# Publish pedagogical results as an undergraduate

As an undergraduate, I became fond of real analysis and complete metric spaces. Regarding completeness (mostly in R), I proved the same theorem in perhaps 10 different ways, using different approaches and results.

Those proofs are of no use for research, but might interest teachers and students willing to go deeper into their analysis course.

Is there a good place to publish them ? A journal for undergraduate education perhaps ? I looked on the MAA website but found the website complicated and ended up with nothing concrete.

• On your website. – PVAL-inactive Oct 5 '15 at 18:24
• This question seems better suited for academia.stackexchange.com – epsilone Oct 5 '15 at 18:27
• A well written survey of the different proofs is well within the scope of a paper for the MAA's Mathematics Magazine or American Mathematical Monthly, especially if you can provide some historical nuggets about some (or all, if possible) of the proofs and/or show how the different proofs lead to different avenues of mathematics. In the past they've published papers on different ways to evaluate $\int \frac{1}{x^4+1}dx,$ different ways to evaluate $\sum_{n=1}^{\infty}\frac{1}{n^2},$ different ways to prove $\mathbb R$ is uncountable, etc. – Dave L. Renfro Oct 5 '15 at 18:34
• You may enjoy Real Analysis in Reverse by Propp. – lhf Oct 5 '15 at 18:38
• Thanks for the reference lhf. I didn't know that article and it's amazing to see that we wrote almost exactly the same thing ! My introduction isn't the same but the content is. Thank you for your answer @DaveL.Renfro, you can post it as an answer if you want – Julien__ Oct 14 '15 at 6:13

(a copy of my comment posted as answer, as you suggested I do) A well written survey of the different proofs is well within the scope of a paper for the MAA's Mathematics Magazine or American Mathematical Monthly, especially if you can provide some historical nuggets about some (or all, if possible) of the proofs and/or show how the different proofs lead to different avenues of mathematics. In the past they've published papers on different ways to evaluate $\int \frac{1}{x^4 + 1}dx,$ different ways to evaluate $\sum_{n=1}^{\infty}\frac{1}{n^2},$ different ways to prove $\mathbb R$ is uncountable, etc.
(ADDED 2 WEEKS LATER) An example that just appeared in print is To be (a circle) or not to be? by Hassan Boualem and Robert Brouzet in College Mathematics Journal 46 #3 (May 2015), pp. 197-206. On pp. 198-201 they give 14 different proofs that the graph of $\sqrt{x} + \sqrt{y} = 1$ for $0 \leq x,y \leq 1$ is not an arc of a circle.