observation about Fibonacci Polynomial identities.
- Optionally, begin revising your solution to the \(\pi\) Project. Revisions are due Monday, March 6.
Wednesday
March 1
March 1
Generalized Fibonacci numbers
MSCS Colloquium: T.J. Reinartz, "From Objects to N-grams: Programming the Journey with Data and Data Structures," Wednesday, March 1, 3:30pm in RNS 310
Do the following before next class:
- Read Section 2.5 through page 80 in Computational Mathematics.
- Complete the Lucas Identities practice problems and upload your solution to the Lucas Identities assignment on Moodle.
- Optionally, work on revising your solution to the \(\pi\) Project. Revisions are due Monday, March 6.
- Take a look at the Generalized Fibonacci Project. Optionally, start experimenting with generalized Fibonacci sequences.
Friday
March 3
March 3
Generalized Fibonacci numbers
MSCS Research Seminar: Prof. Kendra Killpatrick (Pepperdine University), "Fibonacci Numbers, Catalan Numbers, and the Super FiboCatalan Numbers," Friday, March 3, 3:30pm in RNS 204; video
OleHacks Guest Speakers: Dr. Dustin Dannenhauer, March 3, 7:30pm on Zoom and Dr. Leilani Gilpin, March 4, 1pm on Zoom
Do the following before next class:
- Finish reading Section 2.5 in Computational Mathematics.
- Complete the Pell Identities practice problems and upload your solution to the Pell Identities assignment on Moodle.
- Optionally, finish revising your \(\pi\) Project and resubmit your project to the Pi Project assignment on Moodle.
- Begin the Generalized Fibonacci Project. Experiment with generalized Fibonacci sequences.
MSCS Colloquium: Prof. Layla Oesper (Carleton College), "Combining CS and Biology: Algorithms for comparing and summarizing tumor trees," Monday, March 6, 3:30pm in RNS 310
Do the following before next class:
- Read pages 85–90 in Computational Mathematics, Chapter 3.
- Complete the Collatz Practice Problems and upload your solutions to the Collatz Practice assignment on Moodle.
- Work on the Generalized Fibonacci Project. Experiment with generalized Fibonacci sequences.
Wednesday
March 8
March 8
Heights of Collatz sequences
Do the following before next class:
- Read pages 90–96 in Computational Mathematics, Chapter 3.
- Finish on the Generalized Fibonacci Project. Upload your project to the Generalized Fibonacci Project assignment on Moodle.
Friday
March 10
March 10
Collatz Stopping Times
MSCS Research Seminar: Prof. Kristopher Hollingsworth (MN State University, Mankato), "Discrete Frames for High-Dimensional Data" Friday, March 10, 3:30pm in RNS 204; video
BRIDGES Part 3: Pathways Friday, March 10, 5–7pm in Buntrock Sun Ballroom
Do the following before next class:
- Watch The Simplest Math Problem No One Can Solve - Collatz Conjecture by Veritasium. Come prepared to discuss something interesting from this video at the beginning of class on Monday.
- Read the rest of Section 3.1 in Computational Mathematics, Chapter 3.
- Complete the Collatz Stopping Times practice problems and upload your solutions to the Collatz Stopping Times assignment on Moodle.
Monday
March 13
March 13
Collatz sequences
MSCS Colloquium: Prof. Michael Orrison (Harvey Mudd College), "Voting and Linear Algebra: Connections and Questions," Monday, March 13, 3:30pm in RNS 310; video
Do the following before next class:
- Read the Section 3.2 (pages 99–106) in Computational Mathematics, Chapter 3.
- Read Mathematician Proves Huge Result on 'Dangerous' Problem in Quanta magazine.
- Complete the Collatz Variant practice problems and upload your solutions to the Collatz Variant assignment on Moodle.
Wednesday
March 15
March 15
The logistic map
Do the following before next class:
- Read Section 3.3, at least through page 116, in Computational Mathematics
- Complete the Logistic Map practice problems and upload your solutions to the Collatz Variant assignment on Moodle.
- Optionally, work on revising your Generalized Fibonacci Project. You may resubmit your project to the Generalized Fibonacci Project assignment on Moodle.
Do the following before next class:
- Read Section 3.3, at least through page 121, in Computational Mathematics.
- Complete the Bifurcations practice problems and upload your solutions to the Bifurcations assignment on Moodle.
- Take a look at the Iterated Functions Project, which is due on Friday, April 7.
Monday
March 20
March 20
Logistic map bifurcation diagrams
MSCS Colloquium: Claire Kelling (Carleton College) Monday, March 20, 3:30pm in RNS 310
Do the following before next class:
- Read the rest of Section 3.3 in Computational Mathematics.
- Watch This equation will change how you see the world (the logistic map) by Veritasium. Come to the next class prepared to discuss something you learned from the video.
- Complete the Chaos and Stability practice problems and upload your solutions to the Chaos and Stability assignment on Moodle.
- Optionally, finish revising your Generalized Fibonacci Project. You may resubmit your project to the Generalized Fibonacci Project assignment on Moodle.
Have a great spring break! No class March 24–31.
Monday
April 3
April 3
Introduction to Python
Do the following before next class:
- to be announced...
Wednesday
April 5
April 5
Prime Numbers
Do the following before next class:
- to be announced...
Do the following before next class:
- to be announced...
Monday
April 10
April 10
Prime numbers: Sieve of Eratosthenes
Do the following before next class:
- to be announced...
Wednesday
April 12
April 12
Properties of prime numbers
Do the following before next class:
- to be announced...
Friday
April 14
April 14
Counting Primes
Do the following before next class:
- to be announced...
Monday
April 17
April 17
Counting Primes and the Riemann Zeta Function
Do the following before next class:
- to be announced...
Wednesday
April 19
April 19
Counting Primes and the Riemann Zeta Function
Do the following before next class:
- to be announced...
Friday
April 21
April 21
To be determined
Do the following before next class:
- to be announced...
Monday
April 24
April 24
To be determined
Do the following before next class:
- to be announced...
Wednesday
April 26
April 26
To be determined
Do the following before next class:
- to be announced...
Friday
April 28
April 28
To be determined
Do the following before next class:
- to be announced...
Monday
May 1
May 1
To be determined
Do the following before next class:
- to be announced...
Wednesday
May 3
May 3
To be determined
Do the following before next class:
- to be announced...
Friday
May 5
May 5
To be determined
Do the following before next class:
- to be announced...
Monday
May 8
May 8
Final projects
Do the following before next class:
- to be announced...
Wednesday
May 10
May 10
Final projects
Do the following before next class:
- to be announced...
Friday
May 12
May 12
Final projects
Do the following before next class:
- to be announced...
Monday
May 15
May 15
Final projects
We've made it to the end of the semester! A few last things to do:
- to be announced...
Friday
May 19
May 19
Math 242B: Final Presentations 9:00–11:00am
Monday
May 22
May 22
Math 242A: Final Presentations 9:00–11:00am
