Schedule
Review before classes start: Basic Set Theory and Logic. (Self-study)
- Videos covering this background prerequisite material are posted in the course Blackboard website learning modules under Week 0.
Week of Jan 17
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Note: First class on Wednesday, Jan 17
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Topics:
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Chapter 1, Munkres + Handouts.
- Set Theory notation
- Basic Logic
Week of Jan 22
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Homework 1 Due Saturday, Jan 27, 11:59PM
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Topics:
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Chapter 2, Munkres: Sections 12.
- Ordered Sets
- Topological spaces
Week of Jan 29
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Homework 2 Due Saturday, Feb 3, 11:59PM
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Topics:
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Chapter 2, Munkres: Sections 13, 14, 15, 16.
- Basis for Topologies
- Order Topologies
- Product Topologies
- Subspace Topologies
Week of Feb 5
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Homework 3 Due Saturday, Feb 10, 11:59PM
- Topics:
- Chapter 2, Munkres: Section 17, 18.
- Closed sets and limits points
- Hausdorff spaces
- Continuous functions
Week of Feb 12
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Homework 4 Due Saturday, Feb 17, 11:59PM
- Topics:
- Chapter 2, Munkres: Section 18, 19.
- Continuous functions
- Homeomorphisms
- Topologies on infinite product spaces
Week of Feb 19
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Homework 5 Due Saturday, Feb 24, 11:59PM
- Topics:
- Chapter 3, Munkres: Section 20.
- Metric spaces, Part 1.
Week of Feb 26
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Homework 6 Due Saturday, March 2, 11:59PM
- Topics:
- Chapter 3, Munkres: Section 21.
- Metric spaces, Part 2.
Week of March 4
The midterm will be on Wed, March 6, 7:30-9PM (Rochester night) in TBA.
- Topics:
- Chapter 2: Supplement, Handouts.
- Topological Manifolds
- Smooth Manifolds
SPRING BREAK IS MARCH 9 THROUGH MARCH 17. Classes resume Monday, March 18.
Week of March 18
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Homework 7 Due Saturday, March 23, 11:59PM
- Topics:
- Chapter 2, Munkres: Sections 22.
- Groups
- Topological Groups
- Lie groups
Week of March 25
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Homework 8 Due Saturday, March 30, 11:59PM
- Topics:
- Chapter 2, Munkres: Sections 22. Handouts.
- Quotient Topology and Quotient Constructions
- Mobius band, Torus, Klein Bottle, Projective spaces.
Week of April 1
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Homework 9 Due Saturday, April 6, 11:59PM
- Topics:
- Chapter 3, Munkres: Sections 23, 24, 25.
- Connected Spaces.
- Connected Subspaces of the Real Line.
- Components and Path Components
Week of April 8
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Homework 10 Due Saturday, April 13, 11:59PM
- Topics:
- Chapter 3, Munkres: Sections 26, 27.
- Compact Spaces.
- Compact Subspaces of the Real Line.
Week of April 15
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Homework 11 Due Saturday, April 20, 11:59PM
- Topics:
- Chapter 3, Munkres: Sections 28, 29(skim).
- Classification of compact, connected surfaces.
- Limit Point and Sequential Compactness.
- Local Compactness.
Week of April 22
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Homework 12 Due Saturday, April 27, 11:59PM
- Topics:
- Chapter 3, Munkres: Sections 30-33.
- Countability and Separation Axioms.
- Normal Spaces.
- Urysohn’s Lemma.
Week of April 29
- Topics:
- Assorted final topics.
Monday, April 29 is the last day of class.
FINAL
The final will be on Monday, May 6, 8:30-11:30 AM (Rochester morning) in Gavett 310.