Modern Computational Math

• Complete the Introductory Survey, if you haven't done so already.
• 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.

• Read the Syllabus and complete the Syllabus Quiz on Moodle.
• Watch the video Hands-On Start to Mathematica by Wolfram.
• Read pages 1–12 of Experimental Mathematics. Come to class prepared to summarize Archimedes's method for computing \(\pi\).
• Complete the Intro Mathematica homework problems and submit your notebook to the Intro Mathematica assignment on Moodle.

• 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 assignment on Moodle.
• Read pages 13–25 in our Experimental Mathematics text. 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.

Bonus video: Paths to Math: John Urschel

• Read the following pages about the Wolfram Language: Functions and Programs, Operations on Lists, and Assigning Names to Things
• Complete the Madhava series practice problems and upload your solutions to the Madahava Series assignment on Moodle.
• Read Section 1.4 (pages 29–33) in our Experimental Mathematics text. Come to class ready to discuss how sums arising from arctangent formulas can be used to compute digits of \(\pi\).

• Complete the Inverse Tangent Formulas practice problems and upload your solutions to the Inverse Tangent Formulas assignment on Moodle.
• Read Section 1.5 (pages 33–38) in our Experimental Mathematics text. Do Exercise 1.27 (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 Friday. You don't need to write any code for this yet, but start thinking about the problem and planning the methodology you will use for this project.

MSCS Colloquium: "When statistical modeling and machine learning collide: collider bias in genetic association studies" Monday, September 15, 3:30–4:30pm in RNS 210

• 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 (first draft due Friday). Look at the Sample Project Report to see an example of the sort of report you will turn in.
• Read Section 1.6 (pages 38–44) in our Experimental Mathematics text. Come to class prepared to discuss the "dart board" method for computing \(\pi\).

Bonus video: Eugenia Cheng on The Late Show

• Finish your \(\pi\) Project. Your first draft is due Friday (Moodle link). Remember that after the initial grading, you will have a chance to revise and resubmit for a higher grade.
• Optionally, read how Google computed 100 trillion digits of \(\pi\) or see the current record of 300 trillion digits.
• Optionally, work on the Dart Board \(\pi\) practice problems. These are due on Monday.
• Read the following pages about the Wolfram language: Ways to Apply Functions, Pure Anonymous Functions, and Tests and Conditionals
• Read Section 2.1 (pages 51–53) in our Experimental Mathematics text. Come to class ready to say what recursive means (in the context of a recursive sequence or a recursively-defined function).

• Finish the Dart Board \(\pi\) practice problems from Wedneseday and upload your solution to the Dart Board Pi assignment on Moodle.
• Watch The magic of Fibonacci numbers, a 6-minute TED talk by Arthur Benjamin.
• Read Section 2.2 (pages 51–60) in our Experimental Mathematics text.
• Recommended: Read Chapter 1, "Flourishing," in Mathematics for Human Flourishing by Francis Su, available here on JSTOR. (If necessary, log into JSTOR using your St. Olaf account.) By next Wednesday, you will answer two reflection questions (see below) based on this text about mathematics as a human activity.

• Read Chapter 1, "Flourishing," in Mathematics for Human Flourishing by Francis Su, available here on JSTOR. (If necessary, log into JSTOR using your St. Olaf account.) Then answer the following questions, writing at least one paragraph per question.
  1. Describe any virtues you have acquired as a result of doing mathematics. (Think of virtues as aspects of character that mathematics might build, such as habits of mind, that shape the way you approach life.)
  2. What value is there in studying math if you'll never use what the math that you're learning?
  The important thing is to be thoughtful about your answers. Submit your answers to the Flourishing assignment on Moodle.
• Read Section 2.3 up to the "Further Generalizations" heading on page 72 in our Experimental Mathematics text. 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.
• Optionally, begin revising your \(\pi\) Project. Talk with the professor if you have questions about how to do this. Revisions are due Monday, September 29. You may submit your revisions to the same project link on Moodle.

