Difference between revisions of "Conservapedia:Critical Thinking in Math"

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(Puzzled about "controversy about proof by contradiction")
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*I'm really interested in this.  Any idea of when it's due to start? [[User:KTDiputsho|KTDiputsho]] 14:53, 15 April 2008 (EDT)
 
*I'm really interested in this.  Any idea of when it's due to start? [[User:KTDiputsho|KTDiputsho]] 14:53, 15 April 2008 (EDT)
 
*What is the "controversy about proof by contradiction" that you mention? It's news to me that there's any controversy about one of the standard tools of a mathematician. [[User:Googly|Googly]] 19:47, 6 August 2008 (EDT)
 
*What is the "controversy about proof by contradiction" that you mention? It's news to me that there's any controversy about one of the standard tools of a mathematician. [[User:Googly|Googly]] 19:47, 6 August 2008 (EDT)
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:: You'll learn lots of new things here, if you keep an open mind.  When resorting to proof by contradiction, it is impossible to know if the result is due to the falsehood of the proposition or an undetected contradiction in the math itself.--[[User:Aschlafly|Aschlafly]] 20:25, 6 August 2008 (EDT)

Revision as of 18:25, 6 August 2008

"Critical Thinking in Math" is an experimental course with four independent purposes in mind:

  • sharpen the analytical skills of students and improve their math College Board scores
  • encourage adults to keep their minds sharp through mathematics, and fend off mental decline
  • help parents who would like to teach math to their homeschooled children

The experiment is to use only fundamental or elementary techniques to accomplish the above results. No tools beyond about 9th grade math are required, and motivated students younger than 9th grade will not have difficulty with the concepts.

This course seeks the contributions of both teachers and students to make it as effective as possible. It will begin in September. Possible topics include:

  • a comparative look at different techniques of proof
  • major problems that remain unsolved using elementary techniques
  • a look at the history of the development of math
  • an analysis of what skills College Board exams test, and how to improve those skills

Please feel free to add other topics and suggestions, and add your name below as a teacher or student interested in this field: --Aschlafly 16:08, 5 August 2007 (EDT)

Draft Curriculum

  • different methods of proof: constructive proof, elementary proof, induction, contradiction, existence, infinite descent
  • defining and redefining key concepts: integers, infinity, prime numbers, proof
  • controversy about proof by contradiction
  • 17 different ways to prove that there are an infinite number of prime numbers
  • transcendental numbers - how do we know they exist?
  • Goldbach's Conjecture and Fermat's Last Theorem
  • Unsolved problems: proving that there are infinitely many twin primes
  • Brun's constant
  • Problems solved only with proof-by-contradiction: always a prime between n and 2n (n>1)
  • perfect numbers
  • additive factoring
  • prime number theorem
  • Types of math problems presented in College Board exams, American math contests and UK math contests [1][2][3]
  • Interesting problems in number theory and Euclidean geometry
  • greatest mathematicians in history, and why
  • Axiom of Choice, why it has been controversial, and its use in Wiles' proof of Fermat's Last Theorem
  • Set theory in general
  • Kurt Gödel's incompleteness theorems are interesting; they are applicable not only in maths and logic, but also move into philosophy.
  • Hilbert's program (although of course the above renders null its aims!)
  • Formal mathematical logic

Students on the course

  • I would like to join this. Is it alright if I live in the UK? Your profile suggests that you live in the US, but I am always eager for maths. AungSein 18:13, 5 August 2007 (EDT)
That's fantastic. Of course you're welcome in the UK. You have great colleges there, and produced some fantastic physicists. Please help build a curriculum (see above). Lord willing, maybe we can make some inroads into some unsolved problems.--Aschlafly 19:29, 5 August 2007 (EDT)
Well I come from Burma, but the colleges and university there are good. Your point about unsolved problems is good, too - have you heard of the folding@home project? It is a different concept, I know, but perhaps relevant - maybe what one brilliant mathematician might struggle at, us many lesser minds might gain insight into! I would also recommend for point 3 the UKMT papers [4][5][6] - I do not know about how it is in the USA, but they are typical here. AungSein 20:06, 5 August 2007 (EDT)
Your additions to the above curriculum are superb! Thanks much, and thanks also for the links to those U.K. tests. I just printed one out am reviewing it. Questions look challenging but doable, which is what we want. Lord knows that students can really improve after practicing on lots of those types of tests. We also have high school contests in the U.S. here: Math contests.--Aschlafly 20:37, 5 August 2007 (EDT)
AungSein, a second student in this class took the UKMT Junior contest you cited, and she marked 17 correct, 5 wrong, and 3 non-answered. How did you do on that test?--Aschlafly 21:54, 6 August 2007 (EDT)
  • I'm interested in this math critical thinking class too. --Luke314 16:38, 9 August 2007 (EDT)
Fantastic! Welcome and Godspeed. Please click "Watch" on this page so that you can easily see updates as September approaches. This will be a great learning experience. Feel free to make suggestions on the curriculum.--Aschlafly 16:42, 9 August 2007 (EDT)
  • I'm interested also, as a teacher. (Credentials on request, of course.) Is this class going to happen? What I see here doesn't look very well-subscribed. Is there another page somewhere, listing details of the class? Details of the Curriculum? Discussion of same? Teaching the axiom of choice or Gödel's incompleteness theorems really correctly sounds like quite an ambitious undertaking, but I'd like to give it a try. Robert 20:42, 23 August 2007 (EDT)
That's great, Robert! We don't have a lot of students yet but it is still only August. We plan to start mid-September and I welcome your input on the curriculum. I expect the interest in this to grow as it has in the American Government course (now up to 45 participants). Much will be accomplished by this math course for the immense benefit of the participants. Godspeed.--Aschlafly 23:08, 23 August 2007 (EDT)
  • I am also interested in participating in the project as an adult student. StevenW 20:46, 7 October 2007 (EDT)
  • I'm just wondering. How can things like axiom of choice, Fermat & Wiles, open problems, etc, can be covered. They say that nothing above 9th grade math is required. Will there be two different classes? Rincewind 11:58, 4 November 2007 (EST)
  • I'd love to join, I'm just a bit confused on the requirements in terms of homework, editing, et cetera. GlobeGores 18:07, 19 December 2007 (EST)

I'm interested in joining the course by I'm not sure how it all works. Can someone steer me in the right direction?- Schaefer 21:57, 20 December 2007 (EST)

  • I'm really interested in this. Any idea of when it's due to start? KTDiputsho 14:53, 15 April 2008 (EDT)
  • What is the "controversy about proof by contradiction" that you mention? It's news to me that there's any controversy about one of the standard tools of a mathematician. Googly 19:47, 6 August 2008 (EDT)
You'll learn lots of new things here, if you keep an open mind. When resorting to proof by contradiction, it is impossible to know if the result is due to the falsehood of the proposition or an undetected contradiction in the math itself.--Aschlafly 20:25, 6 August 2008 (EDT)