This course explores major modern mathematical developments and helps students to understand and appreciate the unique approach to knowledge employed by mathematics. The course is organized around three major mathematical ideas that have emerged since the time of Sir Isaac Newton. These three ideas may be drawn from: game theory, graph theory, knot theory, logic, mathematics of finance, modern algebra, non-Euclidean geometry, number theory, probability, set theory and the different sizes of infinity, and topology. Students will learn how to solve basic problems in the three areas covered in the course and how to present their solutions concisely, coherently, and rigorously. |