Department of Mathematics
West Chester University
Mathematics Information
Office: Room 101
25 University Avenue
West Chester, PA 19383
Phone (610) 436-2440
Fax (610) 738-0578
Email: Department Chair
Spring 2012 Colloquium/Seminar Schedule
Each Thursday there will be a mathematics seminar (usually in UNA 120 from 3:15-4:15), while colloquium talks will normally be on a Wednesday (usually in UNA 158 from 3:15-4:15).
These seminars/colloquium talks may be by visiting speakers, WCU faculty, or WCU students, and are open to all interested students and faculty.
Send an e-mail to jmclaughl@wcupa.edu, if you would like to be on the e-mail list to receive advance notice of upcoming talks.
Previous Semesters: Fall 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009, Spring 2009, Fall 2008, Spring 2008, Fall 2007, Spring 2007, Fall 2006, Summer 2006, Spring 2006,
Wednesday, February 15th, 2012
3:15 to 4:15PM Anderson 111
Spring 2012 Mathematics Colloquium
John H. Conway (Princeton University)
“The First Field”
We all know one field that contains 0,1,2,..., but, logically, there is an earlier field that is defined as follows. We first fill in the addition table, subject to the condition that before we fill in the entry for a+b, we must have already filled in all entries a'+b and a+b' with a'<a and b'<b. Then, the entry at a+b is to be the least possible number that is consistent with the result's being a part of the addition table of a field.
We then tackle the multiplication table of a field with the given addition. Again, the entries are to be the least possible one's subject to this requirement; this construction produces a very strange field in which 8 is a fifth root of unity. Amazingly, this field actually has practical applications.
John H. Conway is a prolific mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He has also contributed to many branches of recreational mathematics, notably the invention of the cellular automaton called the Game of Life.
Conway is currently Professor of Mathematics and John Von Neumann Professor in Applied and Computational Mathematics at Princeton University. He studied at Cambridge, where he started research under Harold Davenport. He received the Berwick Prize (1971), was elected a Fellow of the Royal Society (1981), was the first recipient of the Pólya Prize (LMS) (1987), won the Nemmers Prize in Mathematics (1998), and received the Leroy P. Steele Prize for Mathematical Exposition (2000) of the American Mathematical Society.
For further information e-mail mfisher@wcupa.edu or sgupta@wcupa.edu.
Tuesday, March 20th, 2012
3:15 to 4:15PM UNA 162
Spring 2012 Mathematics Colloquium
STEFAAN DELCROIX (California State University, Fresno)
"A Generalization of Bertrand's Postulate"
Born and raised in Belgium, Stefaan finished his masters in mathematics at the University of Ghent (in Belgium). He spent the next three years working on his Ph.D. at Michigan State University under the guidance of Prof. Ulrich Meierfrankenfeld. The subject of his thesis was locally finite simple groups of p-type and alternating type. In June 2000, Stefaan finished his Ph.D. at the University of Ghent. For two years, he
worked as a Visiting Assistant Professor at the University of Wyoming in Laramie. Since 2002, Stefaan has worked at California State University, Fresno.
For further information e-mail mfisher@wcupa.edu or sgupta@wcupa.edu.
Wednesday, March 21st, 2012
3:20 to 4:15PM UNA 155
Spring 2012 Mathematics Colloquium
Shiv Gupta (West Chester University)
“On Euler's Proof of Fermat's Last Theorem For Exponent Three”
We shall discuss some aspects of Euler's proof of Fermat's Last Theorem for exponent three.
This talk will be suitable for students who have taken (or currently taking) a course on Theory of
Numbers (Mat 414/514).
For further information e-mail mfisher@wcupa.edu or sgupta@wcupa.edu
Thursday, March 29th, 2012
3:15 to 4:15PM UNA 162
Spring 2012 Mathematics Seminar
Jimmy Mc Laughlin (West Chester University)
"Hybrid Proofs of the q-Binomial Theorem and other q-series Identities."
