EXPANDING
HORIZONS XIV
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
Richard Barney, PhD, FSA
Phone: (518) 585-9809
“Actuarial Science: The Road to Applied Mathematics”
If your interest in mathematics is more practical than theoretical, you should
consider taking actuarial exams while in college. This presentation will discuss the nature
of actuarial work and how it applies mathematics in order to
“substitute demonstrations for impressions.” Basic mathematics will be applied to
real-world situations to
illustrate the power of applied mathematics.
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.
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.
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
“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
"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
Bill Peterson
Phone: (802) 443-5417
Fax: (802)
E-mail: wpeterso@middlebury.edu
"Benford‘s Law"
In 1938 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. Some years ago, Marilyn von Savant's
solution in her Sunday column in Parade generated a lot of irate mail from professional mathematicians—all
of whom turned out to be mistaken. More
recently, the problem has appeared in the novel The Curious Incident of the Dog in the Night-Time and the movie 21. What makes this problem so
intriguing? And why won’t it stay
“solved”?
Length of Presentation: 40 – 80
minutes (80 preferred)
“Great
Expectations: From Huygens to Hedging”
Probability emerged
with the first book published in this field by Christian Huygens. This presentation
will begin with Huygens’ “expected value” of a wager and
trace some elementary ideas leading to applications in the modern world of
mathematical finance.
"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.
“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
Rob Poodiack
Phone: (802) 485-2339
E-mail:
"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
Tony Trono
Phone: (802) 863-4363
E-mail:
"A Quick Look at
Problem Solving"
Some math problems
only take a few minutes to solve. Others have taken many years. This
presentation will examine a variety of interesting problems along with their
creative solutions.
Length of Presentation: 40 – 80 minutes
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