Welcome to the wonderful world of undergraduate algebraic topology!
Topology, more or less, is the study of spaces, or more specifically spaces where you can reasonably talk
about continuity and convergence. Topological spaces can be quite crazy, but we will usually consider fairly
nice spaces (like "manifolds" and "CW-complexes"). Some of the most basic questions we can ask are what do these
things look like? How many are there? How can we tell two of them apart? What interesting properties do they have?
Algebraic topology is a set of tools we can use to try to answer some of these questions. In particular, we
will associate algebraic things --- like numbers, vector spaces, polynomials and groups --- to topological spaces.
With these algebraic invariants we will be able to do some amazing things.
Initially we will consider some questions that seem rather basic, like "how can you tell the difference
between the surface of a ball and a doughnut?" and "how can you tell if a closed loop is knotted?", but
we will see that in answering these questions we learn surprising things, like "if you want a non-zero
vector field tangent to the boundary of a region in three space then that region better, more or less, look
like a doughnut" and "at any given moment there are two antipodal points on the earth that have the same
temperature and humidity".
Final Exam:
The final exam will be Wenesday, May 3rd from 8:00-10:50 in Skiles 240. Here is a practice exam.
Notes:
- Notes from Jan 31 to Feb 7.
- Notes from Feb 14 to Feb 26.
- Notes from Feb 21 to Feb 28.
- Notes from March 2 to March 14.
- Notes from March 16 to March 28.
- Notes from March 30 to April 4.
- Notes from April 4 to April 11.
- Notes from April 11 to April 20.
Course Information:
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