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**

### Fall 2017

## 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.

## 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, 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, 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.