EXPANDING
HORIZONS XVII
A project of the
Bring college and university
mathematicians to your classroom!
DIRECTIONS
- Choose a topic which would be of interest to
your students.
- Contact the presenter directly by phone, fax,
e-mail, or postal mail.
- 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: devino07@myfairpoint.net
George Ashline
Saint Michael’s College
Phone: (802) 654-2434
E-mail:
“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
Phone: (802) 626-6489
Fax: (802) 626-9770
"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
Phone: (802) 443-5555
E-mail:
“William R. Hamilton
and the Quaternions”
In 1843, while strolling across a bridge in
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
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
"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.
Karla Karstens
Phone: (802) 878-7322
“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
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
Phone: (802)
626-6260
"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
“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:
Michael Olinick
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
Mathematics provides
the answer.
"The Near-Sighted
Fly: A Topological View of the Universe"
Length of
Presentation: 40 – 80 minutes
Darlene M. OlsenNorwich University Phone: (802) 485-2875E-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 levelLength 45 minutes
Rob Poodiack
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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