# Spring 2015 MATH 191 002 SEM

Section | Days/Time | Location | Instructor | CCN |
---|---|---|---|---|

002 SEM | MWF 11-12P | 5 EVANS | HICKS, J S | 54254 |

Units/Credit | Final Exam Group | Enrollment |
---|---|---|

4 | 8: TUESDAY, MAY 12, 2015 7-10P | Limit:16 Enrolled:10 Waitlist:0 Avail Seats:6 [on 03/22/15] |

**Note:** Also: LOTT, J W

**Office:** 935 Evans**Office Hours:** TBA**Prerequisites:**Ability to write proofs and willingness to work on open-ended problems a must. At least one 100 level math course strongly recommended. Math 55 or other exposure to combinatorics required. **Syllabus:**Historically, the first topological invariants used by mathematicians were from combinatorial construction. More recently, combinatorial topology has been used to attack problems in knot topology, partially ordered sets, polytopes, and matroids. In class we will develop some of the classical combinatorial techniques used in topology. Possible topics covered in this class include planar graphs, colorability, Kuratowski's theorem, simplicial complexes, combinatorial fixed point theorems, simplicial homology, knot theory, braid groups, knot polynomials, fundamental groups, and additional topics based on student's input. Projects include applications in algebraic combinatorics, algebraic topology, computational topology, differential geometry, and knot theory.

Students will apply their knowledge from class to learn advanced methods independently or work on open ended projects. Each student will have considerable latitude in finding problems that fit his or her interest. Students will work in small groups on these problems, with the majority of this work completed outside of class. **Course Webpage:** http://math.berkeley.edu/~jhicks/classes/spring15math191/courseindex.html **Grading:** One short and one long project. Weekly progress reports, an in-class presentation, and a final write-up using LaTeX will be required for each project. Exercises will occasionally be assigned.