# Seminar Series

Unless otherwise noted, the Spring Semester Seminars will be held on the third and fourth Thursday of the month from 1:00pm - 2:00pm in UBC 192.

## Upcoming Seminars for Spring Semester

**April 16, 2015; 1:00pm in UBC 192: Eleina Aceves (Fresno State University)**

**Title: **From Knot Theory to Pseudoknots

**Abstract: **In knot theory, mathematicians study mathematical knots which are circles embedded in a three dimensional space. Because of this research, we have found several connections between knots and objects in the real world. Sometimes, however, when observing an object, we may not have all of the information about the object. For example, we may not know which strand lies over the other at a crossing if we have a blurry picture of the object. Thus, the theory of pseudoknots was created to approach this problem. Pseudoknots are mathematical knots where crossing information is missing at some of the crossings. This presentation explores the concept of pseudoknots, the ability to determine if a given pseudoknot represents a trivial circle or a nontrivial knot, and invariants that can be used to distinguish between pseudoknots.

## Past Seminars for Spring Semester

**March 9, 2015; 9:00am in PB 390: Jenna Tague (Ohio State University)**

**Title: **Conceptions of Rate of Change: An Exploratory Study

**Abstract: **Jenna Tague's dissertation focuses on mapping a trajectory of how students understand rate of change from middle school through post-calculus undergraduate. This presentation will offer an analysis of 191 responses by 7^{th} and 8^{th} grade students and 167 responses by 5^{th} grade students to two rate of change tasks and sources that may have contributed to the types of responses they produced. One task involved describing change as depicted graphically. The second task required the students to discern rate of change within a pattern context. The findings indicated that the participants viewed rate as discrete and categorical in graphic context and tented to produce patterns with additive growth. This may be due to their early exposure to graphs as tools for organizing categorical data in elementary school and a lack of experience with patterns that represent multiplicative growth.

**March 11, 2015; 9:00am in PB 390: Ravi Somayajulu (Eastern Illinois University)**

**Title: **Preservice Teachers' Noticing and Analysis of Students' Geometric Work

**Abstract: **Dr. Somayajulu’s talk will consist of two parts. The first part will focus on the results of his dissertation research in which he traced changes in pre-service secondary teachers' evaluation of school learners' dilemmas associated with Geometry. This was traced through case based scenarios of student work as pre-post technique for cohort data analysis. Results indicted there was a mismatch between what the program had intended to nurture and what preservice teachers seemingly gained from those experiences. These findings inspired the second line of inquiry, currently ongoing, focusing on what preservice teachers' actually notice when they consider school learners' mathematical work. Dr. Somayajulu's work is geared towards building a developmental theory of teacher growth that offer an explanation for why certain elements of teacher education programs may go unnoticed by novice teachers.

**February 18, 2015; 9:00am in PB 390: Khang Tran (Truman State University)**

**Title: **Zero Distribution of Sequences of Polynomials.

**Abstract: **We introduce an approach which shows that the zeros of various sequences of polynomials lie on fixed curves on the complex plane. In a simple application of this approach, we prove that the zeros of the polynomial, obtained from the expansion of the binomial polynomial by only keeping the terms whose exponents are in the same congruence class modulus *n*, lie on the *n* radial rays emanating from the origin. In another application, we study the complex zeros of a sequence of polynomials satisfying a three-term recurrence of degree *n*. In particular, given any two polynomials *A(z)* and *B(z)* with complex coefficients, we form a sequence of polynomials defined recursively by taking *A(z)* times the previous polynomial in the sequence plus *B(z)* times the *n*-th polynomial before that. We prove that with appropriate initial conditions, the zeros of all the large degree polynomials in this sequence lie exactly on a curve whose equation is given explicitly by the two polynomials *A(z)* and *B(z)*. The zeros will be dense on this curve when the degree approaches infinity. At the end of the talk, we provide a list of experimental conjectures to which this approach may apply. The author appreciates any possible extension of this list from the audience.

**If you need a disability-related accommodation or wheelchair access information, please contact the Mathematics Department at 559.278.2992 or e-mail** math.office@csufresno.edu. **Requests should be made at least one week in advance of the event.**

## Archived Seminars

• AY2014/15 • AY2013/14 • AY2012/13 • AY2011/12

• AY2010/11 • AY2009/10 • AY2008/09 • AY2007/08

• AY2006/07