Introduction to Mathematical Thinking

The course does not carry Stanford credit. If you finish the course, you will get a Certificate of Completion, and for those who do well on the coursework and the final exam the certificate will indicate Completion with Distinction.

At the end of each lecture, you will be given an assignment (as a downloadable PDF file, released at the same time as the lecture) that is intended to guide understanding of what you have learned. Worked solutions to problems from the two weekly assignments will be described the following Wednesday (so in weeks 2 through 6) in a video tutorial session given by the instructor.

Using the worked solutions as guidance, together with input from other students, you will self-grade your assignment work for correctness. The assignments are for understanding and development, not for grade points. You are strongly encouraged to discuss your work with others before, during, and after the self-grading process. These assignments (and the self-grading) are the real heart of the course. The only way to learn how to think mathematically is to keep trying to do so, comparing your performance to that of an expert and discussing the issues with fellow students and – as far as possible – with “course tutors” who will self-identify themselves as such in the questionnaire at the start of the course.

A designation of “tutor” will be assigned to individuals who indicate (in the questionnaire at the start of the course) that they are familiar with the course contents or else have direct access to someone who is (such as being a current students in a similar class at a physical college or university). Tutors will be so designated in their on-line identity, so others will recognize them. We will also ask them if they are willing to monitor the online forum discussions and jump in if they see an individual or group who has got something wrong or otherwise needs help.

At the start of week 6, you will be given an open-book exam to be completed by the end of the week. Completed exams will have to be uploaded as either images (or scanned PDFs) though if you are sufficiently familiar with TeX you have an option of keyboard entry on the site. The exam will be graded during week 7 by a calibrated peer review system. The exam will be based on material covered in the first 8 lectures, but completion of lectures 9 and 10 and their associated assignments (which look at some examples of the notions developed in the earlier lectures) will likely improve your performance on the exam.

There are two final grades: “completion” and “completion with distinction”. Completion requires viewing all the lectures and completing all the quizzes (both in-lecture “progress quizzes” and weekly “credit quizzes”). Distinction depends on the scores in the weekly credit quizzes and the result of the final exam.