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| − | ==Project 1==
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| − | *I have assigned you to a team on Blackboard. Please contact your other team members via Blackboard and start working on the first project.
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| − | *1. Introduction and Syllabus (19 min.) [Sorry for that little transparent rectangle in the video.]<br>
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| − | <html><iframe width="280" height="160" src="https://utep.yuja.com/V/Video?v=3490973&node=11649760&a=1851157731&preload=false" frameborder="0" webkitallowfullscreen mozallowfullscreen allowfullscreen></iframe></html>
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| − | *2. Intro to the Project and ''Mathematica'' (16 min.):<br>
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| − | <html><iframe width="280" height="160" src="https://utep.yuja.com/V/Video?v=1660526&node=5839016&a=1250321241&preload=false" frameborder="0" webkitallowfullscreen mozallowfullscreen allowfullscreen></iframe><p></html>
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| − | *''Mathematica'' Notebook(s): [http://helmut.knaust.info/class/202210_2325/1Iteration.nb 1Iteration.nb]
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| − | *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.
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| − | * Here are [http://helmut.knaust.info/class/202110_2325/Guidelines.pdf guidelines for writing your project reports].
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| − | *3. A Remark on Question 6: (4 min.)<br>
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| − | <html><iframe width="280" height="160" src="https://utep.yuja.com/V/Video?v=1720817&node=6200091&a=1273399462&preload=false" frameborder="0" webkitallowfullscreen mozallowfullscreen allowfullscreen></iframe></html>
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| − | ==Project 2 (Chapter 3)==
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| − | *''Mathematica'' Notebook(s): [http://helmut.knaust.info/class/202120_4370/2Euclid.nb 2Euclid.nb]
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| − | * 4. Introduction to Project 2 (18 min.):
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| − | <html><iframe width="280" height="160" src="https://utep.yuja.com/V/Video?v=1781327&node=6421296&a=211614421&preload=false" frameborder="0" webkitallowfullscreen mozallowfullscreen allowfullscreen></iframe></html>
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| − | *Things to do:
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| − | #Explain how and why the EA works.
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| − | #Investigate Questions 1-6. What are your conjectures? Why are your conjectures true?
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| − | #(Skip Section 3.4.)
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| − | #Investigate the questions posed in Section 3.5: Are there GCD and EA for polynomials?
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| − | *5. Speed test: EA vs. PF (<2 min., interesting, but not really relevant):
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| − | <html><iframe width="280" height="160" src="https://utep.yuja.com/V/Video?v=1781821&node=6423008&a=583545906&preload=false" frameborder="0" webkitallowfullscreen mozallowfullscreen allowfullscreen></iframe></html>
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| − | ==Project 3 (Chapter 9)==
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| − | *''Mathematica'' Notebook(s): [http://helmut.knaust.info/class/202110_2325/3Parametric.nb 3Parametric.nb] (There is now a little "reset" button at the upper right corner of each animation.)
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| − | *[http://www.sosmath.com/trig/Trig5/trig5/pdf/pdf.html Trigonometric Identities]
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| − | *[http://www.xavier.edu/math-undergraduate-research/documents/Write.pdf How to Write Mathematics, by ''Martin Erickson'']
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| − | *6. Introduction to Project 3 (14 min.):
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| − | <html><iframe width="280" height="160" src="https://utep.yuja.com/V/Video?v=1877364&node=7165149&a=1753085689&preload=false" frameborder="0" webkitallowfullscreen mozallowfullscreen allowfullscreen></iframe></html>
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| − | *There are lots of definitions in the text. Make sure you understand all definitions.
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| − | * 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.)
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| − | * Make lots of '''conjectures''' about symmetries, etc, and '''prove''' as many conjectures of yours as possible.
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| − | *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.
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| − | ==Project 4 (Chapter 11)==
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| − | *''Mathematica'' Notebook: [http://helmut.knaust.info/class/202210_2325/4SeqSer.nb 4SeqSer.nb]
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| − | *7. Introduction to Project 4 (13 min.):
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| − | <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>
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| − | * Things to do: Read and answer all the questions and exercises in Sections 11.1-11.5. Do not do Section 11.6.
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| − | * 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].
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| − | ==Project 5 (Chapter 14)==
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| − | *''Mathematica'' Notebook(s): [http://helmut.knaust.info/class/202110_2325/5QuadIter.nb 5QuadIter.nb] | [http://helmut.knaust.info/class/202210_2325/501Compositions.nb 501Compositions.nb] | [http://helmut.knaust.info/class/202210_2325/502Repeller.nb 502Repeller.nb]
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| − | * 8. Introduction to Project 5 (30 minutes):
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| − | <html><iframe width="280" height="160" src="https://utep.yuja.com/V/Video?v=2105200&node=7916041&a=1324207540&preload=false" frameborder="0" webkitallowfullscreen mozallowfullscreen allowfullscreen></iframe></html>
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| − | *Things to do: Answer all questions in Sections 14.1-14.3 and 14.5.
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| − | * 9. Two ''Mathematica'' Notebooks (8 min.):
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| − | <html><iframe width="280" height="160" src="https://utep.yuja.com/V/Video?v=2144304&node=7996457&a=766636305&preload=false" frameborder="0" webkitallowfullscreen mozallowfullscreen allowfullscreen></iframe></html>
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| − | ==Project 6 (Chapter 8)==
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| − | <!--''Mathematica'' Notebook(s): [http://helmut.knaust.info/class/202120_4370/6Padic.nb 6Padic.nb] | [http://helmut.knaust.info/class/202120_4370/601PadicExp.nb 601PadicExp.nb]-->
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| − | *10. Prelude: The real numbers (17 min.)
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| − | <html><iframe width="280" height="160" src="https://utep.yuja.com/V/Video?v=2194729&node=8095673&a=709644111&preload=false" frameborder="0" webkitallowfullscreen mozallowfullscreen allowfullscreen></iframe></html>
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| − | *11. p-adic norms (11 min.)
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| − | <html><iframe width="280" height="160" src="https://utep.yuja.com/V/Video?v=2194966&node=8096099&a=1327452865&preload=false" frameborder="0" webkitallowfullscreen mozallowfullscreen allowfullscreen></iframe></html>
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| − | * Things to do: Work all the exercises and answer all the questions in the chapter.
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| − | * A recent popular science article about p-adics: ''Kelsey Houston-Edwards'', [https://www.quantamagazine.org/how-the-towering-p-adic-numbers-work-20201019/ An Infinite Universe of Number Systems], [https://www.quantamagazine.org/ Quanta Magazine] (10/19/2020)
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