The proof of a q-series identity, whether a series-to-series identity such as the second iterate of Heine’s transformation, a basic hypergeometric summation formula such as the q-Binomial Theorem or one of the Rogers-Ramanujan identities, generally falls into one of two broad camps.
In the one camp, there are a variety of analytic methods.
In the other camp there are a variety of combinatorial or bijective proofs, the simplest of course being conjugation of the Ferrer’s diagram for a partition.
In this series of talks we use a “hybrid” method to prove a number of basic hypergeometric identities. The proofs are “hybrid” in the sense that we use partition arguments to prove a restricted version of the theorem, and then use analytic methods (in the form of the Identity Theorem) to prove the full version.
Wednesday, April 11th, 2012
3:20 to 4:15PM UNA 155
Spring 2012 Mathematics Colloquium
Sergei Sergeev (University of Birmingham, UK.)
Abstract: Tropical mathematics emerged in 1960's as a linear encoding of some problems in discrete
optimization and scheduling. In a nutshell, it studies "spaces" over the max-plus algebra, which is the set of
real numbers where taking maximum plays the role of addition, and addition plays the role of multiplication.
In the tropical mathematics, negative infinity plays the role of zero, hence any real number is "positive"
in the tropical sense. Hence, there are connections with nonnegative linear algebra (in particular, Perron-
Frobenius theory), and convex geometry. To this end, tropical spaces can be viewed as an analogue of convex cones, and many results of convex analysis have their tropical analogues, which will be reviewed.
Tropical linear two-sided systems Ax = Bx, where matrix-vector multiplication is defined using the
tropical arithmetics, are the algebraic encoding of tropical convex cones. Geometrically, such systems represent the tropical convex cones as intersection of tropical halfspaces. Methods for finding a solution to such two-sided systems stem from combinatorial game theory, more specifically, from the theory of deterministic mean-payoff games. We will also touch upon some problems like the tropical linear programming that can be viewed as parametric extension of two-sided systems, and give rise to parametric extensions of mean-payoff games.
All are welcome to join for tea in Students Lounge after the talk.
Wednesday, April 18th, 2012
3:20 to 4:15PM UNA 155
Spring 2012 Mathematics Colloquium
Hal Switkay (West Chester University)
"The Sensible Communication of Abstract Information"
We consider the engagement of the senses in the process of communicating and learning the abstractions of mathematics. Examples are provided from the history of mathematics continuing through current developments, including Markov processes, analytic geometry, statistics, decision theory, 24-dimensional geometry, and the musical representation of groups.
This talk should be easily accessible to undergraduates.
Hal M. Switkay earned his Ph.D. in mathematics at Lehigh University in the study of set theory. After graduation, his interests shifted towards symmetry, lattices, groups, and higher-dimensional geometry. He has taught mathematics, from remedial to advanced, has done public speaking, is a musician and composer, and has earned certification as a teacher of Tai Chi Easy and as a practitioner of reiki and Thai massage. He is currently enrolled in West Chester Universitys graduate certificate program in applied statistics. His business card lists the following interests: mathematics; music; philosophy; health and wellness; and syncretic
panendeism.
All are welcome to join for tea in Students Lounge after the talk.
Monday, April 23rd, 2012
3:15 to 4:15PM Anderson 103
Spring 2012 Mathematics Colloquium
Keith Devlin (Stanford University)
“Leonardo Fibonacci and Steve Jobs”
The first personal computing revolution took place not in Silicon Valley in the 1980s but in Pisa in the 13th Century. The medieval counterpart to Steve Jobs was a young Italian called Leonardo, better known today by the nickname Fibonacci. Thanks to a recently discovered manuscript in a library in Florence, the story of how this little known genius came to launch the modern commercial world can now be told.
Based on Devlin’s latest book The Man of Numbers: Fibonacci’s Arithmetical Revolution (Walker & Co, July 2011) and his co-published companion e-book Leonardo and Steve: The Young Genius Who Beat Apple to Market by 800 Years.
