Geneseo Mathematics Colloquium Schedule
Wednesday, April 16 2:30-3:20pm
Kristin Camenga, Houghton College
The Numerical Range of a Matrix: Theme and Variations
The numerical range of a matrix is a set of numbers defined by how the matrix acts on the unit sphere. Most frequently, we work with matrices with complex numbers as entries and the resulting numerical range is a set of complex numbers, which can be visually represented on the complex plane. The resulting numerical range is convex and contains the eigenvalues of the matrix. Based on this foundation, we can ask many different questions. Given a specific type of matrix, what shapes of numerical range result? Which transformations of the matrix leave the numerical range the same? What happens if we use different fields for the matrix entries? What if we associate a set of numbers to a pair of matrices instead of just one? In this talk we will define numerical range precisely and look at some of the different questions that can be explored. Previous experience with linear algebra is recommended, but all definitions will be reviewed.
Tuesday, February 18, 2:45 - 3:35pm
Alden Edson, Western Michigan University
Problem-Based Instruction in a Digital World: Technology Affordances for Task Design and Enactment
Digital instructional resources are rapidly replacing print materials offering a promising direction for education at all levels. In this interactive session, we will examine pedagogical and tool features of a highly interactive digital instructional unit focusing on binomial distributions and statistical inference. This experience will be connected to a summary of how tasks originating in print curriculum materials can be adapted for highly interactive digital instructional materials and their affordances for student learning. We will next examine more closely the additional affordances of the tool features of the digital materials.
Thursday, February 20, 2:30 - 3:20pm
Michael Pawlikowski, Depew High School and University at Buffalo
Promoting Mathematical Discourse
This presentation includes key ideas from my doctoral research and how I use this research to enhance my mathematics instruction. These key ideas engage how small groups of students can work together to solve problems. Using a topic from calculus I will demonstrate how math educators can create a lesson designed to promote mathematical talk, argumentation, and reasoning. This demonstration will also provide mathematics majors an opportunity to see how innovative problem posing can lead to an increased conceptual understanding of mathematics.