An online course should either be free or it should focus on a specific domain and cater to students already established in that domain. Devlin's course certainly satisfies this rule. It is free. And it doesn?t cater to students already established in mathematics.
However, in the email you receive upon registering for the course, he states?
"If you are starting a college math major (or another math-dependent major) this year or next, this online course helps you make the transition from school math, which focuses on learning procedures to solve highly stereotyped problems, to university mathematics, which is about how to think a certain way to solve real problems, problems that can arise from the everyday world or from science, or from within mathematics itself. (Your college may well have what is called a transition course; this online course ie designed to be valuable as a supplement to that class.) Because mathematical thinking is a valuable life skill, however, anyone over the age of 17 or so could benefit from taking the course.?
There are a number of issues with this statement.
1. I realize that it became common practice for students with little or no prerequisite success in academics to continue forth and choose an academic major, regardless. Those students are now working at Starbucks and sitting on a pile of tuition debt that they will struggle to repay for decades. Except for the most exceptional circumstances, a math major does not (should not) be majoring in math, if by college they are still struggling with the notion of ?mathematical thinking?. Being unsure of what your major might be is entirely not the same thing as being unsure what the major is or what the subject is. It is the later that has landed students in finical ruin. It is an issue that is easily fixed if we stop marketing college degrees to unsuspecting and unknowing students as if we were selling them a car.
2. Devlin describes ?school math? as focusing on learning procedures to solve stereotypical problems. Nothing new here. Just the usual mis-characterization by reformers of school math. Devlin goes on to say that pure math (this is what his course talks to) is designed to solve real everyday problems. I am not sure how he got pure math and applied math so mixed up. He seems to understand what pure math is so I have to assume that he doesn?t understand what applied math is. Nonetheless, I like pure math, and I solve everyday technical problems, every day. My ability to do so did not begin with nor does it have anything to do with pure math. It began with algebra and continued on through the topics of precalculus and calculus. The bulk of it is simply really good algebraic reasoning.
That being said, I think what he is offering is valuable, even if I find his commentary to be ill reasoned. The class doesn?t start till February but I have read the textbook. I think the choice of topics is good but presented in terms not tuned for a math major. At least not a math major with reasonable prospects. He calls this a ?transitional? course and for math majors there is a need for such a thing. Pre-collegiate math is mostly applied math (but not the way Devlin describes it). It isn?t pure math because pre-collegiate students generally lack the formal skills and majority to deal with pure math. That is why I like the topics in his text. They provide a good representation of the logical foundations of mathematics. Some of them, like the topic of induction, are gems. But not the way he presents them.
His presentation is very layman. I suspect that his being a populist author of math books is the reason the textbook reads as it does. But this is hardly the treatment I was expecting for math majors. Maybe for mathy non math majors. In my mind, a transitional course would shift the focus from applied math to the logical foundations of mathematics, and the topics he has selected would are perfect for this, if he had treated them for this purpose.
In any event, the course is free and it does give a taste of several important mathematical topics even though it doesn?t develop them.