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I love Euclid's elements, and would like to base a course around them. Before I can pitch it to my supervisors, I need to know where it would fit in the curriculum. While it begins from elementary principles, it requires a high level of logic.

What would be an appropriate prerequisite(s) for this class?

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    $\begingroup$ I am not sure I agree with the phrase "high level of logic". I think what it requires is that the reader has some familiarity with basic rules of propositional logic. In any case, can you clarify who the intended audience of your class is? High school students? College students? $\endgroup$
    – Willie Wong
    Mar 14, 2014 at 13:20
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    $\begingroup$ I just have to plug Robin Hartshorne's book "Geometry: Euclid and Beyond" which offers a guided reading of The Elements, along with the needed missing axioms to make it completely rigorous (the axioms were incomplete until Hilbert)! $\endgroup$
    – Steven Gubkin
    Mar 19, 2014 at 21:53
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    $\begingroup$ A 2,300-year old textbook is an odd basis for a class, especially with its disjoint treatment of disparate subjects, and with flaws that were well-discussed 1,500 years ago. There are class topics nearby I could pitch more easily: "Euclid's geometry and others", "Euclid's Elements and its readers", or "Ancient Greek mathematics". $\endgroup$
    – user173
    Mar 20, 2014 at 1:05

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I really think this depends on what you intend to cover and what you want students to learn from it.

Do you hope for your students to work through the major parts of the books and develop a true appreciation for it? Good luck; you'll need to presume they already have a level of mathematical maturity and enthusiasm that is difficult to quantify and pin to a certain set of prerequisites.

Do you hope to inspire a group of not-necessarily-math-oriented folks to develop an appreciation for mathematical rigor and proofs? Perhaps you hope to inspire visual learners to dig deeper into mathematics, to see that it's not all about numbers and calculating? Then, you might not presume much more than an interest in pictures and some modicum of logic.

Are you working with high school students? College students? Math majors or not? All of these will affect your answer.

Ultimately, I think there is not much mathematical content with which you need to presume familiarity. I disagree with your "high level" assessment of requisite logic: working with hypotheses and conclusions, as well as some understanding of reductio ad absurdum should suffice. Other than that, a working familiarity with plane geometry should be an advantage but not technically a prerequisite.

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Here is a thought that might help in your development. Write up a sample lecture/class period to describe the material and how it goes. Get two others to help you run through a trial and videotape it. (Or should I say "Cell-phone it"?) Publish on the net the written material and representative samples from the video of how the class might go. Include contact information for anyone who is interested in the class.

I agree with the other poster that writing down a specific set of prerequisites beyond mathematical maturity will be a challenge. Giving an idea of what you want the course to be about should not be, and communicating the style above should be wonderful preparation for the audience, at least in determining if they want to be a part of it.

I can flesh out the ideas for such "promotional material" if you are interested.

Gerhard "Not Yet A Hollywood Producer" Paseman, 2015.06.06

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