21-260: Differential Equations

Schedule and Homework

For each week there will be a link to a page with a reading assignment and a homework assignment.

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.

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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.