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 |
Geometry and Topology: Compare and Contrast.
The Fundamental Group of a Metric Space. (51, 52) Topological Spaces. (12, 13) |
Week #2:
Jan 23 - 27 Homework |
The Product and Subspace Topologies. (15, 16)
Closed Sets, Limit Points and Continuous Functions. (17, 18) The Product Topology Revisited. (19) |
Week #3:
Jan 30 - Feb 3 Homework |
The Fundamental Group Revisited. (52)
Connected Spaces and Subspaces. (23, 24) |
Week #4:
Feb 6 - 10 Homework |
Components and Local Connectedness. (25)
Compact Spaces. (26, 27) |
Week #5:
Feb 13 - 17 Homework |
Other Notions of Compactness. (28, 29)
Covering Spaces. (53) |
Week #6:
Feb 20 - 24 Homework |
The Fundamental Group of the Circle. (54)
Retractions and Fixed Points. (55) |
Week #7:
Feb 27 - Mar 3 Homework |
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. |
Week #8:
Mar 6 - 10 Homework |
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. |
Week #9:
Mar 20 - 24 Homework |
The Uryshonn Lemma. (33)
The Fundamental Group of Some Surfaces. (60) |
Week #10:
Mar 27 - 31 Homework |
Direct Sums of Abelian Groups. (67)
Free Groups and Free Products. (68, 69) |
Week #11:
Apr 3 - 7 Homework |
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. |
Week #12:
Apr 10 - 14 Homework |
The Seifert-van Kampen Theorem. (70)
The Fundamental Group of a Wedge of Circles. (71) |
Week #13:
Apr 17 - 21 Homework |
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. |
Week #14:
Apr 24 - 28 Homework |
Fundamenmtal Groups of Surfaces. (74)
Homology of SUrfaces. (75) Cutting and pasting. (76) |
Week #15:
Mar 1 - 5 Homework |
The Classification THeorem. (77)
Constructing Compact Surfaces. (78) ?. 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. |
Final Exam
|
The Final Exam will be given as a take home exam during the finals period. |