Borough of Manhattan Community College
The City University of New York
199 Chambers St.
New York, NY 10007
Organizers: Margaret H Dean, Claire Wladis, and Marcos Zyman.
March 1, 2011.
Jaewoo Lee (BMCC, CUNY)
Title: Erdos-Turan conjecture and representation function of additive bases
Abstract: Given a subset of nonnegative integers, representation function tells us how many times a given integer can be written as a sum of two elements of the set. Erdos and Turan conjectured that the number of this representation is unbounded when the set is a basis, i.e. any nonnegative integer can be written as a sum of two elements of the set. This became one of the main problems in additive combinatorics. I will discuss some results related to this conjecture as well as some results in other settings such as integers instead of nonnegative integers and some groups.
March 22, 2011.
Harry Khamis (Wright State University)
Title: The Multigraph for Loglinear Models
Abstract: In the last 30 years graph theory has been used, with great success, to analyze and interpret a statistical model called the loglinear model (LLM). In short, the goal of a LLM is to identify the structural associations among a set of categorical variables, a task that can be daunting as the number of variables increases. In a landmark 1980 paper Markov fields and chordal graphs were used to analyze LLMs, and since then many researchers have cultivated this marriage between graph theory and statistics. In this talk, a crash course will be given on the LLM and then the generator multigraph will be used to analyze and interpret the LLM. Actual client data sets will be used to illustrate the techniques.
Tuesday, April 12, 2011
Jason Samuels (BMCC, CUNY)
Title: The Use of Visualization and Technology in Calculus Instruction
Abstract: This research was inspired by a history of student difficulties in calculus, and innovation in response to those difficulties. The goals of the research were fourfold. First, to design a mathlet for students to explore local linearity. Second, to redesign the curriculum of first semester calculus around the use of technology, an emphasis on visualization, and the use of local linearity to introduce the concept of the derivative, while delaying formal limits until later in the semester. Third, to design a framework to assess learning outcomes on the derivative. Fourth, to conduct a study to assess the impact of the course on the learning and attitudes of students. The study also aimed to assess the impact of learner characteristics, the role of technology, and the role of visualization, as they related to learning and attitude outcomes.
The development and justification of the local linearity mathlet, the redesigned first semester calculus curriculum and the framework to assess derivative proficiency are reported. A mathlet is a computer application typically accessed over the internet which allows exploration of a specific mathematical concept. Students in this study developed a robust knowledge of the derivative as measured by the framework. Overall they demonstrated facility with stating definitions, finding the derivative and tangent lines, determining non-differentiability, and optimization. They demonstrated these proficiencies in multiple representations. Prior knowledge in rate and slope as well as proficiency translating between mathematical representations were significant determinants of eventual calculus proficiency. Spatial ability and prior knowledge of function were weaker predictors. There was clear evidence that the use of mathlets and graphs had a positive impact on student learning, and students were very positive about their use in this course. They experienced minimal changes in attitude regarding mathematics and technology in general, except for visually oriented students, who had very positive changes in attitude. The students in the experimental group were significantly more positive about their experiences using technology to learn calculus than students studying calculus with a traditional curriculum and labs using Maple which were not discussed in lecture.
Tuesday, May 3, 2011
Yibao Xu (BMCC, CUNY)
Title: Mathematical Content of Newly-Published Bamboo Strips of the Qin Dynasty
Abstract: In December of 2007, the Yuelu Academy of Changsha, China, purchased a collection of bamboo strips from an antiques dealer in Hong Kong. Among these strips are more than 220 whose contents are clearly mathematical. Due to the fact that one strip in the group mentions the thirty-fifth year of the reign of the first Emperor of Qin, the dating of these mathematical strips is believed to be no later than 212 BCE. At the moment, nothing is known about the archaeological provenance or the condition of the bamboo strips when they were first discovered, nor is it known exactly when or from where they were unearthed. But because these strips are apparently at least twenty-five years earlier than those of the previously earliest-known mathematical work from ancient China, the Suan shu shu (Book on Numbers and Computations), found in a Western Han tomb in December-January of 1983-1984, the Yuelu strips are extremely important primary sources for studying Chinese mathematics of the Qin and Han periods (221BCE-220CE). Based on recently released reports as well as several published papers by researchers at the Yuelu Academy and other institutions, this talk will consider the nature of these strips, analyze their contents, and explore their relations with both the Suan shu shu and the well-known Chinese classic text, Jiuzhang suanshu (Art of Mathematics in Nine Chapters).