Bonus video: Francis Su — Mathematics for Human Flourishing short version and long version

Learn about opportunities in math, stats, and computer science at the MSCS Showcase — Thursday, September 25, 4:30pm, Buntrock Commons Ballrooms

• Complete the Fibonacci Identities practice problems and upload your solutions to the Fibonacci Identities assignment on Moodle.
• Finish reading Section 2.3 (pages 63–76) in our Experimental Mathematics text.
• Optionally, work on revising your \(\pi\) Project. Talk with the professor if you have questions about how to do this. Revisions are due Monday, September 29. You may submit your revisions to the same project link on Moodle.

• Read Section 2.4 (pages 76–84) in our Experimental Mathematics text.
• 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, finish revising your \(\pi\) Project. Talk with the professor if you have questions about how to do this. Revisions are due Monday, September 29. You may submit your revisions to the same project link on Moodle.

Northfield Undergraduate Mathematics Symposium (NUMS): Tuesday, September 30, 3:30–7:30pm in RNS 290

• Read Section 2.5 through page 89 in our Experimental Mathematics text.
• Complete the Lucas Identities practice problems and upload your solution to the Lucas Identities assignment on Moodle.
• Take a look at the Generalized Fibonacci Project. Optionally, start experimenting with generalized Fibonacci sequences.

Bonus video: Moon Duchin: "Political Geometry" and DistrictR

• Finish reading Section 2.5 in our Experimental Mathematics text.
• Complete the Pell Identities practice problems and upload your solution to the Pell Identities assignment on Moodle.
• Begin the Generalized Fibonacci Project. Experiment with generalized Fibonacci sequences. The first draft of this project is due Monday, October 6.

MSCS Lightning Talks: learn about the research areas of your MSCS faculty — Friday, October 3, 3:30–4:30pm in RNS 210

• Read pages 95–100 in our Experimental Mathematics text.
• Finish (the first draft of) your Generalized Fibonacci Project. Upload your project to the Generalized Fibonacci Project assignment on Moodle.

MSCS Colloquium: "A Wrinkle in Time (to Event): A Model for Alternating Recurrent Events" Monday, October 6, 3:30–4:30pm in RNS 210

• Finish reading Section 3.1 (pages 96–110) in our Experimental Mathematics text.
• 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 Wednesday.
• Complete the Collatz Patterns practice problems and upload your solutions to the Collatz Patterns assignment on Moodle.
• Recommended: Start reading Chapter 2, "Exploration," in Mathematics for Human Flourishing by Francis Su, available here on JSTOR. (If necessary, log into JSTOR using your St. Olaf account.) By Friday, you will answer two reflection questions (see below) based on this text.
• Optionally, work on a second revision of your Pi Project. Talk with the professor if you have questions about this.

Terence Tao: blog and "Four Minutes with Terence Tao"

• Read Section 3.2 (pages 110–117) in our Experimental Mathematics text.
• Complete the Collatz Extensions practice problems and upload your solutions to the Collatz Extensions assignment on Moodle.
• Read Chapter 2, "Exploration," in Mathematics for Human Flourishing by Francis Su, available here on JSTOR. (If necessary, log into JSTOR using your St. Olaf account.) Then answer the following questions, writing at least one paragraph per question.
  1. Francis Su writes, "Even wrong ideas soften the soil in which good ideas can grow." How have you seen this in your own life? Describe some examples from your own experience that embody this truth.
  2. In what ways have you grown as a mathematical explorer so far in this course? If you're not sure, what could you do to enhance your imagination, creativity, and expectation of enchantment throughout the rest of the semester?
  The important thing is to be thoughtful about your answers. Submit your answers to the Exploration assignment on Moodle.

CURI Showcase:Friday, October 10, 4:00–6:00pm in the King's Dining Room (Buntrock Commons)

• Read Section 3.3, pages 118–126, in our Experimental Mathematics text.
• Complete the Logistic Map practice problems and upload your solutions to the Logistic Map assignment on Moodle.
• Optionally, work on revising your Generalized Fibonacci Project or work on a challenge problem.

