Mathematics: Topology

Capstone course that includes a final project. An introduction to point set topology. Topics include open and closed sets, continuous functions, compactness, connectedness, metric and Hausdorff spaces. Provides a background for analysis and graduate topology courses as well as for topological data science. Prerequisites: MATH 2055 or CS 1640; MATH 2248, MATH 2522, or MATH 2544; one 3-credit course in WIL1.

Prereqs enforced by the system: (MATH 2055 or CS 1640) and (MATH 2248 or MATH 2522 or MATH 2544); Open to Degree and PACE students

Dive into the foundational concepts of topology. Designed for students with a strong interest in mathematical rigor, this course emphasizes proof-based learning and project-based applications. Throughout the semester, you will explore key topics such as open and closed sets, continuity, and compactness. These concepts form the backbone of topology and are essential for understanding more advanced mathematical theories. You will engage in deep theoretical discussions and a hands-on final project that illustrate the practical applications of topology.

By the end of the course, you will have a solid grasp of the fundamental principles and be well-prepared for further studies in mathematics. Ideal for advanced undergraduates, this course requires a strong foundation in mathematical reasoning and a willingness to engage with complex proofs. Whether you aim to pursue research or simply deepen your understanding of mathematics, this course will provide the tools and knowledge you need to succeed.