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* Make lots of '''conjectures''' about symmetries, etc, and '''prove''' as many conjectures of yours as possible. | * 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: [http://helmut.knaust.info/class/202210_2325/301CurveSalad.nb 301CurveSalad.nb] and [http://helmut.knaust.info/class/202210_2325/302ProofwithoutWords.nb 302ProofwithoutWords.nb]. Read the accompanying text carefully. | *I posted two more notebooks for you to look at: [http://helmut.knaust.info/class/202210_2325/301CurveSalad.nb 301CurveSalad.nb] and [http://helmut.knaust.info/class/202210_2325/302ProofwithoutWords.nb 302ProofwithoutWords.nb]. Read the accompanying text carefully. | ||
| + | |||
| + | ==Project 4 (Chapter 11)== | ||
| + | *''Mathematica'' Notebook: [http://helmut.knaust.info/class/202210_2325/4SeqSer.nb 4SeqSer.nb] | ||
| + | *7. Introduction to Project 4 (13 min.): | ||
| + | <html><iframe width="280" height="160" <iframe width="560" height="315" src="https://utep.yuja.com/V/Video?v=3755190&node=12849977&a=404725743&preload=false" frameborder="0" webkitallowfullscreen mozallowfullscreen allowfullscreen></iframe></html> | ||
| + | * 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 [https://en.wikipedia.org/wiki/Lev_Vygotsky Lev Vygotsky] and centers around the concept of [https://www.simplypsychology.org/Zone-of-Proximal-Development.html ''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 [http://www.inquirybasedlearning.org/ Academy for Inquiry Based Learning]. | ||
Revision as of 23:15, 24 October 2021
Contents |
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:
- Explain how and why the EA works.
- Investigate Questions 1-6. What are your conjectures? Why are your conjectures true?
- (Skip Section 3.4.)
- 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.
