**Congratulations, PSG!**

**Come and be a part of the Problem Solving Group (PSG) group.**

The Problem Solving Group (PSG) at Ashland University's Math and Computer Science Department, submitted 4 problems last year. They received acknowledgement for 3 correct solutions and their solution to Problem 5332 from School Science and Mathematics website (April 2015) was selected to be published.

**Congratulations, PSG!**

**Come and be a part of the Problem Solving Group (PSG) group.**

Pick’s Theorem offers an elegant formula that
allows us to find the area of a lattice polygon – whether it be as simple as
the former or as convoluted as the latter – in a matter of seconds. The theorem
obviates the need to trudge through the tedious set of calculations that would
otherwise be required to find the area of a polygon, and all we have to do is
count the lattice points it encompasses.

Sounds easy enough,
right?

Although the result itself is straightforward,
proving that it holds for all polygons is anything but. Drawing from three
classic papers on topics closely related to Pick’s Theorem, this presentation
will take a deep dive into the intriguing foundations upon which Pick’s famous
result is built.

The Problem Solving Group's first meeting is Tuesday, September 22, at 7:00 p.m. in Patterson 324. PSG will meet Bi-Weekly at 7:00 p.m. in Patterson 324. Call Dr. Chris Swanson for details.

Quiz!!

1. How
many ways can you paint your fingernails with three different colors?

2. How
many ways are there to color a disk divided into three equal parts with one of
two colors per section?

3. How
many ways can you color an icosahedron with one of *n* colors per face?

Asking simple questions that are
difficult to answer is common in mathematics. The first question seems pretty
straight forward. Yet the second
requires a bit more understanding, one of basic geometry, group theory and
combinatorics.

Using Burnside’s Lemma, sometimes, called
the orbit-counting theorem, we will explore this question and others like it,
considering
the much needed rotation of an object,
looking at it from all sides.

By solving a much simpler problem, we will
build to the question of the icosahedron, showing with the proper ‘tools’, the
problem-solving approach needed is not that hard after all.

Bargh, B. Chase, J. Wright, M. (2014). Colorful Symmetries.*
Math Horizons,* April 2014, pp 14-17

In the board game *RISK*, players attempt to conquer the world by capturing all territories on the board, with battle outcomes determined by dice rolls. Let A be the number of attacking armies and D be the number of defending armies in two adjacent territories. This talk will present the probability the defending territory will be captured and the expected number of armies lost by the attacking territory in the capture.

**Math 450 Senior Seminar Presents**
**"Evaluating Risk in the Board Game ***Risk*"
**by: Dr. Christopher N. Swanson**
**Tuesday, September 15, 1:40 p.m.**
**in Patterson 301**

Subscribe to:
Posts (Atom)