Exam syllabus/curriculum

This list grew into the exam syllabus, over the course of the semester.  The date shows when the material was discussed.

• Section 1: Fundamental Concepts (21/8)
• Section 2: Functions (21/8)
• Section 3: Relations (up to Order Relations) (25/9)
• Section 5. Cartesian Products (25/8)
• Section 6: Finite Sets (25/8)
• Section 7: Countable and Uncountable Sets (23/10)
• Section 12: Topological Spaces (25/8)
• Section 13: Basis for a Topology (28/8)
• Section 15: The Product Topology on X x Y (1/9)
• Section 16: The Subspace Topology (4/9)
• Section 17: Closed Sets and Limit Points (8/9)
• Section 18: Continuous Functions (11/9)
• Section 19: The Product Topology (18/9)
• Section 20: The Metric Topology (22/9)
• Section 21: The Metric Topology (continued) (25/9)
• Section 22: The Quotient Topology (29/9)
• Section 23: Connected Spaces (2/10)
• Section 24: Connected Subspaces of the Real Line (6/10)
• Section 25: Components and Local Connectedness (9/10)
• Section 26: Compact Spaces (13/10)
• Section 27: Compact Subspaces of the Real Line (16/10)
• Section 28: Limit Point Compactness (20/10)
• Section 29: Local Compactness (20/10)
• Section 30: The Countability Axioms (23/10)
• Section 31: The Separation Axioms (23/10)
• Section 32: Normal Spaces (27/10)
• Section 33: The Urysohn Lemma (27/10)
• Section 34: The Urysohn Metrization Theorem (30/10)
• Section 35: The Tietze Extension Theorem (without proof) (3/11)
• Section 36: Embeddings of Manifolds (3/11)
• Section 37: The Tychonoff Theorem (without proof) (6/11)
• Section 43: Complete Metric Spaces (6/11)
• Section 45: Compactness in Metric Spaces (10/11)
• Section 46: Pointwise and Compact Convergence (10/11)
• Section 51: Homotopy of Paths (13/11)
• Section 52: The Fundamental Group (13/11)
• Section 53: Covering Spaces (17/11)
• Section 54: The Fundamental Group of the Circle (17/11)
• Section 55: Retractions and Fixed Points (20/11)
• Section 56: The Fundamental Theorem of Algebra (23/11)