Math 109 is the year-long undergraduate survey of topology and geometry. The second term focuses on surfaces, that is, topological spaces locally homeomorphic to R2. We'll start by looking at their global topology, and then turn to understanding their intrinsic and extrinsic metric geometry when embedded as subsets of R3. The required text is:
Ethan D. Bloch, A First Course in Geometric Topology and Differential Geometry, Birkhäuser, 1997.Another book you may want to consult is
Manfredo P. do Carmo, Differential Geometry of Curves and surfaces, Prentice Hall, 1976.
This is the text that was used in past years. Copies of it will be on reserve at the Millikan.
Prerequisites: Ma 109a or equivalent.
Your grade in the course will be based on the weekly homework (50%), the midterm (20%) and the final (30%). Your lowest homework score will be dropped when computing your final grade.
The weekly homework will be due on Wednesdays at 10:00am. If you will not be in class that day, please turn it in to the 109 box near the math office on the 2nd floor of Sloan. Late homework will not be accepted, except in certain extreme circumstances, in which case you must ask me, not the TA, for an extension prior to the due date. Such an extension will not be beyond the date when the graded HWs are returned (typically, the Monday after they are due). Of course, since the lowest HW score is dropped, effectively you are allowed one (infinitely!) late HW.
You are allowed, nay encouraged, to work with other people on the HW. However, you must write up your answers individually, and credit your collaborators. Of course, there is to be no collaboration on exams.
The midterm will replace the 5th HW assignment. It will be handed out on Wednesday, February 1, and due Wednesday, February 8. It will be a timed exam, lasting 4-5 hours.
The final will be given out on Wednesday, March 8, and due Thursday, March 16 at 10:00am. It will be a timed exam with a very long time limit, probably 48 hours.
All problem numbers refer to the textbook, unless otherwise noted.