Spring 2018 Seminars
Quadratic Orbits Modulo n: A Familiar Object Viewed from a Different Vantage Point
Rob Sulman, Mathematics, SUNY Oneonta
Friday, 26 January at 3pm in Fitzelle 205
Abstract: We consider repeated iterations of quadratic functions f acting on the ring (Z/nZ, +n , •n). The result is a rich variety of structures, the orbits consisting of cycles as well as whiskers when a given f is not one-to-one. In addition, some of the structure of the group of units of the ring are seen in these graphs. We begin with moduli a power of 2, where inverse-connections (between units) are included in the orbit graphs. We shall see that as the powers increase (for a fixed f ), the corresponding orbit graphs grow in a consistent manner. For the modulus not a power of two, there is a different kind of variety, with a tendency to produce cycles containing various whisker structures. This talk is accessible to students with good calculating ability. The knowledge of the notion of a group would be helpful.
Computation in Algebra
Eran Crockett, Mathematics - Binghamton University
Friday, 23 February at 3pm in Fitzelle 205
Abstract: An example of an algebraic computation you may have done is to use Gaussian elimination to solve a system of linear equations. Assuming basic arithmetic operations take 1 second of time, Gaussian elimination can be completed in roughly n^3 seconds (here n is the maximum of the number of variables and number of equations). After working through this carefully, we show there is another efficient algorithm that answers a similar question for finite groups. Finally, we generalize this question to arbitrary finite algebraic structures and ask when are there efficient solutions.
Quantum Theoretic Reality: the EPR Experiment
David Clark, Mathematics, SUNY New Paltz
Friday, 23 March 2018 at 3 pm in Fitzelle Hall 205
Abstract: Since its inception a century ago, quantum theory has served to accurately predict behavior at the atomic and subatomic levels. In his famous statement, “God does not play dice!”, Albert Einstein objected to its probabilistic formulation, maintaining that there must be a more fundamental theory that would supply the missing information. This lecture will present a famous thought experiment which he and two colleagues devised to establish their point of view. Years after his passing the technology was developed to carry out this experiment and — contrary to Einstein’s expectations — it showed that there can be no more complete theory. This forces us to accept a reality at the subatomic level that is quite different from our human scale experience.
Muhammad Javaheri, Siena College
Friday, April 20 at 3pm
Fall 2017 Seminars
A Bit of Metric Geometry
By Ulysses Alvarez, Binghamton University
Friday, Sept. 8, 2017, at 3 p.m. in Fitzelle Hall 205
Abstract: We will define a notion of curvature in abstract spaces using triangles.
These are a few of my favorite groups
By Matt Zaremsky, SUNY Albany
Friday, Oct. 06, 2017, at 3 p.m. in Fitzelle Hall 205
Abstract: Group theory can be viewed as the study of symmetries of geometric objects, via abstract algebraic tools called “groups.” In the other direction, when handed an abstract group, one might wonder if there is a nice geometric object whose symmetries it describes. This talk will be an introduction to the interplay between geometry and algebra, via some of my favorite groups. Along the way, I will discuss a colorful cast of characters including groups of permutations, groups of braids, matrix groups, a fascinating class of groups with the unfortunately non-descriptive name “Thompson’s groups,” and more. As time permits, I will specifically discuss some of my results on topological finiteness properties of groups.
Investigating Calculus Students’ Conception of Continuity
By Jayleen Wangle, SUNY Oneonta
Friday, December 01, 2017 at 3:15 p.m. in Fitzelle Hall 205 (Note different time)
Continuity is a central yet subtle concept in Calculus I. Yet very few students seem to grasp the nature of continuity. This study uses a mixed methods model to investigate collegiate calculus students' understanding of continuity. I will discuss participant displayed depth of understanding of function, limit, and continuity in terms of the constructs defined by Dubinsky’s (1991) Action-Process-Object-Schema (APOS) theory. A prominent finding was that participants who demonstrated a stronger conception of the function displayed a more in-depth understanding of continuity.