Keith Devlin is a mathematician at Stanford University in California. He is a co-founder and Executive Director of the university's H-STAR institute, a co-founder of the Stanford Media X research network, and a Senior Researcher at CSLI. He has written 31 books and over 80 published research articles. His books have been awarded the Pythagoras Prize and the Peano Prize, and his writing has earned him the Carl Sagan Award, and the Joint Policy Board for Mathematics Communications Award. In 2003, he was recognized by the California State Assembly for his "innovative work and longtime service in the field of mathematics and its relation to logic and linguistics." He is "the Math Guy" on National Public Radio.
He is a World Economic Forum Fellow and a Fellow of the American Association for the Advancement of Science. His current research is focused on the use of different media to teach and communicate mathematics to diverse audiences. He also works on the design of information/reasoning systems for intelligence analysis. Other research interests include: theory of information, models of reasoning, applications of mathematical techniques in the study of communication, and mathematical cognition. He writes a monthly column for the Mathematical Association of America, "Devlin's Angle”.
For further information e-mail mfisher@wcupa.edu or sgupta@wcupa.edu
Friday, April 27th, 2012
2:00 to 3:00PM UNA 158
Spring 2012 Mathematics Colloquium
ELWYN BERLEKAMP University of California, Berkeley
“Combinatorial Games: Hackenbush and Go”
This talk will review the rudiments of combinatorial game theory [1] as exemplified by a game called Hackenbush. Positions are seen to have values, which are sums of numbers and infinitesimals, such that the winner depends on how the total value compares with zero.
We then discuss how refinements of this theory have been applied to the classical Asian board game called Go. The most important tool is the "cooling operator" [2], which maps combinatorial games into other combinatorial games. In the first application, many late stage Go endgame positions [3] are shown to be combinatorial games which, when cooled by 1, often reduce to familiar numbers and infinitesimals. Combinatorial game theory then enables its practitioner to win the endgame by one point. In the second application, Nakamura[4] has shown that liberties can also be viewed as combinatorial games which become familiar numbers and infinitesimals when cooled by 2. In a large class of interesting positions, this approach identifies the move(s), if any, which win the capturing race.
Although not prerequisite to this talk, more details can be found in these references:
[1] Berlekamp, Conway, and Guy: Winning Ways, Chap 1
[2] Berlekamp, Conway, and Guy: Winning Ways, Chap 6
[3] Berlekamp and Wolfe: Mathematical Go
[4] Nakamura, in Games of No Chance, vol 3
Elwyn Berlekamp was an undergraduate at MIT; while there, he was a Putnam Fellow (1961). Professor Berlekamp completed his bachelor's and master's degrees in electrical engineering in 1962. Continuing his studies at MIT, he finished his Ph.D. in electrical engineering in 1964; his advisors were Claude Shannon, Robert G. Gallager, Peter Elias and John Wozencraft. Berlekamp taught at the University of California, Berkeley from 1964 until 1966, when he became a researcher at Bell Labs. In 1971, Berlekamp returned to Berkeley where, as of 2010, he is a Professor of the Graduate School.
He is a member of the National Academy of Engineering (1977) and the National Academy of Sciences (1999). He was elected a Fellow of the American Academy of Arts and Sciences in 1996. He received in 1991 the IEEE Richard W. Hamming Medal, and in 1998 the Golden Jubilee Award for Technological Innovation from the IEEE Information Theory Society.
Berlekamp is one of the inventors of the Welch-Berlekamp and Berlekamp-Massey algorithms, which are used to implement Reed-Solomon error correction. In the mid-1980s, he was president of Cyclotomics, Inc., a corporation that developed error-correcting code technology. With John Horton Conway and Richard K. Guy, he co-authored Winning Ways for your Mathematical Plays, leading to his recognition as one of the founders of combinatorial game theory. He has studied various games, including Fox and Geese and other fox games, dots and boxes, and, especially, Go. With David Wolfe, Berlekamp co-authored the book Mathematical Go, which describes methods for analyzing certain classes of Go endgames.
For further information e-mail mfisher@wcupa.edu or sgupta@wcupa.edu
Note: Talks will be added to the schedule throughout the semester. Check back for updates.
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