Math 531 - Topology I - Point Set Topology

MWF 2:30PM - 3:20PM, Ungar 402

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Office Hours: Tuesdays 3:00 - 4:00pm and by appointment

Course Description: 

Text: Topology, Second Edition, Munkres (ISBN-13: 978-0131816299)
Content: We focus upon the material in Chapters 1-4.

Exams: There will be a midterm and a final exam, both take-home.
      Midterm: around Oct 12    Final: around Dec 7
You will be responsible for the material covered in the lectures, the readings, and the homework.

Homeworks: Homework will be assigned below. It will be due every week or two at the beginning of class on Wednesdays.

Grades: Overall Score = Hwk 40% + Midterm 30% + Final 30%
Letter grades will approximately follow standard cutoffs, e.g. A>90, B>80, C>70 with +/-.

Academic Honesty: Each student will uphold the University of Miami Honor Code.

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Homeworks and Notes

Weeks	Readings	Problems
Aug 24	§1-4	Due Wed Aug 26: What does it mean for a function to be continuous? §1.3,4, §2.6 (Review §1.1,2 )
Aug 31	§5-7,12	Due Wed Sept 2: §1.5,6,9 §3.3,4,8 §5.3 §6.5,6,7 (Review §2.5;  §4.1,2;  §6.3)
Sept 7	§12-14	Due Wed Sept 9: §7.5e,5f §13.1, 4, 5, 8 (Review §7.1,3,5,6;  §13.3,6,7)
Sept 14	§14-17	Due Wed Sept 16: §16.3,5,8 §17.2,3,7,8,9 (Review §16.7,10;   §17.1,4,5,6)
Sept 21	§17-18	Due Wed Sept 23: §17.11,13,19 §18.1,2,5,8,13 (Review §17.10,12,18,20 ;   §18.3,4,6,10) Hitler learns Topology. Some NSFW subtitles...
Sept 28	§19-21	Due Wed Sept 30: §19.3,6,7 §20.1a,2,3 --- Note: We're skipping the uniform topology for now. §21.2,8 (Review §19.1,2,8,5 ;   §20.4,8,10 ;   §21.1,3,5,11 )
Oct 5	§22--23	Due Wed Oct 7: §21.3, 4, 10 §22.2, 4 §23.1, 2, 5 We'll have the midterm after this.
Oct 12	§24-25	Due Mon Oct 19: MIDTERM Due Wed Oct 21: §24.1, 2, 8, 9 §25.4, 8
Oct 19	§26-29	Due Wed Oct 29: §26.6,7,8 §27.5,6 §28.7 Mobius Transformations Revealed
Oct 27	§29-32	Due Wed Nov 4: §29.1,6,8 §30.4, §31.2, §32.1, 5 for product top.
Nov	Curves, Surfaces, Euler characteristic	Due Dec 1: Problem Set Conway's Zip Proof

General Notes

Current research in Topology

• The arXiv prepint server hosts preprints for many topics. I like to use the UC Davis front end however.
  • math.GT Geometric Topology (most of my work fits in here)
  • math.GN General Topology (perhaps closest to Point Set Topology)
  • math.AT Algebraic Topology (algebraic methods for understanding topological objects)
  
  
• MathOverflow -- Research level questions about math
• Mathematics StackExchange -- Up to intro research level questions about math
• /r/puremathematics -- a subreddit devoted to pure mathematics

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