In past semesters, the colloquium met on some Wednesdays in Room N529. Tea was at 2 and talks began around 2:30.Fall of 2010
David S. Lazarus
Title: Some History of the Four Color Problem and Some Questions
Abstract: I will cover some of the history of the Four Color Problem, including Kempe's 1879 ''proof'', Heawood's 1890 refutation, Appel and Haken's (computer intensive) 1976 proof and Seymour's 1995 (also computer intensive) refinement. I will also ask whether another sort of proof is possible.
Along the way I will define graphs, planar graphs, vertex 4-colorings of graphs and Kempe-interchanges . I will show how Kempe-interchanges can be used to ''reduce configurations'', the key idea for both Kempe's failed proof and Appel and Haken's successful proof. The talk will not assume any extensive specialized knowledge.
Eva Antonakos, Bronx Community College, CUNY
Title: A multi-agent LP realizing Justified Common Knowledge.
Abstract: LP, Logic of Proofs (Artemov '94) is a system in which terms t:F can be interpreted as t is evidence for or a proof of F. We'll consider one multi-agent version LP_n(LP) and a corresponding epistemic logic S4_n^J with the special common knowledge operator J. This will be a general talk suitable to any mathematical background.
Date: Dec. 1
Title: he relationship between visual reasoning skills and geometric knowledge
Abstract: Prof. Karrass's research is particularly interested in learning about the differences in visual reasoning between experts and novices as they recognize, interpret, or explain "visual proofs."
Title: Magnetic Field Profiles for Action Potential Propagation in Excitable Tissue
Abstract: The talk will give a brief description on the development of a model equation for action potential propagation in cardiac and nerve tissue and the existance of solutions, followed by a discussion of numerical results of the propagating action potential and associated magnetic field profiles.
Title: p-Capacity Z^n and Zeta function
Abstract: The aim of this talk is to present some concepts and techniques from p-potential theory Riemannian manifolds adapted to finite and infinite graphs. Namely, we will define p-capacity based on a similar concept in continuous settings, which will be used to classify the graphs as p-hyperbolic and p-parabolic. The notions of p-hyperbolicity and p-parabolicity are useful in handling the existence or nonexistence of solutions in the class of p-Dirichlet functions to the Poisson equation of p-Laplacian. In a previous talk we have shown how to get explicit formulas for the computation of the p-capacity of the lattices Z^n and the homogenous trees T_d.
In this talk, we will focus specifically on p-hyperbolic lattices Z^n and highlight the computation of their p-capacity in terms of the Zeta function.
Title: IA-automorphisms of groups with constant upper central series
Let G be any group satisfying the property that Z_1=Z_2 in the upper central series. It will be shown that the subgroup of Aut(G) generated by the inner automorphisms together with the central automorphisms is a direct product of these two subgroups.
I will also offer necessary and sufficient conditions for IA(G) to equal the direct product of the inner automorphisms with those central automorphisms that lie in IA(G), and will apply these results to certain finitely generated center-by-metabelian groups. (joint work with M. Zyman and M. Bonanome)
Title: Rotation distance and Thompson's groups
Abstract: The rotation distance between two trees is the number of "steps" required to transform one tree into the other. This question has important applications in computer science search algorithms, where where an efficient method is needed to turn "stringy" trees into relatively "bushy" and balanced ones. However, currently there is no known polynomial time algorithm for computing rotation distance exactly. Computing rotation distance between two trees is equivalent to computing the distance between two elements of one of the Thompson-Stein groups, because elements of these groups can be represented by tree-pair diagrams. This talk will introduce the Thompson-Stein groups and their metric, and explain how the representation of elements of these groups by tree-pair diagrams provides a good method of attack for developing efficient algorithms for computing rotation distance in binary trees.
Title: Number theory and geometryAbstract: We will review several recent results in combinatorial and additive number theory, revealing interesting connections between combinatorial and additive number theory, geometry and geometric group theory.
Title: IA-automorphisms of various classes of groups
Abstract: The IA-automorphisms of a group G consist of those automorphisms that induce the identity on G abelianized. I plan to discuss some aspects of the IA-automorphisms of the following classes of groups: nilpotent, metabelian, groups with constant upper central series, and center-by-metabelian. In particuar, If G is a group with constant upper central series, I will offer necessary and sufficient conditions for its IA-automorphisms to equal a direct product of subgroups of AutG. (The second part of this talk is joint work with M.H. Dean).
mzyman (at) bmcc (dot) cuny (dot) edu
last updated: 3/11