The Department of Mathematics at Western Michigan University presents colloquiua.

**Time: 4 p.m. (time may vary)**

**Place: 6625 Everett Tower**

**Fall Semester 2017**

**Spring Semester 2018**

### Spring 2018

## thursday, mar. 22

**The Bernstein polynomial basis: a centennial retrospective **presented by Riday Rarouki, Ph.D., University of California Davis

Refreshments served at 3:50 p.m.

Abstract: The Bernstein polynomial basis, introduced in 1912 to provide a constructive proof of the Weierstrass approximation theorem, attracted little applied interest until the advent of computer-aided geometric design in the 1960s. Through the work of Casteljau at Citroen and Bezier at Renault, the remarkable properties and elegant algorithms associated with this basis became more widely appreciated. This talk will provide a brief perspective on the historical evolution of the Bernstein form and the current state of associated algorithms and applications.

## Thursday, feb. 1

**Colorful coverings of polytopes: the hidden topological truth behind different colorful phenomena **presented by Shira Zerbib, Ph.D., University of Michigan

Refreshments served at 3:50 p.m.

Abstract: The topological KKMS Theorem is a powerful extension of Brouwer's Fixed-Point Theorem, and was proved by Shapley in 1973 in the context of game theory. We prove a colorful and polytopal generalization of the KKMS Theorem, and show that our theorem implies some seemingly unrelated results in discrete geometry and combinatorics involving colorful settings. This is joint work with Florian Frick.

### Fall 2017

## Thursday, dec. 14

**Broadening mathematical understanding of the trigonometric functions **presented by Haw-Yaw Shy, National Changhua University (Taiwan)

Refreshments served at 3:50 p.m.

Abstract: This talk discusses a professional development project for 150 middle school teachers in Taiwan aimed at improving the quality of teaching and learning through the process of broadening teachers' understanding of the mathematics they are teaching. We specifically look at developing the fundamental properties of the six trigonometric functions, including how the derivatives are obtained through activities based on visualization and movement.

## Thursday, Oct. 26

**Gamma and factorial in the Monthly **presented by Rob Corless, Western University (Ontario)

Refreshments served at 3:50 p.m.

Abstract: Since its inception in the 19th century, the American Mathematical Monthly has published over fifty papers on the Gamma function or equivalently the factorial function. Over half of these were on Stirling's formula. We survey these papers, which include a Chauvenet prizewinning paper by Philip J. Davis and a paper by the Fields medalist Manjul Bhargava, and highlight some features in common. We also identify some surprising gaps and attempt to fill them, especially on the "inverse Gamma function". This is joint work with the late Jonathan M. Borwein.

## Friday, oct. 13

**Road to Rio, a tale of teaching, athletics and disability **presented by John Kusku, Oakland Schools

Abstract: John Kusko, Distinguished Department of Mathematics Alumni, a 2016 Paralympic silver medalist, will share the story of his life as a Paralympic athlete and a teacher of mathematics. In addition to discussing the Olympics and Paralympics and his sport, goalball, Kusku will also examine the everyday challenges and affordances of having a visual impairment as an athlete, teacher, father, musician, and student. Specifically, he will address teaching mathematics as a person who is blind, concentrating on topics including career-focused education, accessible technology, and teaching children who are blind. Kusku is grateful to be returning to his Alma Mater to receive a Distinguished Alumni Award from the Department of Mathematics. He graduated from Western Michigan University in 2007 and 2009 with his Bachelor's and Master's degrees, respectively, and often thinks fondly on his time spent in Everett and Rood.

Special time: 3 p.m.

## Thursday, Oct. 12

**Strategies for greater integration of active learning in undergraduate calculus courses **presented by David Webb, Ph.D., University of Colorado

Refreshments served at 3:50 p.m.

Abstract: We survey active learning strategies in play at various universities in pre-calculus through calculus 2 (P2C2) courses. Research has demonstrated how students involved in active learning techniques can learn more effectively in their classes, resulting in lower DFW rates, increased persistence in subsequent courses, and improved dispositions towards mathematics. By integrating more active learning into instruction, students are encouraged to articulate conjectures and communicate their reasoning in the process of solving mathematics problems. From these exemplars we will discuss related design principles for active learning, and strategies for infusing active learning into P2C2 courses.

## Thursday, Sept. 28

**Designing systems for continuously improving university mathematics courses **presented by James Hiebert, Ph.D., University of Delaware

Refreshments served at 3:50 p.m.

Abstract: There are no quick fixes to improving the quality of mathematics teaching. With the hindsight of 15 years of steady work, the mathematics education group at the University of Delaware can identify several (difficult) decisions that have been critical to improving its mathematics courses for preservice teachers. A number of these decisions were not predicted based on the research literature or the culture of teaching in the U.S. This talk will explicate these decisions and show the long-term benefits of relentlessly pursuing incremental, evidence-based improvements in mathematics instruction. Small improvements that last can accumulate to yield significant changes over time.

## thursday, SEPT. 14

**The Petersen graph and the Icosahedron **presented by Igor Dolgachev, Ph.D., University of Michigan

Refreshments served at 3:50 p.m.

Abstract: This talk will discuss relationships between two fascinating objects: the regular Icosahedron and the Petersen graph. The Icosahedron has been known since antiquity. The Petersen graph is familiar as a useful example in graph theory; it is less known that it is realized in projective geometry via a Desargues configuration of 10 lines and 10 points, and as such it is related to the theory of algebraic surfaces and Cremona transformations. Each has a large symmetry group: the symmetric group S_{5 }in the case of the Petersen graph and the alternating group A_{5} in the case of the Icasahedron. The same symmetry of other objects in algebraic and hyperbolic geometry relates them to the Petersen graph and the Icosahedron.