Margaret Readdy, University of Kentucky |

Counting, q-counting and negative q-counting |

ABSTRACT: Given a mathematical object, one can simply count it. A more sophisticated method of enumeration, called a q-analogue, is to count an object by keeping track of one or more of its mathematical properties. When setting q=1, one returns to the naive enumeration. After reviewing some classical q-analogues, I will discuss the new idea of a negative q-analogue. This will include recent work of Fu, Reiner, Stanton and Thiem on the negative q-binomial coefficient, and, time permitting, new work of Cai and Readdy on negative q-Stirling numbers. |

# Spring 2013

## Friday, April 12 at 1:30pm in the conference room

Categories: Spring 2013

## Friday, April 5 at 2:00pm in Fretwell 120

Categories: Spring 2013

Megan Wawro, Virginia Tech |

A realistic approach to instruction in linear algebra |

ABSTRACT: The purpose of this study is to investigate how students conceptualize span and linear (in)dependence, and to utilize the construct of mathematical activity to provide insight into these conceptualizations. The data under consideration are portions of individual interviews with students in an inquiry-oriented linear algebra course. Through grounded analysis via the framework of concept image (Tall & Vinner, 1991), the range of student conceptions of span and linear (in)dependence are organized into four concept image categories: travel, geometric, vector algebraic, and matrix algebraic. To further illuminate participantsâ€™ conceptions, a framework was developed to classify engagement in types of mathematical activity: defining, proving, relating, example generating, and problem solving. The coordinated analysis of concept image with engagement in mathematical activity facilitates a nuanced and rich characterization of studentsâ€™ connections within and between the concepts of span and linear (in)dependence. The talk will include a brief description of the curricular materials, based on the instructional design theory of Realistic Mathematics Education (Freudenthal, 1991), that were implemented within this linear algebra course. |

## Friday, April 5 at 11:30am in the conference room

Categories: Spring 2013

Dimplekumar Chalishajar, Virginia Military Institute |

Exact controllability of second order impulsive neutral differential inclusion with infinite delay in Banach spaces |

ABSTRACT: Controllability is one of the fundamental tools of applied differential equations and differential inclusions. I will discuss about the exact controllability of second order impulsive neutral differential inclusion with infinite delay in the Banach spaces. Also we will discuss the glitch in the infinite dimension space. Then I will discuss the new notion of control theory called trajectory-controllability, in finite and infinite dimension spaces. Finally the numerical estimations of the same trajectory control problem will be discussed. |