This course is geared toward students with no prior university math experience. It aims to provide a view of mathematics as a living, growing, creative human endeavor that classifies as both a science and an art, to give a feeling for, and some mastery of, the mathematical way of thinking (including "doing mathematics") as well as an awareness of some of the many applications of mathematics in today's world. Active class participation is an essential component of the course, required along with participation in Professor Keith Devlin's (free) Stanford MOOC "Introduction to Mathematical Thinking." (The course was very popular at Stanford among non-science majors looking to satisfy their Quantitative Reasoning requirement.)
We start out with a general discussion of the nature of mathematics, adopting a broadly historical approach. After that, the main aim will be to investigate several important areas of contemporary mathematics. The exact choice will depend in part on the interests of the class, as determined by a student questionnaire completed during the first class meeting. Students will gain extensive experience at "doing mathematics" in Professor Devlin's online course "Introduction to Mathematical Thinking", which will run at the same time, and students should come to precepts prepared to discuss the issues introduced in the online lectures and present solutions to problems assigned in the online class.
Expect to read, to write a paper, to discuss ideas, and to be creative. Expect to examine our world and ourselves in a novel way, a way developed by thousands of years of combined human intellect. Do not expect to spend a lot of time learning how to 'solve problems' (in the sense of a typical high school math course). This is definitely not a course to improve your math skills (though that may be a by-product for some). The MOOC component focuses on developing mathematical thinking ability, enabling you to learn how to set about solving novel problems.