Projects

Project 1

• I have assigned you to a team on Blackboard. Please contact your other team members via Blackboard and start working on the first project.
• 1. Introduction and Syllabus (19 min.) [Sorry for that little transparent rectangle in the video.]
  

• 2. Intro to the Project and Mathematica (16 min.):
  

• Mathematica Notebook(s): 1Iteration.nb
• Things to do for Project 1: Answer all questions in the chapter. Questions 6 and 8 are central! Section 1.5 may help with understanding what is going on. Remember that answering "why" is always the most important thing in Mathematics.
• Here are guidelines for writing your project reports.
• 3. A Remark on Question 6: (4 min.)
  

Project 2 (Chapter 3)

• Mathematica Notebook(s): 2Euclid.nb
• 4. Introduction to Project 2 (18 min.):

• Things to do:

1. Explain how and why the EA works.
2. Investigate Questions 1-6. What are your conjectures? Why are your conjectures true?
3. (Skip Section 3.4.)
4. Investigate the questions posed in Section 3.5: Are there GCD and EA for polynomials?

• 5. Speed test: EA vs. PF (<2 min., interesting, but not really relevant):

Project 3 (Chapter 9)

• Mathematica Notebook(s): 3Parametric.nb (There is now a little "reset" button at the upper right corner of each animation.)
• Trigonometric Identities
• How to Write Mathematics, by Martin Erickson
• 6. Introduction to Project 3 (14 min.):

• There are lots of definitions in the text. Make sure you understand all definitions.
• Things to do: Exercises 12-14, Questions 13-18, 9.5.3. (If you have the book: Exercise 2-4, Questions 1-6, Question 9.5.3.)
• Make lots of conjectures about symmetries, etc, and prove as many conjectures of yours as possible.
• I posted two more notebooks for you to look at: 301CurveSalad.nb and 302ProofwithoutWords.nb. Read the accompanying text carefully.

Project 4 (Chapter 11)

• Mathematica Notebook: 4SeqSer.nb
• 7. Introduction to Project 4 (13 min.):

• Things to do: Read and answer all the questions and exercises in Sections 11.1-11.5. Do not do Section 11.6.
• I know that many of you want to become teachers. The learning theory behind a class like ours was first articulated by the Soviet psychologist Lev Vygotsky and centers around the concept of Zone of Proximal Development. If the textbook does not suffice as MKO: your instructor is just a Zoom screen away. You may also want to check out the Academy for Inquiry Based Learning.

Project 5 (Chapter 14)

• Mathematica Notebook(s): 5QuadIter.nb | 501Compositions.nb | 502Repeller.nb
• 8. Introduction to Project 5 (30 minutes):

• Things to do: Answer all questions in Sections 14.1-14.3 and 14.5.
• 9. Two Mathematica Notebooks (8 min.):

Project 6 (Chapter 8)

• 10. Prelude: The real numbers (17 min.)

• 11. p-adic norms (11 min.)

• Things to do: Work all the exercises and answer all the questions in the chapter.
• A recent popular science article about p-adics: Kelsey Houston-Edwards, An Infinite Universe of Number Systems, Quanta Magazine (10/19/2020)