Me: We'll see how that goes, as I've been hoping to make it through the Extended Course and get the Statement of Accomplishment With Distinction that comes from passing it. I've found the course highly interesting and will have learned a great deal regardless of how far I get. The overall course emphasizes logic and proofs, and is designed to give a sense of how mathematicians think (in contradistinction to the emphasis on following instructions that characterizes much K-12 math). At times, I have struggled with the concepts, though my weekly test results have been generally decent (with one exception), with scores equivalent to about 87, 87, 41 (oops), 96 (comeback) and 86.Students who struggle with the Basic Course are likely to find the additional two weeks of the Extended Course extremely difficult, if not impossible.Note also that the final two weeks of the Extended Course are more intense than the Basic Course, being in part designed to give students a sense of the pace of a university-level course in pure mathematics. Moreover, in Week 10 there is a series of fairly tight deadlines you must meet, with 48 hour turnaround times. [Emphasis in the original.]

The course is not particularly oriented toward visual thinking, but I have found some visualization helps in grasping the concepts. Here is what I drew and wrote for a homework problem. [Added: SPOILER: Don't read the image first if you want to answer the question yourself.] The question was: "Prove or disprove the claim that there are integers m, n such that m

^{2}+mn+n

^{2}is a perfect square." I drew and wrote the below, and posted it to a class discussion board (along with a question as to whether and to what extent "visual proofs" are acceptable):

^{2}+mn+n

^{2}, which is true. If I were to do it over, I'd leave one of the mn boxes out or cross-hatch it or something. My basic idea that the claim is verified by making n zero seems to have some merit.

Here is a report from someone who took the same course a couple of years ago. I agree with many of the sentiments expressed, including about finding the course very interesting and enjoyable, and also about this:

Assignments are not submitted for marking (but a helpful feedback video is made available in the next week in which Devlin explains how to answer a selection of the questions). In the first few weeks of the course Devlin puts a very prominent amount of emphasis on the need for all students to discuss the course with others in an informally established study group. In my case I chanced on and joined a Google Group called “Mathematical Thinking UK Discussion Group”. This initially had about 40 members. About seven were helpfully active in the first three weeks, but the study group has seemingly since ceased to function. So I am on my own: it feels a bit late in the day to try to find another study group, nor to attempt to breath life into this one.Me: That mirrors my experience very closely, as I was part of a weekly Google Hangout study group, which started off very promising and then progressively wound down into nothingness. I gather the dissolution of such groups has a lot to do with people quitting the course (considerably more that, I suspect, than with people finding the course easy and deciding they don't need a study group). The statistics posted by the professor weekly show that, while a large number of people are enrolled (over 38,000, from all over the world), they vary in activity or lack thereof; and those who actually hand in the weekly test, or Problem Set, are a small and declining subgroup (under 1,500 at last count).

In any case, I've become a big fan of online courses, a remarkable and unprecedented resource (and one that for now at least is often free). Edward Frenkel, who did much to inspire my newly heightened interest in math, has an upcoming (and seemingly not too time-consuming) class, which I've signed up for as well. Whatever limits I encounter in my online education, it's clear to me that I've learned much already, and that this has been time well-spent.