EXPANDING HORIZONS XIX

A project of the Vermont State Mathematics Coalition
Bring college and university mathematicians to your classroom!


DIRECTIONS

  1. Choose a topic which would be of interest to your students.

  2. Contact the presenter directly by phone, fax, e-mail, or postal mail.

  3. Check for prerequisites, if any.

There is no charge for this service. The presenters give of their own time, and they cover their own travel expenses.

For more information contact:

John Devino
Phone: 802-863-5403
E-mail: devino13@comcast.net


George Ashline

Saint Michael’s College

Phone: (802) 654-2434
E-mail: gashline@smcvt.edu

I have much faculty consultant experience in grading AP Calculus Free Response questions, and I would be willing to answer questions that any AP Calculus teachers may have about that.

Correlation Properties and Applications”

Through an activity and examples, we investigate properties of scatter plots and correlation in context, leading to a discussion of the correlation coefficient and challenges inherent in attempting to find causal links between variables.  If time and technology permit, students can explore the online Correlation Guessing Game.

Prerequisite: Familiarity with the concepts of the mean and standard deviation of a variable (also, two-variable statistics calculators are helpful)

An Introduction to Bias and Margin of Error”

Through an initial activity, we explore the potential impact of bias in statistical analysis. We can also consider how bias may arise in survey questions and ways that it can be reduced. In another activity, we can consider different types of error that may impact a survey or experiment and the meaning of margin of error.

Prerequisite: Familiarity with averages, percentages, and surveys

Exponential Functions in Snowflakes, Carpets, and Paper Folding”

Through constructions of initial stages of several fractals, students can explore and represent underlying patterns using exponential functions. Other examples of exponential functions and their properties can be discussed. If time permits, students can play the Chaos Game to “create” the Sierpinski Triangle.

Prerequisite: Familiarity with exponents and functions


James R. Bozeman

Lyndon State College

Phone: (802) 626-6489
Fax: (802) 626-9770
E-mail: james.bozeman@lsc.vsc.edu

"What Your Math Teacher Never Told You"

The talk introduces topics not normally taught in high school which could be. Ex: (a+b)2 = a2 + b2; triangles whose angle sum does not equal 180 degrees; pieces of paper with only one side; bottles with no inside/outside.

Prerequisite: A little algebra and geometry.

"The Mathematics of DNA"

Through hands-on demonstrations and technology, students will discover the formula which describes DNA’s three-dimensional conformation.

Applied Geometry - Nearly Convex Sets and the Shape of Legislative Districts”

In this talk we develop a method for deciding how close a polygonal planar set is to being convex. We introduce 'nearly convex' sets and then 'nicely shaped' legislative districts. Those districts which are not nicely shaped may indicate improper gerrymandering in the redistricting plan.


Joanna Ellis-Monaghan

Saint Michael’s College

Phone: (802) 654-2660
E-mail: jellis-monaghan@smcvt.edu

Willing to do multiple classes at one location.

"Cops and Routers"

Use of graph theory to explore a patrol officer‘s beat, a security officer‘s camera locations, or find route for snowplowing or postal delivery

"Instant Insanity"

A hands-on introduction to mathematical modeling with graph theory.

"Networks and Graphs"

The above model intercommunications, relationships, and conflicts. We will explore a variety of applications from: the internet, the stock market, classroom scheduling, power grids, the Kevin Bacon game, computer chips, social circles, and DNA.

"To Knot or Not"

Is your shoelace really knotted? How can you tell? A gentle introduction to knot theory.

"Geometry in the Real World"

Where does math come from”? We will see some of the new math in network theory being developed today as well as some of the critical applications driving its creation. In particular, we will see new mathematical theory created for DNA origami and tile assembly used for biomolecular computing, nanoelectronics, and cutting-edge medicine. We conclude the talk by showcasing examples of what mathematicians do in real life, and how some of the top jobs use mathematical skills.

Prerequisite: Grade 6 and up
Length of Presentation: 20 min to 2 hours (longer versions may have some hands on activities).


Janel Hanrahan

Lyndon State College

Phone: (802) 626-6370
E-mail: janel.hanrahan@lyndonstate.edu

Mathematics and the Atmosphere”

Our planet is surrounded by a thin fluid envelope of gasses called an atmosphere, and its state at any given time is known as weather. The behavior of this fluid is described by mathematics, and atmospheric science concepts naturally lend themselves to in-class math-based activities at many levels. For this activity, we will measure properties of the air with handheld meteorological instruments to compute the weight of the air in the classroom. Depending on the individual class needs, we will further explore the properties of our fluid atmosphere in the context of algebra, exponentials, graphing, and/or calculus.

