Spring 2018 MATH 191 001 SEM

Experimental Courses in Mathematics
001 SEMTuTh 02:00PM - 03:29PMEvans 2John W. Lott26672
UnitsEnrollment Status
Additional Information: 

Title:   Introduction to Mathematical Research via Knot Theory  (Taught by Morgan Weiler under the Supervision of Professor Lott)

Prerequisites:  Familiarity with mathematical proofs at the level of Math 55 and at least one of Math 110 or Math 113 (can be taken concurrently). Math 104 encouraged. Most importantly, curiosity and a willingness to work on open-ended problems!

Description:  Imagine you have tied a knot in a piece of string, then glued the ends of the string together so well that you can't tell it once had ends. When can you untie the string into a circle? How can you be sure, before you've actually untied the string? There is a rich mathematical history of studying the properties of such knots. This class will prepare you to do your own investigations into the theory of knots, culminating in a self-chosen open-ended project. Topics to be covered include representing knots and links, projections, Reidemeister moves, examples of knots, operations on knots, prime decomposition, fibered knots, fundamental group, simplicial homology, numerical invariants, polynomial invariants. Additional topics will be based on student interest, e.g. Khovanov homology, more polynomial invariants, knots in other three-manifolds, Floer homologies and knots, surgery and Kirby calculus, hyperbolic knots and volume, knots in contact and symplectic geometry, arithmetic topology, links of singularities, knots and gauge theory.


Office:   1039 Evans Hall (Morgan Weiler)


Office Hours:    Wednesdays 12-2

Required Text:    The Knot Book by Colin Adams

Recommended Reading:   see course website

Grading:    see course website

Homework:    see course website

Course Webpage:    https://math.berkeley.edu/~morganw/spring_2018/191/191_main.html