High school mathematics. Specific requirements are familiarity with elementary symbolic algebra, the concept of a number system (in particular, the characteristics of, and distinctions between, the natural numbers, the integers, the rational numbers, and the real numbers), and some elementary set theory (including inequalities and intervals of the real line). Students whose familiarity with these topics is somewhat rusty typically find that with a little extra effort they can pick up what is required along the way. The only heavy use of these topics is in the (optional) final two weeks of the Extended Course.
A good way to assess if your basic school background is adequate (even if currently rusty) is to glance at the topics in the book Adding It Up: Helping Children Learn Mathematics (free download), published by the US National Academies Press in 2001. Though aimed at K-8 mathematics teachers and teacher educators, it provides an excellent coverage of what constitutes a good basic mathematics education for life in the Twenty-First Century (which was the National Academies' aim in producing it).
The Basic Course lasts for eight weeks, comprising ten lectures, each with a problem-based work assignment (ungraded, designed for group work), a weekly Problem Set (machine graded), and weekly tutorials in which the instructor will go over some of the assignment and Problem Set questions from the previous week.
The Extended Course consists of the Basic Course followed by a more intense two weeks exercise called Test Flight. Whereas the focus in the Basic Course is the development of mathematically-based thinking skills for everyday life, the focus in Test Flight is on applying those skills to mathematics itself.
The course does not carry Stanford credit. If you complete the Basic Course with more than a minimal aggregate mark, you will get a Statement of Accomplishment. If you go on to complete the Extended Course with more than a minimal mark, you will receive a Statement of Accomplishment 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 assignments will be described the following week 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.
No. The Test Flight exercise in the final two weeks of the Extended Course is built around a Problem Set similar to those used throughout the course, and your submission will be peer evaluated by other students, but the focus is on the process of evaluation itself, with the goal of developing the ability to judge mathematical arguments presented by others. Whilst not an exam, Test Flight is an intense and challenging capstone experience, and is designed to prepare students for further study of university level mathematics.
In the Basic Course, grades are awarded for the weekly Problem Sets, which are machine graded. The aggregate grade is provided in the cover note to the Statement of Accomplishment, with an explanation of its significance within the class. In the Extended Course, additional grades are awarded for a series of proof evaluation exercises and for the Test Flight Problem Set (peer evaluated). The aggregate grade is provided in the cover note to the Statement of Accomplishment with Distinction, with an explanation of its significance within the class.