This schedule is tentative. It will get more accurate as the semester
progresses. No week's topics should be taken as final until the homework
is linked.
Week #1:
Jan 16 - 20
Homework
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Geometry and Topology: Compare and Contrast.
The Fundamental Group of a Metric Space. (51, 52)
Topological Spaces. (12, 13)
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Week #2:
Jan 23 - 27
Homework
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The Product and Subspace Topologies. (15, 16)
Closed Sets, Limit Points and Continuous
Functions. (17, 18)
The Product Topology Revisited. (19)
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Week #3:
Jan 30 - Feb 3
Homework
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The Fundamental Group Revisited. (52)
Connected Spaces and Subspaces. (23, 24)
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Week #4:
Feb 6 - 10
Homework
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Components and Local Connectedness. (25)
Compact Spaces. (26, 27)
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Week #5:
Feb 13 - 17
Homework
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Other Notions of Compactness. (28, 29)
Covering Spaces. (53)
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Week #6:
Feb 20 - 24
Homework
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The Fundamental Group of the Circle. (54)
Retractions and Fixed Points. (55)
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Week #7:
Feb 27 - Mar 3
Homework
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The Quotient Topology. (22)
Deformation Retracts and Homotopy Type. (58)
The Mid-Term Exam will be given as a take home exam during the seventh
week of class.
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Week #8:
Mar 6 - 10
Homework
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The Fundamental Group of Sn. (59)
Imbeddings of Manifolds. (36)
Administrative note: Friday 10 March is the Mid-Semester Break.
Class will not meet. Additionally, March 13 -17 is Spring Break. Classes
will resume on March 20.
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Week #9:
Mar 20 - 24
Homework
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The Uryshonn Lemma. (33)
The Fundamental Group of Some Surfaces. (60)
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Week #10:
Mar 27 - 31
Homework
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Direct Sums of Abelian Groups. (67)
Free Groups and Free Products. (68, 69)
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Week #11:
Apr 3 - 7
Homework
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The Seifert-van Kampen Theorem. (70)
Administrative Note: Monday 3 November is the Course Drop and Pass/Fail
grade option deadline. Grade of "W" is assigned after this date.
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Week #12:
Apr 10 - 14
Homework
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The Seifert-van Kampen Theorem. (70)
The Fundamental Group of a Wedge of Circles. (71)
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Week #13:
Apr 17 - 21
Homework
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Adjoining a Two-Cell. (72)
The Fundamental Groups of the Torus and the Dunce
Cap. (73).
Administrative Note: May 21 is Spring Carnival. Class will not meet.
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Week #14:
Apr 24 - 28
Homework
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Fundamenmtal Groups of Surfaces. (74)
Homology of SUrfaces. (75)
Cutting and pasting. (76)
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Week #15:
Mar 1 - 5
Homework
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The Classification THeorem. (77)
Constructing Compact Surfaces. (78)
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Administrative note: Friday 5 May is the last day of class.
Friday 5 May is also the course drop deadline to receive a "W" grade.
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Final Exam
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The Final Exam will be given as a take home
exam during the finals period.
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