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High School Visitation

The Department of Mathematics 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 Bob Mann at (309) 298-2037 or you may email Dr. Mann at RR-Mann@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 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.
  


• Combinatorics and Probability
  David Helm
  Description: The presentation will show how the combinations formula can be effectively used to solve probability problems involving drawing balls from an urn or cards from a deck. Some interesting probability questions regarding tossing of dice, matching birthdays, or guessing what is behind a door will also be addressed.
  Appropriate for Algebra II, Precalculus/Trigonometry, Calculus, Statistics.
  Equipment to be provided by the high school: overhead projector and chalkboard.
  


• The Golden Ratio
  David Helm
  Description: The speaker will derive the number phi and show how it relates to design in nature. Various interesting aspects of the Golden Ratio will be explored.
  Appropriate for students in advanced algebra or precalculus (although some of the content seems geometric, students need to have had some work with radicals).
  Equipment to be provided by the high school: chalkboard.
  


• Practical Application of Plane Geometry Constructions
  Larry Kight
  Description: We will apply Torricelli's construction to find a Steiner point. It will require one to copy a line segment, construct a perpendicular bisector of a line segment, and circumscribe a circle about 3 points. I will explain what a network is and why Steiner's point is so important in finding a minimum network.
  Appropriate for Geometry, Algebra II, Precalculus/Trigonometry, Calculus (freshman to seniors).
  Equipment to be provided by the high school: each student would need a compass, protractor, and ruler with cm and mm increments. Western Illinois University can provide if not available at high school.
  


• Conic Sections
  Marko Kranjc
  Description: Conic sections are curves that one gets by intersecting a double cone by a plane. They have some interesting properties and applications, most well known in astronomy and optics (Kepler's Laws, parabolic lenses and mirrors). We will learn how a gardener would make an elliptic flower bed and why a light shining from a focus of an ellipse reflects from the ellipse to the other focus. Some spatial geometry will be needed to arrive to the first item.
  Appropriate for Algebra I, Algebra II, Geometry, Precalculus/Trigonometry, Calculus, Statistics, junior/senior level.
  


• 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/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.
  


• From Launching Calculus Textbooks in Space to Black Holes
  Boris Petracovici
  Description: We will try to answer some questions from Physics using mathematical tools.
  1. How much energy does it take to lift an object up off the surface of the Earth to a distance s from the surface?
  2. If a student would like to shoot up his/her calculus book so that it escapes the Earth's gravity and never comes back, what should the initial velocity be?
  And finally:
  3. What is a black hole really?
  Appropriate for Algebra II, Precalculus/Trigonometry, Calculus, Statistics, juniors/seniors (some introductory Physics recommended, but not required).
  Equipment to be provided by the high school: overhead projector.
  


• First Order Logic - a Logic for Mathematics, Computer Science, and Applications
  Rumen Dimitrov
  Description: We will give an interactive approach to first order logic - its language, synthax, and world semantics with specific examples. We will use the "Tarski's World" software package to go through examples of sentences and their semantics. We will introduce worlds as models of theories.
  Appropriate for Geometry, Calculus, juniors/seniors.
  Equipment to be provided by the high school: none.

Department of Mathematics
476 Morgan Hall | 1 University Circle
Macomb, IL 61455 | mathematics@wiu.edu
Phone: 309/298-1054 | Fax: 309/298-1857