MSCS Colloquium: "Sex Differences in Genomics: Analytical Considerations and Applications to Mental Health" Monday, October 13, 3:30–4:30pm in RNS 210

• Read Section 3.3 through page pages 136 in our Experimental Mathematics text.
• Complete the Bifurcations practice problems and upload your solutions to the Bifurcations assignment on Moodle.
• Optionally, work on revising your Generalized Fibonacci Project. You may resubmit your project to the Generalized Fibonacci Project assignment on Moodle.
• Begin the Iterated Functions Project, due next Friday.

Bonus: Why is Mathematics Useful — Robert Ghrist, and Applied Dynamical Systems Vol. 1

• Read the rest of Section 3.3 in our Experimental Mathematics text.
• Watch This equation will change how you see the world (the logistic map) by Veritasium. Come to the next class prepared to discuss at least two things you learned from the video.
• Complete the Cycles and Chaos practice problems and upload your solutions to the Cycles and Chaos assignment on Moodle.
• Optionally, work on revising your Generalized Fibonacci Project. You may resubmit your project to the Generalized Fibonacci Project assignment on Moodle. If you have questions about completing the project, talk with the professor.
• Take a look at the Iterated Functions Project, due next Friday.

• Read Section 3.4 in our Experimental Mathematics text.
• To learn more about chaos theory, watch The Science of the Butterfly Effect by Veritasium.
• Complete the Feigenbaum Constant practice problems and upload your solutions to the Feigenbaum Constant assignment on Moodle.
• Begin work on your Iterated Functions Project, due Friday.

• Finish your Iterated Functions Project. Upload your project to the Iterated Functions Project assignment on Moodle.
• Read the following pages in the SageMath documentation: Assignment, Equality, and Arithmetic, Getting Help, Functions, Indentation, and Counting, Basic Algebra and Calculus, and Some Common Issues with Functions.

Bonus: MEET a Mathematician — Federico Ardila and Federico Ardila on Math, Music and the Space of Possibilities

MSCS Lightning Talks: learn about the research areas of your MSCS faculty — Friday, October 24, 3:30–4:30pm in RNS 210

• Read the following pages from the Python Land tutorial: Variables, Functions, Booleans, Loops, and Strings.
• Read pages 151–154 in our Experimental Mathematics text. Take note of how the Sieve of Eratosthenes is able to efficiently find all the prime numbers up to some maximum value.
• Complete the four practice problems in the Intro Primes practice problems notebook on CoCalc. For help, talk with the professor or with classmates, or visit the help session on Sunday evening. Simply complete the problems in the file on CoCalc before 5pm Monday, and they will be automatically turned in for grading.

• Finish reading Section 4.1 in our Experimental Mathematics text.
• Read Why prime numbers still fascinate mathematicians, 2300 years later.
• Try to finish your sieve of Eratosthenes code from class, then compare your implementation with that in the "classwork" file linked above.
• Optionally, begin revising your Iterated Functions Project. Revisions are due next Monday, November 3.

Bonus video: Yitang Zhang: An Unlikely Math Star Rises

• Read Section 4.2 in our Experimental Mathematics text.
• Complete the Prime Pairs practice problems that you will find in the Assignments folder on CoCalc. Simply complete the problems on CoCalc and they will be automatically turned in for grading. These practice problems are due Friday at 5pm.
• Optionally, work on revising your Iterated Functions Project. Revisions are due next Monday, November 3.
• Take a look at the Primes Project, due next Friday, November 7. When you're ready to begin, you should work on your Primes Project in CoCalc, in the folder Assigments/Primes Project.

• Read Section 4.3, pages 162–165 in our Experimental Mathematics text.
• Look through the SageMath documentation on 2D plotting to see what types of plots are possible and what functions are used to make them.
• Complete the Counting Primes practice problems that you will find in the Assignments folder on CoCalc. Simply complete the problems on CoCalc and they will be automatically turned in for grading. These practice problems are due Monday at 5pm.
• Optionally, finish revising your Iterated Functions Project. Revisions are due Monday. You may submit your revisions to the Iterated Functions Project assignment on Moodle.
• Begin the Primes Project, due next Friday, November 7. Do your work in CoCalc, in the folder Assigments/Primes Project.

