Algebraic Toplogy I



Basic Information
Instructor Prof. Chris Leininger
411 Mathematics
Phone:  (212)-854-2431
clein@math.columbia.edu
TA info TA: none
Office hours Friday 9:00--10:00 and by appointment
Class times Tuesday and Thursday, 4:10--5:25 (sometimes changing on Thursdays...)
Class location Mathematics 307
Text Algebraic Topology, A. Hatcher.  This is available online (see below), from the CU bookstore, or from the publisher.
Supplemental Texts Basic Topology, M. A. Armstrong
Topology, A first course, J. R. Munkres
Elements of Algebraic Topology, J. R. Munkres
Algebraic Topology, A First Course, M. J. Greenberg and J. R. Harper
Homework This will be assigned weekly or daily, with additional exercises given throughout the course of the lecture.  I will collect three problems a week to give you feedback on your work.
Homework / Handouts  problems1.ps   ;   problems2.ps   ;   problems3.ps  ;  problems4.ps  ;  problems5.ps  ; problems6.ps ; problems7.ps  ;  problems8.ps  ; problems9.ps  ; problems10.ps  ;   problems11.ps  ;  problems12.ps  ;  problems13.ps  ;  problems14.ps  ;  problems15.ps  ;  problems16.ps  ; Surface notes (.ps)   ; 
Midterm Tuesday, October 14.  This, like the homework, will be primarily for the purposes of feedback.  Consequently, your score on the midterm will account for a much smaller portion of your final grade than your score on the final exam.
Final exam Take-home portion:  Take-home final . This is to be turned in at the beginning of the in-class portion of the exam which will be Tuesday December 16 from 4:10 until 7:00.
Course description We will cover roughly the first half of Hatcher's book (chapters 1 and 2).  The intention is to spend the first half of the semester on the fundamental group and covering transformations (and the necessary preparations), and the second half of the semester on homology.
Useful Links For the book: http://www.math.cornell.edu/~hatcher/
For notes from a previous semester:
http://www.math.columbia.edu/~pjlamber/altop/altop.html
Additional info As you likely know by now, talking about mathematics can be invaluable in learning.  I recommend you get together with your classmates and further discuss the concepts introduced in class as well as the homework problems.  That said, it is equally important that you work on the problems yourself...  Struggling with a problem provides insight not available from merely viewing the solution.