Thank you for signing up for Introduction to Mathematical Thinking! The goal of the course is to help you develop a valuable mental ability – a powerful way of thinking that our ancestors have developed over three thousand years.
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.
Mathematical thinking is not the same as doing mathematics – at least not as mathematics is typically presented in our school system. Let me give you an analogy. If we compare mathematics with the automotive world, school math corresponds to learning to drive. In the automotive equivalent to university mathematics, in contrast, you learn how a car works, how to maintain and repair it, and, if you pursue the subject far enough, how to design and build your own car.
The key to success in high school math is to learn to think inside-the-box. In contrast, a key feature of mathematical thinking is thinking outside-the-box – a valuable ability in today’s world,
Apart from the final week of lectures, there’s very little mathematical content in the course, and you won’t learn any new mathematical procedures. The focus is on learning to think a certain way – to think like a mathematician.
If you have read about these new Massively Open Online Courses, or MOOCs, you will be aware that they are all still very much experimental, so everyone involved is learning as we go along, the students, the support staff, the teaching assistants, and the faculty, like myself. I’m excited to be part of this new experiment, and I’m glad you have decided to join me.