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Educational

Juggling Mathematics & Magic

Speaker: 
Ronald Graham
Date: 
Thu, Sep 17, 2015
Location: 
PIMS, University of Calgary
Conference: 
Louise and Richard K. Guy Lecture Series
Abstract: 
The popular Richard & Louise Guy lecture series celebrates the joy of discovery and wonder in mathematics for everyone. Indeed, the lecture series was a 90th birthday present from Louise Guy to Richard in recognition of his love of mathematics and his desire to share his passion with the world. Richard Guy is the author of over 100 publications including works in combinatorial game theory, number theory and graph theory. He strives to make mathematics accessible to all. Dr. Ronald Graham, Chief Scientist at the California Institute for Telecommunications and Information Technology and the Irwin and Joan Jacobs Professor in Computer Science at UC San Diego. Dr. Ronald Graham, Chief Scientist at the California Institute for Telecommunications and Information Technology and the Irwin and Joan Jacobs Professor in Computer Science at UC San Diego, will the present the lecture, Juggling Mathematics & Magic. Dr. Graham’s talk will demonstrate some of the surprising connections between the mystery of magic, the art of juggling, and the some interesting ideas from mathematics. Ronald Graham, the Irwin and Joan Jacobs Professor in Computer Science and Engineering at UC San Diego (and an accomplished trampolinist and juggler), demonstrates some of the surprising connections between the mystery of magic, the art of juggling, and some interesting ideas from mathematics. The lecture is intended for a general audience.

A topological look at the vector (cross) product in three dimensions

Speaker: 
Peter Zvengrowski
Date: 
Sat, May 9, 2015
Location: 
PIMS, University of Lethbridge
Conference: 
Alberta Mathematics Dialog
Abstract: 
The vector product (or cross product) of two vectors in 3-dimensional real space $\mathbb{R}^3$ is a standard item covered in most every text in calculus, advanced calculus, and vector calculus, as well as in many physics and linear algebra texts. Most of these texts add a remark (or “warning”) that this vector product is available only in 3-dimensional space. In this talk we shall start with some of the early history, in the nineteenth century, of the vector product, and in particular its relation to quaternions. Then we shall show that in fact the 3-dimensional vector product is notthe only one, indeed the Swiss mathematician Beno Eckmann (a frequent visitor to Alberta) discovered a vector product in 7-dimensional space in 1942. Further- more, by about 1960 deep advances in topology implied that there were no further vector products in any other dimension. We shall also, following Eckmann, talk about the generalization to r-fold vector products for $r\geq 1$ (the familiar vector product is a 2-fold vector product), and give the complete results for which dimensions n and for which $r$ these can exist. In the above work it is clear that the spheres $S^3$, $S^7$ play a special role (as well as their “little cousin” $S^1$). In the last part of the talk we will briefly discuss how these special spheres also play a major part in the recent solution of the Kervaire conjecture by Hill, Hopkins, and Ravenel, as well as their relation to the author’s own research on the span of smooth manifolds.

It’s All in the Follow Through – what research in math education says ... and doesn’t say

Speaker: 
Rob Craigen
Date: 
Sat, May 9, 2015
Location: 
PIMS, University of Lethbridge
Conference: 
Alberta Mathematics Dialog
Abstract: 
We’ll be examining a few classic cases of how educational research has been handled that explain a lot about how we got where we are in public school math education today.

Robustness of Design: A Survey

Speaker: 
Doug Wiens
Date: 
Fri, May 8, 2015
Location: 
PIMS, University of Lethbridge
Conference: 
Alberta Mathematics Dialog
Abstract: 

When an experiment is conducted for purposes which include fitting a particular model to the data, then the ’optimal’ experimental design is highly dependent upon the model assumptions - linearity of the response function, independence and homoscedasticity of the errors, etc. When these assumptions are violated the design can be far from optimal, and so a more robust approach is called for. We should seek a design which behaves reasonably well over a large class of plausible models. I will review the progress which has been made on such problems, in a variety of experimental and modelling scenarios - prediction, extrapolation, discrimination, survey sampling, dose-response, etc

Measurement, Mathematics and Information Technology

Speaker: 
M. Ram Murty
Date: 
Fri, May 8, 2015
Location: 
PIMS, University of Lethbridge
Conference: 
Alberta Mathematics Dialog
Abstract: 

In this talk, we will highlight the importance of measurement, discuss what can and cannot be measured. Focusing on the measurement of position, importance, and shape, we illustrate by discussing the mathematics behind, GPS, Google and laser surgery. The talk will be accessible to a wide audience.

