Mark Pullins (CU Boulder) Linear Algebraic Groups: From Spaces to Groups
Wed, Oct. 2 5pm (Math 350)
Harrison Stalvey (CU Boulder) Epistemology, Psychology, and the Concept of Function
In the past two talks, we have explored the Zariski topology and projective space. In this talk, we will begin in familiar territory and review the Zariski topology and varieties. Then, we will introduce linear algebraic groups from a (hopefully) more intuitive perspective and explore the wonderful (and mildly surprising) structural properties gifted from the Zariski topology. Please note that the past two talks are in no way required!
Epistemology is the philosophy of knowledge. What is knowledge? Where does it come from? How does it develop? Two particular epistemologies are constructionism and constructivism, which view knowledge as a construction, not a discovery, even if it is influenced by social factors. Under the assumption that knowledge is constructed, it is natural to wonder about the psychology behind learning. We will explore some epistemology and psychology as they pertain to a concept central to mathematics: the function. In particular, we will survey the history of the concept as an illustration of constructionism. We will also discuss a particular constructivist learning theory that has been used to describe how an understanding of mathematics can develop in the mind of the learner. Then we will apply this learning theory to the concept of function. This talk will conclude with examples of various avenues of research in mathematics education and what that research might look like.