Geneseo Mathematics Colloquium Schedule
Wednesday, February 13, 2:30 - 3:20pm
Gillian Galle, University of New Hampshire
The Trouble with Trigonometry
Students that enroll in algebra-based physics courses for life science may be less prepared mathematically than their counterparts in the engineering, physical science, or mathematics majors. This means it can be especially difficult for them to develop conceptual understandings of equations that possess both physical and mathematical interpretations within the same context. Based on such students’ answers to a particular question on simple harmonic motion equations, this study undertook to systematically probe the following questions: What is the range of students’ initial knowledge with respect to trigonometry? Is reviewing trigonometric concepts valuable and/or necessary? Can students see the trigonometric equations describing oscillations as conveying an idea, in addition to being a tool to get "the answer?"
In this talk I focus on the efforts of my colleague and I to answer this last question through the design and timely implementation of a trigonometric intervention and motivational activity meant to help these students reason through the underlying connections between trigonometry and modeling simple harmonic motion. In addition to discussing the research the intervention was based on, I will address the development of our motivational activity, our finding that students can learn to see trigonometric equations describing oscillations as conveying an idea, and what implications this may have for the way we address this topic in both high school and undergraduate physics courses.
Friday, February 15, 3:30 - 4:20pm
Valentina Postelnicu, Arizona State University
The Functional Thinking in Mathematics Education: A Cultural Perspective
One of the most important ideas that influenced the mathematics education of the last century is the idea of educating functional thinking, particularly a kinematic-functional thinking. Bringing students up to functional thinking has proved to be a difficult task for mathematics educators. We examine the current state of mathematics education with respect to functional thinking by considering different curricular approaches to functions in the United States and other parts of the world. We closely look to one problem and the way it may appear in different cultural settings. We focus on issues related to the covariational approach to functions, the rise of digital technologies, and the need for symbolic representations.
Thursday, February 21, 4:00 - 4:50pm
Amanda Beeson, University of Rochester
Did Escher know what an elliptic curve is?
We will give a naïve introduction to elliptic curves. Then we will discuss whether the 20th century Dutch artist M.C. Escher knew what an elliptic curve is. Along the way, we will discover many wonderful things about his piece called "Print Gallery". This talk will be enjoyable if you remember how to add and multiply, but some paper-folding skills never hurt. This talk is based on work of H. Lenstra.
Monday, February 25, 4:00 - 4:50pm
Carlos Castillo-Garsow, Kansas State University
Chunky and smooth images of change
Students have well documented difficulties with graphs. In this talk, I discuss recent and current research that investigates connections between these difficulties and student difficulties in forming images of change, the impact that these student difficulties have on more advanced mathematical reasoning at the secondary and undergraduate level, the damage that developing these difficulties can do to the preparation of teachers, and the potential role of technology in developing solutions to these systemic and persistent problems.
Wednesday, February 27, 3:30 - 4:20pm
May Mei, University of California, Irvine
Attack of the Fractals!
You may not know it, but you're surrounded by fractals! They are all around you and even inside of you. In this talk, we will explore the prevalence of fractal structure in the natural world and in mathematics. Then we will construct the standard Cantor set and show you how you can construct your own fractals.
Friday, March 1, 3:45 - 4:35pm
Emma Norbrothen, North Carolina State University
Number Systems Base p
Rational numbers can construct the real numbers by using the absolute value norm. Under different norms, rationals can construct different types of numbers. In particular, the p-norm evaluates how much a prime, p, is a factor in a given rational. We will explore some consequences of the p-norm and what kind of numbers it creates from the rationals
Friday, April 5 2:30 - 3:30pm
Sue McMillen, Buffalo State
President, Association of Mathematics Teachers of New York State (AMTNYS)
Explore interesting properties of the Fibonacci sequence. Look for patterns and make conjectures. Learn about connections between matrices and the Fibonacci sequence. Bring your calculator. If you would like to know more about graduate studies at Buffalo State or about AMTNYS, please stay around after the talk to converse with Dr. McMillen.
Thursday, April 25 2:30 - 3:30pm
Arunima Ray, Rice University
SUNY Geneseo, Class of 2009
A friendly introduction to knots in three and four dimensions
If you've ever worn sneakers or a necktie, or ever been a boy scout, you know a lot about knots. Knot theory is also an exciting (and young) field of mathematics. We will start from scratch to define and discuss some basic concepts about knots in three dimensions, such as how to quantify the 'knottedness' of a knot and how to tell if two knots which look different are secretly the same. We will also see how a four dimensional equivalence relation reveals a simple and elegant algebraic structure within the set of knots.
This talk will be very visual with lots of pictures and will be accessible to students at all levels.