CRN 28702: Projects

Project 6 (Chapter 8)

Mathematica Notebook(s): 6Padic.nb | 601PadicExp.nb

• 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)

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 4 (Chapter 4)

• Mathematica Notebook(s): 4Primes.nb
• Things to do: There are no questions in this chapter. Do all the exercises. (As you can see in the notebook, the computational limits mentioned in the textbook no longer apply. You can try some bigger numbers, too.)

Project 3 (Chapter 9)

• Mathematica Notebook(s): 3Parametric.nb
• Trigonometric Identities
• How to Write Mathematics, by Martin Erickson
• 6. Introduction to Project 3 (14 min.):

• 6A. Addendum (<1 min.):

• • There are lots of definitions in the text. Make sure you understand all definitions.
  • Exercise 12-14, Questions 13-18, 9.5.3. (If you have the book: Exercise 2-4, Questions 1-6, Question 9.5.3.)
  • Prove as many conjectures of yours as possible.

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.):

Project 1

• I have assigned you to a team on Blackboard. (Currently there is only one team.) Please contact your other team members via Blackboard and start working on the first project.
• 1. Syllabus and Introduction (15 min.):
  

• 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.
• 3. A Remark on Question 6: (4 min.)