• Finish reading Section 4.3 (pages 165–172) in our Experimental Mathematics text.
• Complete the Primes and Zeta practice problems that you will find in the Assignments folder on CoCalc. Simply complete the problems on CoCalc and they will be automatically turned in for grading. These practice problems are due Wednesday at 5pm.
• Watch The Riemann Hypothesis, Explained by Quanta Magazine (16 min). Bring your answers to the following two questions to class on Wednesday:
  1. What did Riemann hypothesize in his 1859 paper?
  2. According to the video, how do the zeta zeros relate to the prime numbers?
• Work on the Primes Project, which is due Friday. Do your work in CoCalc, in the folder Assigments/Primes Project.

Kathryn Hess: interview in the AMS Notices and TEDx Talk: Digital Neuroscientist of the Future

• Read Section 4.6 (pages 196–211) in our Experimental Mathematics text.
• Optionally, to better understand complex functions and the Riemann zeta function, watch But what is the Riemann zeta function? Visualizing analytic continuation by 3Blue1Brown.
• For a spectacular visualization of the Riemann Zeta function, see The Riemann Zeta Function Visualized by The Mathemagicians' Guild.
• Finish your Primes Project, due Friday. Do your work in the Primes Project assignment folder on CoCalc, and it will be automatically available for grading.

• Read Section 4.4 (pages 173–183) in our Experimental Mathematics text. If you want to see how large primes are used in cryptography, read Section 4.5.
• Complete the Large Primes practice problems that you will find in the Assignments folder on CoCalc. Simply complete the problems on CoCalc and they will be automatically turned in for grading. These practice problems are due Monday at 5pm.
• Optionally, work on project revisions or challenge problems.

Math Faculty Candidate Colloquium: Monday, November 10, 3:30–4:30pm in RNS 310

• Read Section 5.1, (pages 213–228), in our Experimental Mathematics text.
• Complete the Pseudorandom Numbers practice problems that you will find in the Assignments folder on CoCalc. Simply complete the problems on CoCalc and they will be automatically turned in for grading. These practice problems are due Wednesday at 5pm.
• Take a look at the Final Project Information. Begin thinking about possible topics and groups for your project.
• Optionally, work on revising your Primes Project. Revisions are due next Monday, November 17.

Bonus: video How Not to Be Wrong: The Power of Mathematical Thinking - with Jordan Ellenberg and article The Psychology of Statistics by Jordan Ellenberg

BRIDGES: Pathways Thursday, November 13, 5–6pm, RNS 356: pizza and discussion with senior STEM majors

• Read Section 5.3 (pages 238–244) "Basics of Simulation" in our Experimental Mathematics text. Also read Page 246–247 about the coupon collector problem.
• Optionally, read Section 5.2 to learn about how to generate nonuniform random numbers.
• Try to finish your simulation code for the Birthday Problem. Take a look at the solution in the classwork file linked above (also on CoCalc).
• Complete the Simulation practice problems that you will find in the Assignments folder on CoCalc. Simply complete the problems on CoCalc and they will be automatically turned in for grading. These practice problems are due Friday at 5pm.
• Take a look at the Final Project Information. Thinking which topics interest you and who you would like to work with for the final project.
• Optionally, revise your Primes Project (revisions due Monday) or work on a challenge problem.

Math Faculty Candidate Colloquium: Friday, November 14, 3:30–4:30pm in RNS 210

• Read Section 5.5 through Figure 5.7 on Page 259 in our Experimental Mathematics text.
• Complete the 1D Random Walks practice problems that you will find in the Assignments folder on CoCalc. Simply complete the problems on CoCalc and they will be automatically turned in for grading. These practice problems are due Monday at 5pm.
• Take a look at the Final Project Info. Start thinking about which topics interest you and who you would like to work with.
• Optionally, revise your Primes Project or work on a challenge problem.

Math Faculty Candidate Colloquium: Monday, November 17, 3:30–4:30pm in RNS 210

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• If there is a project from earlier in the semester that you have not turned in yet, you may still use a token to turn it in. Break could be a good time to work on that project.
• Optionally, work on a challenge problem.

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