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Topic: How do we do proofs?
Replies: 6   Last Post: Nov 11, 2009 7:11 AM

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Bob Burn

Posts: 48
Registered: 12/3/04
Re: How do we do proofs?
Posted: Oct 22, 2009 9:23 AM
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I listened to your screencast with interest, and am sure the students who came found it profitable.
I have two comments.
The major one is that I recognise an assumption behind the presentation that the university maths course in Nottingham consists of lectures in a "Definition, Theorem, Proof, Exercise" format. Nothing unusual about that. But there are alternative ways of running a course in which the problems of proof come up rather differently. I think, for example, of the recent publications of the M.A.A, on the method of R.L.Moore. There are also courses which consist of problems and there are undergraduate courses in which a thesis forms a significant part.
The minor one is that asking a group of maths undergraduates why they thought they should do proofs, a researcher got the dominant answer "because we have to do proofs in the exam". Surely the motivation can be better than that. The first question in your presentation was "If n is an odd integer, prove that n^4 - 1 has a factor 8." The same mathematics could be rephrased in the form:
3^4 - 1 = 80
5^4 - 1 = 624
7^4 - 1 = 2400
Do you think 1 less than the fourth power of an odd number must have a factor 8 ?

This gives a different slant, and a slightly different motivation. The distinction between evidence, conjecture and proof emerges.

[By the way I was a bit puzzled why the simpler question: if n is an odd integer prove that n^2 - 1 has a factor 8, was not offered. This has a geometrical solution as well as modular arithmetic and factorisation solutions.]

Thank you for the screencast. It made me think.
Bob Burn
University Fellow, Exeter University
Barrack Road
Exeter EX2 6AB
From: Post-calculus mathematics education [MATHEDU@JISCMAIL.AC.UK] On Behalf Of Joel Feinstein [Joel.Feinstein@NOTTINGHAM.AC.UK]
Sent: 20 October 2009 19:36
Subject: How do we do proofs?

The second of my screencasts on how and why we do proofs,
"How do we do proofs? (Part I)", is now available at
The final episode of the trilogy will be in two weeks time.
I should, perhaps, clarify that I am running these as optional workshops for the second-year maths students at Nottingham: About 30-50% of the students came.

Joel Feinstein

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