Exam syllabus/curriculum

This is the planned exam syllabus.  Dates (day/month) will show when the material is first discussed.

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