Spring 2011

General Information | Textbook | Problem Sets | Links

**Instructor:**
Jeremy Martin

623 Snow, 864-7114

**KU course number:** 69608

**Meeting times:**
MWF, 1:00-1:50 PM, 456 Snow **(note change)**

**Office hours:** Tuesdays 1:00-2:00, Wednesdays 2:00-3:00, or by appointment

Discussion group on Google (requires membership)

**Prerequisites:** Officially, "Math 820 or permission of instructor."
Not all of the material covered in Math 820 will be necessary for Math 821,
but you should know what a topological space is and what "continuous", "connected", and "compact" mean
outside the context of metric spaces.
You should also be comfortable working with vector spaces and groups --- i.e., you should
have taken or be taking Math 790/791, and preferably Math 830 as well.

The main textbook is *Algebraic Topology* by Allen Hatcher
(Cambridge U. Press, 2002).
The book is available as a free download from the author's
website. If you choose to use the downloaded version, *do not
print out a copy on the department printer!* You can also
buy a paperback copy (e.g., from Cambridge
U. Press or
Amazon) for roughly $30.

Other books that may be helpful:

- J. Munkres,
*Topology: A First Course*(a.k.a. "the red book") (Prentice-Hall, 1975). An excellent reference for basic topology. If you are comfortable with the material in the first three chapters of Munkres and you know some algebra, then you should be ready to take Math 821. - G. Bredon,
*Topology and Geometry*(Springer, 1993; reprinted 1997). I don't know this book well first-hand, but it has a good reputation. The topics covered and level of exposition are comparable to Hatcher's book. - J. Munkres,
*Elements of Algebraic Topology*(Addison-Wesley, 1984). Again, I don't know this book well first-hand, but Munkres' basic book is so good that this one probably is too. - W. Massey,
*Algebraic Topology: An Introduction*(Springer, 1977). A standard book with a focus on covering spaces and the fundamental group; does not discuss homology. - M.J. Greenberg and J.R. Harper,
*Algebraic Topology: A First Course*(Benjamin/Cummings, 1981). A standard textbook with a fairly abstract, algebraic treatment. - E. Spanier,
*Algebraic Topology*(Springer, 1966; reprinted 1981). Ditto.

Problem sets will be posted on Fridays, starting 1/28/11, and
will be due on the following second Monday (i.e., ten days later)
at 5:00 PM.
*You must submit typed solutions*, preferably using LaTeX.
Hand-drawn figures are acceptable.
You can either submit hard copies or send me the PDF version by e-mail.

# | Assigned date | Due date | LaTeX source | PDF document | Figures (if any) |
---|---|---|---|---|---|

1 | Fri 1/28/11 | Mon 2/7/11 | hw1.tex | hw1.pdf | |

2 | Fri 2/11/11 | Mon 2/21/11 | hw2.tex | hw2.pdf | |

3 | Fri 2/25/11 | Mon 3/7/11 | hw3.tex | hw3.pdf | rotategraph.eps |

4 | Fri 3/11/11 | Mon 3/28/11 | hw4.tex | hw4.pdf | dunce.eps | torus-decomp.eps |

5 | Fri 4/1/11 | Wed 4/13/11 | hw5.tex | hw5.pdf | |

6 | Fri 4/15/11 | Wed 4/27/11 | hw6.tex | hw6.pdf | |

7 | Fri 4/29/11 | Wed 5/11/11 | hw7.tex | hw7.pdf |

- I'll post the LaTeX source files for at least some problem sets. They will all rely on this header file, which you may use in your own problem sets (updated 2/17/11; should be backwards-compatible)
- KU Math Department LaTeX page (includes getting-started links and information about TeXMaker and TeXShop workspaces)
- TeX resources from the American Mathematical Society
- LaTeX symbols (short list, contains most standard symbols)
- The Great Big List of LaTeX Symbols (long list, lots of fancy stuff)
- The Comprehensive LaTeX Symbol List (
**extremely**long list; probably more symbols than anyone would ever need!) - Xy-pic, a standard package for typesetting commutative diagrams. See in particular the user's guide. I will post examples eventually.

- Writing in the Sciences (UNC Chapel Hill Writing Center)
*A Guide to Writing Mathematics*and Mathematical Writing Checklist (Prof. Kevin Lee, Purdue)

- Jeremy's home page
- KU Mathematics Department
- KU Registrar
- KU Bookstore
- KU policies on academic misconduct
- KU Office of Disability Resources

- KU Math Department LaTeX page
- Sage (free, open-source mathematical software)
- Acrobat Reader (to read PDF files on this page)

Last updated Fri 4/29/11 4:00 PM CST