Introduction to Topology
MATH 581
Overall Course Reflection
Topology is often called “rubber-sheet geometry”, because it studies properties of shapes and spaces that do not change when they are bent, stretched, or twisted. For example, in topology, a coffee mug and a doughnut are considered the same when looking at it from a topological standpoint. For this class, we focused on concepts including topological spaces, separation, open and closed sets and spaces, connectedness, metric spaces and manifolds.
This was one of the first classes that I took throughout this program, and it definitely challenged me to think about mathematics in a completely different and more abstract way. I strengthened my proof writing skills and learned how to approach problems by looking at the underlying structures rather than just specific calculations.
Course Artifacts
Homework Assignment
These are the homework assignments from this course. They demonstrate my ability to engage with topology at a graduate level, particularly through constructing rigorous proofs and analyzing key topological concepts. They show not only my understanding of topological structures and properties but also my ability to communicate abstract mathematical reasoning clearly and effectively.
(Creation time: 6-9 hours per assignment)