Junior Colloquium - Honors Seminar
                         
                   Thursday April 26, 2012, 3:35 pm
                    Ayres 4th floor colloquium room

                          * * * * * * * *

          Pizza will be served before the talk at 3:15 pm

                          All are welcome!

                          * * * * * * * *


Speakers:  Frederick Byrd and Yiyang Sun, Honors Undergraduate Students


                          * * * * * * * *


                         Mr. Frederick Byrd
            Applications of Ultraproducts in Ring Theory

 The concept of an ultraproduct leads to many interesting results
 in ring theory. Using this construction, it is possible to create
 new rings from old ones, which may have entirely different properties
 than the original rings. Though the component rings of an ultraproduct
 may have many restrictive characteristics, their ultraproduct typically
 will not have these characteristics unless it is a field. This can be
 used to generate counterexamples to many conjectures about ring theory
 while still retaining the familiarity of well-known rings. Of particular
 interest is the use of ultraproducts in factorization problems. In this
 thesis we attempt to use an ultrapower to find an example of an element
 with non-unique irreducible factorizations whose lengths are unbounded,
 as well as examine and review many interesting properties of ultrapower
 rings.


                          * * * * * * * *


                           Ms. Yiyang Sun
               Mathematical Analysis of Poker Games

 Poker is an intriguing game which has attracted many scholars' attention
 throughout History. The study of two-person zero-sum poker models with
 independent uniform(0,1) hands goes back to Borel and von Neumann.
 In this presentation we will take a look at three different mathematical
 poker game models. First we will start with von Neumann's simplified two
 player poker model where each player antes the same amount to form the
 initial amount to start the game, then we will change up the betting
 rules to make it a blind bet poker model.  Finally, we will throw in an
 extra variable to capture the other uncertainties in a poker game.

This e-mail list is intended for those who have an interest in mathematics at the University of Tennessee. All current UT math majors and minors should be on this list in order not to miss important announcements. To add or remove yourself from the list, visit listserv.utk.edu.