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Mathematics Department

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Pi Mu Epsilon Conference

Peter Engel Science Center

Saint John's University

Judy Walker received her undergraduate degree from the University of Michigan and both her master's degree and her Ph.D. from the University of Illinois at Urbana-Champaign. She has been at the University of Nebraska Lincoln since 1996, and currently serves as Aaron Douglas Professor and Chair of the Department of Mathematics there. She spent much of the fall 2011 semester as a Visiting Professor at Centre Interfacultaire Bernoulli, EPFL in Lausanne, Switzerland as part of a special program in her research area of coding theory. Among her invited lectures are the AMS-MAA Joint Invited Address at the 2013 MathFest in Hartford, CT and a plenary lecture at the 2015 SIAM Conference on Applied Algebraic Geometry in Daejeon, South Korea. Walker is a co-founder of the Nebraska Conference for Undergraduate Women in Mathematics and has served as an elected member of the AWM Executive Committee and the AMS Council. She has won several teaching awards, including the Deborah and Franklin Tepper Haimo Award from the MAA and the Outstanding Teaching and Instructional Creativity Award from the University of Nebraska system. She served as the MAA's Polya Lecturer for 2009-2011 and received the 2016 Louise Hay Award for Contributions to Mathematics Education. She is a Fellow of the American Mathematical Society.

Whenever information is transmitted or stored, errors are bound to occur. It is the goal of coding theory to find efficient ways of adding redundancy to the information so that these errors can be corrected. The mathematical study of error-correcting codes began with Claude Shannon's groundbreaking 1948 paper, in which he proved probabilistically that good codes exist. The subsequent challenge has been to actually find or design these good codes; this problem has occupied the minds of many mathematicians, computer scientists and electrical engineers ever since. In addressing Shannon's challenge, many areas of mathematics have been drawn upon, including several that are not typically thought of as "applied math". This talk will give a mathematical tour through coding theory, focusing especially on the wide range of areas such as algebraic geometry, number theory, and graph theory that have played a crucial role in the development of this field.

As each of three people enter a room, either a red hat or a white hat (with the color chosen randomly and independently) is placed on his head. Each person can see the other hats but not his own. They can discuss strategy before they enter the room, but after they've entered no communication is allowed. Once they've looked at the other hats, the players must simultaneously guess their own hat colors or pass. The group shares a prize if at least one person guesses correctly and no one guesses incorrectly. The "obvious" strategy (one person guesses "Red" no matter what and the other two pass) yields a 50% success rate. Is there a better strategy? What if there are more than three players? We will use the theory of error-correcting codes to find the optimal strategy for this game in many situations.

**Upcoming Conference Speakers**

- 2016 Judy Walker

**Former Conference Speakers**

- 2015 Ami Radunskaya
- 2014 Hal Schenck
- 2013 Annalisa Crannell (Videos: Friday's Lecture, Saturday's Lecture)
- 2012 Kenneth Millett
- 2011 William Dunham
- 2010 Claudia Neuhauser
- 2009 Joe Gallian
- 2008 (Conference cancelled due to weather)
- 2007 Carlos Castillo-Chavez
- 2006 Edward Burger
- 2005 Jennifer Quinn
- 2004 Frank Farris
- 2003 Colin Adams
- 2002 David Bressoud
- 2001 Underwood Dudley
- 2000 Sam Patterson
- 1999 Robert L. Devaney
- 1998 Richard Guy
- 1997 Ron Graham
- 1996 Frank Morgan
- 1995 Carl Pomerance
- 1994 Philip Straffin
- 1993 Thomas Banchoff
- 1992 Judith Grabiner
- 1991 Raymond Smullyan
- 1990 Joan Hutchinson
- 1989 Richard Askey
- 1988 Sherman Stein
- 1987 Reuben Hersh
- 1986 Peter Hilton
- 1985 I.N. Herstein
- 1984 Ruth Struik
- 1983 Joan Fisher Box, George Box
- 1982 Alfred Willcox (in conjunction with the North Central Section Meeting)
- 1981 Doris Schattschneider, Leonard Gillman, Don Koehler
- 1980 Mary Ellen Rudin
- 1979 Paul Halmos

**Lectures will be geared toward a general audience**

*Funding for travel to SJU Pi Mu Epsilon conference is provided by NSF grant DMS‐0846477 through the MAA Regional Undergraduate Mathematics Conferences program.*