A Triangle has Eight Vertices (but only one center)

Speaker: 
Richard Guy
Date: 
Fri, May 8, 2015
Location: 
PIMS, University of Lethbridge
Conference: 
Alberta Mathematics Dialog
Abstract: 
Quadration regards a triangle as an orthocentric quadrangle. Twinning is an involution between orthocentres and circumcentres. Together with variations of Conway’s Extraversion, these give rise to symmetric sets of points, lines and circles. There are eight vertices, which are also both orthocentres and circumcentres. Twelve edges share six midpoints, which, with six diagonal points, lie on the 50-point circle, better known as the 9-point circle. There are 32 circles which touch three edges and also touch the 50-point circle. 32 Gergonne points, when joined to their respective touch-centres, give sets of four segments which concur in eight deLongchamps points, which, with the eight centroids, form two harmonic ranges with the ortho- and circum-centres on each of the four Euler lines. Corresponding points on the eight circumcircles generate pairs of parallel Simson-Wallace lines, each containing six feet of perpendiculars. In three symmetrical positions these coincide, with twelve feet on one line. In the three orthogonal positions they are pairs of parallel tangents to the 50-point circle, forming the Steiner Star of David. This three-symmetry is shared with the 144 Morley triangles which are all homothetic. Time does not allow investigation of the 256 Malfatti configurations, whose 256 radpoints probably lie in fours on 64 guylines, eight through each of the eight vertices.

Native American Mathematics

Speaker: 
Edward Doolittle
Date: 
Thu, Sep 18, 2014
Location: 
PIMS, University of Calgary
Abstract: 

One sometimes hears that the indigenous peoples of the Americas are for some reason not predisposed to be able to do mathematics. This belief is surprising, since the mathematical traditions of the Western Hemisphere prior to European contact were already rich and extensive. This talk will focus on some of those traditions, primarily Central American but with some information about mathematical traditions in Algonkian cultures such as the Blackfoot.  Almost all of this talk will be accessible to any interested listener, with perhaps five minutes in the middle using a small amount of very elementary number theory. Along the way any listener who has ever eaten an 18 Rabbits granola bar will learn why doing so celebrates indigenous mathematics. 

 

ABOUT THE RICHARD AND LOUISE GUY LECTURE SERIES:
The Richard & Louise Guy lecture series celebrates the joy of discovery and wonder in mathematics for everyone. Indeed, the lecture series was a 90th birthday present from Louise Guy to Richard in recognition of his love of mathematics and his desire to share his passion with the world. Richard Guy is the author of over 100 publications including works in combinatorial game theory, number theory and graph theory. He strives to make mathematics accessible to all. The other contributions to the lecture series have been made by Elwyn Berlekamp (2006), John Conway (2007), Richard Nowakowski (2008), William Pulleyblank (2009), Erik Demaine (2010), Noam Elkies (2011), Ravi Vakil (2012) and Carl Pomerance (2013).

Emerging Aboriginal Scholars

Speaker: 
Debra Martel
Date: 
Wed, May 22, 2013
Location: 
University of British Columbia, Vancouver, Canada
Conference: 
Emerging Aboriginal Scholars Summer Camp
Abstract: 
This five week summer camp is for students currently attending grades 9 to 12. The main purpose of this camp is to help students with their academics and for them to get work experience at the university. Students take 90 minutes of math and English every day and three days a week they will be working with a faculty member in the area of their choice. Students will get $100 a week for 7.5 hours of work experience. The summer camp takes place at UBC, and students will take classes at PIMS and the Long House. Last year we had students working with the nuclear accelerator, and working at labs in the physics and chemistry departments, among other opportunities. For more information on the program see Emerging Aboriginal Scholars Program.

Indigenous Knowledge in STEM Education

Speaker: 
Ron Eglash
Date: 
Fri, Mar 8, 2013
Location: 
PIMS, University of British Columbia
Conference: 
Special Lecture
Abstract: 
Computing with Culture From fractals in African architecture to algorithms in First Nations beadwork, simulations of indigenous designs reveal complex concepts and practices that can be mapped onto analogous principles in math, science and computing. Applications for this work include outreach to K-12 students as well as contributions to sustainable development.
Ron Eglash
Dr Ron Eglash is an American cyberneticist, university professor, and author widely known for his work in the field of ethnomathematics, which aims to study the diverse relationships between math and culture.
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