## Department of Mathematics and Philosophy

### High School Visitation

The Department of Mathematics and Philosophy is pleased to offer presentations for high school students. These presentations are designed to show some interesting aspect of the use of mathematics. To arrange for a presentation, please complete the presentation request form and return it to us by mail, fax, or email. The appropriate faculty member will contact you directly to schedule a mutually convenient date. Responses or questions may be directed to Kim Hartweg at (309) 298-2313 or you may email Dr. Hartweg at KK-Hartweg@wiu.edu.

Presentations are offered for the topics listed below. Suggested subject matter levels are included for each presentation. Discussion of other topics of special interest to classes that do not appear on the list might also be designed.

• The Mathematics of Poker: Odds, Outs and Oscillations
J. Thomas Blackford

Description: Over the past three years, poker has enjoyed a dramatic surge in popularity. Each day tens of thousands of people play poker at home, in casinos and on the internet. Yet few players are aware of the mathematical theory that lies behind winning strategies. In particular, many fail to see poker for what it is: a long term game.

In this talk we will review the basic concepts of probability, including counting techniques, odds and expected value. We will then apply these concepts to the game of Texas Hold'em. After reviewing the rules of the game, we will see how pot odds, implied odds and position affect how one plays his or her cards. In particular, we will see how to analyze starting hands. I will also mention an alternative way to look at variance and "bad beats".

Appropriate for Algebra II, Precalculus/Trigonometry, Calculus, Statistics, junior or senior level.

Equipment to be provided by the high school: overhead projector.

• Sequences, Sums, and Starbursts
Bob Mann

Description: The sums of some common sequences will be investigated using a numeric, geometric, and algebraic representation. The emphasis will be on mathematical thinking and the connections between different patterns and depictions.

Appropriate for Algebra II, Precalculus/Trigonometry, Calculus, Statistics, junior or senior level.

Equipment to be provided by the high school: screen and LCD projector for laptop computer. (Speaker can provide, if necessary.)

• Some Really Cool Things Happening in Pascal's Triangle
Jim Olsen

Description: Pascal's Triangle is full of really cool relationships. It is a prime example of the beauty of mathematics. Pascal's Triangle is very rich in connections, problem solving, reasoning, and representations. For a plethora of mathematics problems (applied or otherwise), if one does Polya's fourth problem-solving step of look-back-and-extend, the analysis often leads one to Pascal's Triangle. Three characteristics that Pascal's Triangle exhibits are that it is:

1. simple - can be thought about by students from elementary school through graduate school,
2. conceptual - it shows ideas and relationships between ideas (as opposed to being procedural),
3. rich - related to numerous problems and numerous areas of mathematics.

The combination of these characteristics lead to its beauty and its power for helping students of all ages gain a deeper understanding of fundamental ideas of mathematics. In this presentation we will explore eleven characteristics of Pascal's Triangle as a way of looking at the beauty and cool relationships it holds.

Appropriate for juniors and seniors, or freshman and sophomore honors students.

Equipment to be provided by the high school: screen (will bring own computer and projector) and two tables.

• Make it True or Make it False - It is Your Turn
Rumen Dimitrov

Description: The truth or falsity of a statement depends on the world (the situation) to which this statement is applied. But what is a world? Can you construct different worlds in which all, some, or none of the statements from a given set are true? In this talk we will use the interactive and intuitive approach of the "Tarski's World" software package to find an answer to these questions.

• You Can Learn a Lot From a Note Card
Bob Mann

Description: The seemingly simple but deceptively versatile note card can be used to explore interesting and challenging mathematics' problems that integrate the Common Core Standards and the Mathematical Practices. Students will investigate different mathematical concepts including fractions, perimeter, area, volume, proportions, number sense, and algebra.

Appropriate for Algebra I or higher.

• Dividing the Goods
John Chisholm

Description: When Mom gets tired of the twins fighting over the last piece of cake, she can tell them to work out a fair division themselves, using the time-honored method of having one twin cut the cake and letting the other twin have first choice among the two pieces. But it wasn't until the twentieth century that mathematicians successfully devised "fair division" methods for dividing 'goods' among more than two people.

This talk will address such questions as: What should it mean to say a division is "fair"? Are there different possible meanings? What happens if we want to divide an inheritance consisting of several pieces of furniture? (We don't want to be cutting any furniture into pieces!) We will conclude with a recently discovered "envy-free" method for this situation.

• Most Interesting Curves Are Not Graphs of Function
Boris Petracovici

Description: High school students are familiar mostly with curves that are graphs of functions (that pass the vertical line test). However, intricate curves and patterns do not exhibit this property. In this talk we will explore other ways to describe curves using implicit equations, parametric equations and polar equations. Many of these curves can be graphed using a standard TI 83/84 calculator. However, some limitations exist, and a more  powerful computer software such as Maple or Mathematica will be used.

Appropriate for Precalculus/Trigonometry, Calculus, junior and senior level.

• Interesting Properties of the Archimedean Solids
Jim Olsen

Description: I will start a brief overview of the five Platonic solids (cube, tetrahedron, etc.). The Archimdean polyhedra, tend to be reclusive and rather mind-boggling, due to the fact there are 13 solids in the group, each with a long, bizarre name. However, they are "not too bad" if we look at the structure and properties.

In this session I will show the structure of the Archimedean solids, show how they all can be derived nicely from the Platonic solids, make sense of the naming conventions, and look at some interesting properties. We will look at some interesting counting methods for counting vertices, edges, and faces (other than the standard Euler's formula). I will use computer graphics and animations. I will bring some models and build some models.