This course is strongly recommended for students considering graduate work in mathematics. Senior standing and permission of instructor Methods of and materials and technology for teaching mathematics in secondary school. Issues in contemporary mathematics education. Regular visits to secondary school classrooms and teaching a class are required. Normally taken in the senior year.
Topology studies invariants of spaces.
Coffee cups and donuts are indistinguishable to topologists, because they each have one hole. This course will be a introduction to point-set, geometric, and algebraic topology. You'll learn about the Klein bottle, classification of surfaces, space-filling curves, connectedness, orbit spaces, fundamental groups, fixed points, simplicial approximation, and knots. Neat stuff, cool pictures. Along the way, he developed a fascinating theory of infinite sets, and devised several ingenious proof techniques that have become part of mathematicians' standard repertoire.