The goal is to introduce you to contemporary mainstream 20th and 21st century mathematics. This is not an easy task. Mathematics is like a giant scaffolding. You need to build the superstructure before you can ascend for the view. The calculus and algebra you will learn in college is an essential part of this scaffolding and is fundamental for your further mathematics, but most of it was discovered in the 18th century. We will take a few short cuts and only use calculus later in this course. We will investigate some very exciting and useful modern mathematics and get a feeling for “what mathematics is all about”. The mathematics you will see in this course is usually not seen until higher level courses in second or third year at University