This course will be devoted to the topic of "number", exploring ways of writing and talking about numbers, special kinds of numbers, interesting facts about numbers, stories from history, counting problems, and extensions of the concept of number from counting numbers and rational to irrational numbers and then to complex numbers and infinite numbers. This study will follow the remarkable (and readable) book, The Book of Numbers, by John Conway and Richard K. Guy. This book is rich in fascinating ideas, with beautiful visualizations and examples. Additional problems and explorations will be brought in from other sources.
Much of each class time will be devoted to solving problems by group discovery, but there will be explanations, hands-on experiments and computer demonstrations as well. Between classes, students will be expected to do reading and problem assignments. Grades will be based on the assignments, active class participation, and grades on several quizzes. The final assignment will be a project in lieu of an examination.
There are no formal prerequisites beyond school mathematics and a willingness to think about mathematics and stretch problem-solving and reasoning skills.
For additional information (including links to reviews of the text), check the course web page. The instructor's email is <king@math.washington.edu>.