Grade level: Middle school or above
Length: 40 – 80 minutes


Karla Karstens

University of Vermont

Phone: (802) 878-7322
E-mail: karla.karstens@uvm.edu

The Mathematics of Sharing: Getting Your Piece of the Pie”

Your family inherits some artifacts that need to be distributed among all the relatives, or you want to divide a pizza among friends. How can you accomplish this so everyone involved gets a fair share? Principles of fair division lead to the solution of this class of problems.

Prerequisite: Middle School level or above
Length 40 – 50 minutes


Gerard T. LaVarnway

Norwich University

Phone: (802) 485-2325
Fax: (802) 485-2333
E-mail: lavarnwa@norwich.edu

Cryptology: The Art and Science of Secret Writing”

An introduction to cryptology will be given. The history of cryptology will be discussed from the time of Caesar to the present. Various ciphers will be demonstrated. The mathematical foundations of ciphers will be discussed.

Prerequisite: Grades 9 – 12
Length 40 – 50 minutes


Michael Olinick

Middlebury College

Phone: (802) 443-5559
Fax: (802) 443-2080
E-mail: molinick@middlebury.edu

"Cryptology: The Mathematics of Making and Breaking Secret Codes"

Mathematics provides the answer

"The Near-Sighted Fly: A Topological View of the Universe"

Length of Presentation: 40 – 80 minutes


Darlene M. Olsen

Norwich University

Phone (802) 485-2875
E-mail: dolsen1@norwich.edu

"Maximizing the Flight Time of a Paper Helicopter"

The mission is to design a paper helicopter that remains aloft the longest when dropped from a certain height. Various combinations of design factors contribute to the flight time.

Response surface methodology (RSM) is a statistical technique that explores optimization through experimentation. Three tools in RSM are design of experiments, multiple regression, and optimization. These tools will be used to explore efficiently the combination of design factors that will improve the performance of the paper helicopter.

Grade Level: 10 – 12
Length 30 – 45 minutes

Mathematical Ties to Tying Neckties”

Did you ever ask the question of how many possible ways there are to tie a necktie? Furthermore, what factors determine an aesthetic tie knot? This problem can be answered using mathematics. We will discover the mathematical ways for describing how to tie necktie knots. We will also classify knots according to their size and shape.

High School level
Length 45 minutes


Rob Poodiack

Norwich University

Phone: (802) 485-2339
E-mail: rpoodiac@norwich.edu

"Paradoxes in Probability"

In certain games, our intuition will tell us one thing, when probability calculations clearly tell us to do another. We will investigate the effect of human nature on probability using: “Let’s Make a Deal” and the Hershey’s Kiss Challenge. If time permits, we’ll engage in a series of three-way duels (“truels”).

Prerequisite: At least Algebra
Length of Presentation: 45 – 75 minutes


Bill Peterson

Middlebury College

Middlebury, Vermont 05753
Phone: (802) 443-3711 Ext. 5417
Fax: (802) 443-8652
E-mail: wpeterso@middlebury.edu

"Benford‘s Law"

In 1838 a physicist named Frank Benford observed that the earlier pages of logarithmic tables showed more wear. There is a message here about the distribution of "naturally occurring" numbers. This property will be explored along with some applications such as detecting fraud in financial statements.

"The Cars and the Goats"

This "game-show" puzzle is a variant of a famous problem in conditional probability. A few years back Marilyn von Savant's solution in her Sunday column generated a lot of irate mail from professional mathematicians-- all of whom turned out to be mistaken. Does the person in the street have any hope of understanding such a problem? I think the answer is yes.

Length of Presentation: 40 to 80 minutes (80 preferred)

"How Many Times Should You Shuffle?"

In 1991 Harvard mathematician Persi Diaconis announced that, to insure that the cards were well mixed, seven was the answer. Simple models of card shuffling will be presented in order to motivate Diaconis’ result, and give an elementary introduction to the mathematics involved in the analysis.

e: The Miniseries”

One cannot study probability theory for long without being struck by the many occurrences of 'e' (or its reciprocal) as the answer to questions that at first glance appear unrelated. In this talk, we will meet four examples. Each can be solved by applying single-variable calculus involving the natural log and exponential function.

Prerequisite: Enrollment in Calculus



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Latest Update:
August 18, 2014
by David Hathaway