Vermont State Mathematics Coalition

EXPANDING HORIZONS XVIII

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

 

“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.

 


 

Priscilla Bremser

Middlebury College

Phone:       (802) 443-5555

E-mail:      Bremser@middlebury.edu

 

William R. Hamilton and the Quaternions

 

In 1843, while strolling across a bridge in Dublin, Hamilton had a flash of insight and discovered the Quaternions, a new number system he had been searching for 15 years. What did he hope his discovery would do, why did it fail, and why was it nevertheless a major contribution in mathematical history?

 

Prerequisites:  None

Length 40 or 80 minutes

 

Symmetry

 

What do wallpaper patterns, prints of M.C. Escher, and molecular structure have to do with mathematics? We will discuss what symmetry means to mathematicians.

 

“The Mathematics of Change Ringing”

 

Change Ringing is the art of ringing a set of bells in specific sequences.

It started in England, where it is still popular, and is practiced in

various places around the world. In this session we will discuss the

history of this art as well as the mathematical principles involved.

Students will get a chance to practice on handbells. This presentation is

appropriate for middle school and high school.

 


 

Joanna Ellis-Monaghan

Saint Michael’s College

Phone:       (802) 654-2660

E-mail:      jellis-monaghan@smcvt.edu


"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).

Willing to do multiple classes at one location.

 


 

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

 


 

Daisy McCoy

Lyndon State College

Phone:       (802) 626-6260

E-mail:      daisy.mccoy@lsc.vsc.edu

 

"The Magic of Nine"

 

There are a number of special properties of the number 9. This session will look at these properties and other properties of our number system such as "casting out nines" and doing number tricks.

 

Prerequisite: Can be adapted to various levels.

Length of Presentation: 40 – 80 minutes

 

"Math Like an Egyptian"

Four thousand years ago the Egyptians were writing numbers and doing mathematics. Try out some of the computational methods they used and look at some of the problems they did.

Prerequisite: Multiplication and Fractions
Length of Presentation: 40 to 80 minutes
Travel Limitations: Northern or Eastern Vermont

 

“Mayan Mathematics”

 

The Mayan numeration system, the first to develop the concept of zero, will be investigated. Pictures of monuments will be used to identify the numerals. Mayan arithmetic and the development of a calendar will also be covered.

 

Grade Level: Adapted to 3 – 12

Travel Limitations: Northeast Vermont

 


 

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"

 

“Is There a Fair Way to Vote?”

 

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

 


 

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Latest Update:
October 1, 2013
by David Hathaway