Discrete Mathematics Seminar
Fall 2015  Thursday or Friday at 11:00 a.m. in Lytle 136
Thursday, September 24  Dr. Brian Kronenthal
"An Immensely Interesting Integer Sequence"
Can you fill in the blanks in the following sequence of integers? No internet please!
2, 6, 8, 10, 32, 84, 128, 186, _____, _____, 2048, 3172, 8192, 19816, ...
In this talk, we will explain where this sequence comes from, along the way discussing some special polynomials and introducing you to incidence geometry (generalized quadrangles in particular) and algebraically defined graphs. Don't worry, we will also fill in the blanks and give a formula to calculate every term of the sequence!
Friday, September 4 and Friday, September 11  Faculty presentations
Ideas for student research, projects, and independent studies.
Friday, August 28  Organizational meeting
Spring 2015  Alternating Thursdays and Fridays at 11:00 a.m. in Lytle 203
May 1  Wrapup and plans for next semester
April 23  Dr. Rajeev Kumar, College of Business
"A Smart Market of Personal Information."
April 17  Still more discussion on the graceful labeling problem!
April 10 (Lytle 226)  Kenneth Zyma (Masters Thesis Defense)
"Solving MediumScale Instances of the CableTrench Problem Applied to the Proposed LOFAR Super Station in Nancay France."
April 2  Even more discussion on the graceful labeling problem.
March 27  More discussion on the graceful labeling problem.
March 19  The second half of the movie, "Counting from Infinity: Yitang Zhang and the Twin Primes Conjecture."
March 6  The first half of the movie, "Counting from Infinity: Yitang Zhang and the Twin Primes Conjecture."
March 5  Review of a proof that all binary trees can be labeled gracefully.
February 26  Dr. Amy Lu
"Adapting the TeachingLearningBased Optimization Metaheuristic to the Weighted Set Covering Problem."
February 20  The Graceful Labeling Problem (continued!)
February 12  The Graceful Labeling Problem
February 6  The Graceful Labeling Problem and the kEquitable Labeling Problem
January 29  kequitable tree labelings and graceful labeling of trees
January 23  Organizational meeting
Fall 2014  Friday at 11:00 a.m. in Lytle 203
November 20  Dr. Greg Schaper, Computer Science
"A Model of Computation for Teaching and Learning C++."
November 14  Dr. Ge Xia, Department of Computer Science at Lafayette College
"The Stretch Factor of the Delaunay Triangulation is less than 1.998 ."
November 7  FixedParameter Tractable algorithms
October 31  Dr. Yong Zhang, Computer Science
"Introduction to parametrized algorithms and complexity."
October 24 (Lytle 108)  Fun problem session
October 17  Adib Farah, Computer Science
"Introduction to Big Data"
October 10  Open Mic
October 3  ProblemSolving Session
September 26  ProblemSolving Session
September 19  Dr. Eric Landquist
"Making Cryptanalysis Less Cryptic and Fried Eggs on Friday: Cracking early versions of the UberCrypt stream cipher"
In this talk, I'll give a quick overview of last week's talk and then poke around with pseudorandom number generators as a way of practically implementing a onetime pad, the only cryptosystem with perfect security. This provides the motivation for the stream cipher UberCrypt, developed by Mr. Joe Chiarella of Colloid, LLC, based in the Harrisburg area. UberCrypt aims to create a cryptographically secure pseudorandom number generator in order to provide perfect security. I'll describe the essential components of UberCrypt and show how one can crack earlier versions of the cipher via a chosen plaintext attack. The approach uses linear algebra with slightly more sophistication than you would see in a high school algebra course (the only difference is that all arithmetic is performed modulo 2, that is, over the binary field {0, 1}). The current version of UberCrypt has not been cracked as of the writing of this abstract, and so remains an open problem.
September 12  Dr. Eric Landquist
"Making Cryptography Less Cryptic"
In this talk, I will give an overview of cryptography and go over enough mathematical background to help everyone follow next week's talk on how to crack a stream cipher. We'll talk about private key versus public key cryptography, but will focus on different kinds of private key cryptosystems. We'll then get into different kinds of attacks on a cryptosystem and the attributes of a secure cipher.
Spring 2014  Friday at 11:00 a.m. in Lytle 136
April 25  Professor John Botzum
"Don't Stand So Close to Me or: How I Learned to Stop Worrying and Love the Twin Prime Conjecture"
Number theory  the most easily accessible, but possibly the least penetrable of branches of mathematics has intrigued professional and amateur mathematicians for centuries. In honor of the monumental paper published by Yiteng Zhang last April 17th, I will present an introduction to the Twin Prime Conjecture and discuss Zhang's work and the work of Polymath 8a, an international group of renowned mathematicians led by Terrence Tao.
April 14  Combinatorical Problems (continued)
April 11  Combinatorical Problems

The CableTrench Problem

Analyze the game Flow Free  For a board of a given size and a given number of dots, how many different games are there? How many give you a unique solution or no solution?
April 4  Dr. Greg Schaper
ProblemSolving Processes
The key to success isn't knowing what to think, but knowing how to think. Dr. Schaper will give an overview of the process that he uses to solve problems and how different brances of Math, Computer Science, and other disciplines factor into this problemsolving process.
March 28  Dr. Fran Vasko
Dr. Vasko will explain how he has applied the matching problem in graph theory to the problem of determining optimal cuts of rectangular pieces of stock. This work was successfully implemented for Bethlehem Steel and published the Journal of the Operational Research Society in 2000.
March 14  Bitcoin Part 4
Computer Science undergraduates discuss cryptocurrency.
March 7  Bitcoin Part 3
Hacks of the Online Cryptocurrency Exchange Mt. Gox
February 28  Bitcoin Part 2
February 19 (Wednesday)  Dr. Brian Kronenthal
"Two Perspectives on Generalized Quadrangles"
February 7  Bitcoin
Bitcoin is a decentralized digital currency whose security relies on various cryptographic protocols and mathematically and computationally hard problems. It is a fascinating protocol in many regards.
Fall 2013  Alternating Thursdays and Fridays at 11:00 a.m. in Lytle 109
December 6 Dr. Amy Lu
"Homogeneous structures and their reducts."
November 22 Dr. Tony Wong
"A problem on matroid theory by Dominic Welsh."
November 14 Dr. Joshua Goodson
"Orbits of an Action Involving Extraspecial Groups."
November 8 Dr. Eric Landquist
"The Hunt for Primes and Perfection and How You Can Win $3000."
October 31  Dr. Greg Schaper, Computer Science
"Conjecture: (P = NP) and (P ≠ NP)."
October 24  Dr. Ju Zhou
"Pancyclicity of Clawfree Graphs."
October 11  More interesting problems in discrete mathematics
October 3  Dr. Tony Wong
"Some interesting problems in combinatorics."
September 26  Dr. Brian Kronenthal
"Generalized quadrangles, algebraically defined graphs, and permutation polynomials: an introduction."
September 19 Faculty presentations of interesting discrete mathematics (research?) problems
September 12 Dr. Eric Landquist
"What is Discrete Math? Making Discrete Math Less Discreet!"