Math 194: Senior Seminar (Spring 2019)

• Classes: M,W,F 1:20pm - 2:25pm, McHenry 4130.

• Instructor: Robert Boltje;
  Office: McHenry 4190;
  Tel.: 459-5001;
  Email: boltje at ucsc dot edu;
  Office hours:
  • Week 1 and 6-10: M 2:30pm - 3:45pm and W 12:00pm - 1:15pm.
  • Week 1-5 M,W,F 1:15pm - 2:30pm.

• Passing requirement: Active participation in class, satisfactory presentation, and satisfactory paper, to be submitted by Friday, June 7.

• Format of class: The first step in this class is that you pick a topic, either one of your own interest or one from this list of suggested topics. We meet Monday, April 1st, in class and the topics on the list will be introduced. For the rest of Week 1 - 5, you will immerse yourself in your chosen topic by reading relevant literature and preparing a presentation. Presentations will be scheduled from the end of Week 5, Friday, May 3, through the end of Week 10, June 7, during class time, 2 presentations per session, each about 30 minutes. Presentations can be made on the board or via beamer. A paper on your topic, between 10 and 20 pages long, is due at the end of Week 10, Friday, June 7. The paper has to be typed, for instance using LaTeX.

• Please make sure that all source you use in your talk and in your paper are properly cited. This website helps you with questions related to citations. Please also be sure to understand the definition of academic integrity and consequences of academic misconduct.

• Dates and topics of presentation:
  • Friday, May 3:
    • The RSA crypto-system (Gersain Ch.)
    • Group extensions and H² (Nathan Q.)
  • Monday, May 6:
    • Sums of three and four squares (Wesley S.)
    • Fermat's Last Theorem for exponent 4 and some history (Adriana R.)
  • Wednesday, May 8:
    • Representations of finite groups (Nick N.)
    • TBA
  • Friday, May 10:
    • Geometry: Euler's formula for polyhedra and the regular Platonic solids (Jae S.)
  • Monday, May 13:
    • Continued fractions (Eduardo G.)
    • Steiner systems (Logan G.)
  • Wednesday, May 15:
    • SL(2,R) (Timofey P.)
    • Partially ordered sets and the Möbius function (Daniel A.)
  • Friday, May 17:
    • Pell's equation (Alyssa A.)
    • Algebraic and transcendental numbers; Liouville numbers (Johanna N.)
  • Monday, May 20:
    • Sums of two squares (Tianhang L.)
    • Game theory (Zijie L.)
  • Wednesday, May 22:
    • Transcendence of e (Linyin Y.)
    • Transcendence of π (Edwin T.)
  • Friday, May 24:
    • Knot theory (Ryan S.-C.)
    • Pascal's triangle (Saul R.)
  • Wednesday, May 29:
    • Wallpattern classification (Zhidun X.)
    • Derived categories (Shane K.)
  • Friday, May 31:
    • Eisenstein Integers (Jasmine L.)
    • Prime numbers and Tschebyschev's Theorem (Xun X.)
  • Monday, June 3:
    • Symmetry groups of Platonic solids (Yanting H.)
    • TBA

• Topics that are already taken:
  • The RSA crypto-system.
  • Sums of three and of four squares.
  • Steiner systems.
  • Geometry: Euler's formula for polyhedra and the regular Platonic solids.
  • Group extensions and H².
  • Fermat's Last Theorem for exponent 4 plus some history.
  • Continued fractions.
  • Sums of two squares.
  • Partially ordered sets and the Möbius function.
  • Algebraic and transcendental numbers. Liouville numbers.
  • Prime numbers and Tschebyschev's Theorem.
  • Wall pattern classification.
  • Transcendence of e.
  • Knot theory.
  • Transcendence of π.
  • Symmetry groups of Platonic solids