"Problems solved only with proof-by-contradiction". As above, I consider the method of contradiction to be so fundamental that I'd be reluctant ever to say that somethng can be proved '''only''' that way. Better: In the introductory explanation of proof by contradiction, using the "always a prime between N and N+1" theorem, or the "infinite number of primes" theorem, as an example to motivate it.
Definition of the integers. Do you really want to do a Peano-postulate program here? As in Landau's "Foundations of Analysis"? I don't think people in this age group will actually appreciate that the tediousness of this is worth it. (Of course, '''we''' know that it's worth it, but '''they''' donndon't.) Also, a Dedekind-cut construction of the reals would actually contain material that the students don't already "know", in that it shows, for example, that the square root of 2 really exists. But of course, skipping over the integers and going straight to the reals is somewhat unesthetic! The students already "know" the result of the Peano program, they just don't realize that they don't really know it.
"Interesting problems in number theory and Euclidean geometry". Yes! There's a lot of really cool, engaging, and surprising material in geometry, above and beyond its use to show the axiomatic method. Geometrical inversion, for example.
::Well, I'm chagrined and disappointed by this, but I'm always willing to admit my ignorance and learn new things. So please change my status from instructor to student -- I'm still very much interested in this. Also, can you recommend any books that can fill me in on some of these issues? [[User:Robert|Robert]] 20:27, 13 September 2007 (EDT)
== Course Purposes ==
The course outline suggests that in learning maths the student will stave off 'mental decline'. There are a number of problems with this remark; not least because the author assumes that an understanding of numbers will prevent such an infliction. To be perfectly clear; one can interpret this remark as suggesting that, had my auntie taken to solving mathmatical problems regulary she would not have fallen victim to Alzheimers. I suggest editing the benefits that this course has to offer the student.--[[User:GrahamMcKnight|GrahamMcKnight]] 08:35, 13 November 2007 (EST)
== Additive Factoring ==
I believe "additive factoring" in the course description is a typo. I have not encountered such a term in my study of mathematics and have been unable to locate this on the internet. I did not change it, because I was not sure what it was intended to be. If it is not a typo and this is a new or unconventional topic, then it would be good to provide some explanation following it, or a link to a page about it. --[[User:PhineasBogg|PhineasBogg]] 23:03, 28 December 2007 (EST)
My best guess is this may be a reference to the Goldbach Conjecture about even numbers being expressable as the sum of primes. --[[User:PhineasBogg|PhineasBogg]] 18:09, 29 December 2007 (EST)