MA327: Low Dimensional Topology
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Winter Quarter |
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Instructor: Professor SteveCarlson
Time: Period 7 MTRF
Prerequisite: MA 113 or permission of instructor
Credits: 4
How
do mathematicians visualize objects in 4-dimensional space?
Are Moebius bands and Klein Bottles just novelties,
or do they have some real mathematical significance?
What is topology? How is it related to other areas of mathematics? And what
are its applications?
What is the essential mathematical nature of continuity?
If any of these questions intrigue you, then maybe this course is for you! It will offer an investigation of basic notions of topology, especially manifolds.
Topics will include:
- intuitive ideas of point-set topology
- one-, two- and three-dimensional manifolds
- compact surfaces and their classification
- the Euler characteristic
- patterns and complexes on surfaces
- coloring maps on surfaces
- embedding graphs in surfaces
- knots and knot invariants
- modern day applications of topology
This course is recommended for any student with an interest in mathematics (not just math majors). It should be fun and informative! Below are some interesting websites related to parts of the course. Enjoy!
- Here’s cool site on the
Klein bottle from the
- Here’s a site that contains a timeless classic work motivating understanding of higher dimensions -- "must reading" for the break before taking a topology course: http://www.geom.umn.edu/~banchoff/Flatland/
- An introduction to the broad field of topology is available through the Rose-Hulman Logan Library link to Encyclopedia Brittanica. See http://www.search.eb.com/eb/article-9108691
Any questions? Just send me mail. carlson@rose-hulman.edu