Introduction to Topology

Description

An introduction to point-set and algebraic topology, intended for students who want to go on to further study of geometry or analysis. Topics include topological spaces; maps; product and subspace topologies; properties of topological spaces; the fundamental group and applications. Learning Hours: 120 (36 Lecture, 84 Private Study) Requirements: Prerequisite MATH 280 /3.0 and MATH 281 /3.0. Exclusion MATH 499 /3.0 (Topic title: Introduction to Topology - Fall 2019, Winter 2024); MATH 499 /3.0 (Topic title: Introduction to Topology and Metric Spaces - Fall 2022). Course Learning Outcomes: - Use the ideas in the course fluently. Indicators of fluency include: being able to use the ideas in a new situation; being able to use the ideas in a different order or manner than they have been presented; being able to construct minor extensions or use minor variations of the ideas. - Write clear, clean, and well-reasoned mathematical arguments. - Understand the standards for such arguments. - Master the ideas of topological spaces, subspaces, product and quotient spaces, continuity, compactness, separation and countability conditions, metric spaces and metrizability, the fundamental group and some applications. Assessment/Exam Context: Course assessment and examinations vary by course; Queen's notes that eligible exchange students whose first language is not English may receive extra final-exam time. Exchange Registration Note: Arts and Science courses are open to exchange students subject to prerequisites and space. Most courses should be in Arts and Science; other faculties may be limited. Education, Medicine, and Nursing are not open to incoming exchange enrolment.