Algebraic Topology

This course will introduce the point of view, framework and most important tools of Algebraic Topology. Algebraic Topology is the mathematical theory whose fundamental problem is the investigation of topological spaces and related concepts using tools from abstract algebra. The ideas and tools from Algebraic Topology are important in many parts of pure mathematics and are becoming increasingly important in physics and in data science. The course aims to give students a foundational understanding in the two most important topics within Algebraic Topology. 1. The theory of homology. 2. The theory of fundamental group and covering spaces. The aim is for students to be sufficiently prepared to continue deeper study in this topic, perhaps at the graduate level. The aim is also to equip students so that when they encounter these ideas in different topics (such as in physics or in data science) then they have the ability to bring in an expert understanding of the theory and the ability to deepen their learning as is needed in the context