EXPANDING HORIZONS XII
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.
For more information contact:
John
Devino
Phone: 802-863-5403
E-mail: devino07@verizon.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
Richard Barney, PhD, FSA
54 Stoughton Drive
Ticonderoga, New York 12883
Phone: (518) 585-9809
E-mail: rbarney1010@yahoo.com
“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
Lyndon State College
Phone: (802) 626-6489
Fax: (802) 626-9770
E-mail: james.bozeman@lyndonstate.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.
Phone: (802) 485-2501
E-mail: sdiesel@norwich.edu
“The Amazing
Worldwide Popularity of Sudoku”
We'll look at the brief
history of these puzzles, the somewhat longer history of Latin squares, and
strategies people have come up with to solve these sometimes fiendishly
difficult puzzles.
Prerequisites: None
“Caesar Ciphers
and Secret Messages”
Creating unbreakable
ciphers, and trying to decrypt them, has occupied mathematicians, linguists,
and others for a long time. Find out about the Caesar cipher and other
ciphers from history, and about the public key cryptography of today.
Prerequisites: None,
but exposure to percents, prime numbers, and frequency is useful.
Jeff Dinitz
University of Vermont
Phone: (802) 656-4292
E-mail: Jeff.Dinitz@uvm.edu
“Scheduling Leagues and Tournaments”
In this talk
we’ll look at different kinds of league schedules and learn an extremely
easy method to generate a round-robin tournament for any number of players.
Additionally, I can talk about my short experience in constructing the schedule
of play for a professional football league.
Prerequisites: None
Level: 7
– 12
“Planar Graphs”
Why
can’t three utilities be connected to three houses without crossing the
utility lines? In this talk we will prove this fact and give some general facts
about which graphs can be drawn in the plane without crossing edges.
Prerequisites: Algebra and geometry.
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.
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
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.
Ted Marsden
Norwich University
Phone: (802) 485-2326
E-mail: marsden@norwich.edu
"A
Probability Problem and Its Solution by the Area Model."
Using Experimental
Probability along with the Area model to Understand a
Probability Problem and Solution.
Length of Presentation: 50
to 80 minutes
“Factor Diagrams
and Perfect Numbers”
Length of Presentation: 75
minutes
"Some Counting
Problems and Probability"
Use of
combinatorial rules to help understand some problems in probability.
Length of Presentation: 40
to 80 minutes
Travel Limitations: Within
90 minutes of
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
to 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
5-12
Travel Limitations:
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
to 80 minutes
Phone: (802) 485-2875
E-mail: dolsen1@norwich.edu
"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. You will be provided with a list of all 10 ?aesthetic?
knots as determined by Thomas Fink and Yong Mao
Grade Level: 7 -12
Length 30 - 45 minutes
Phone: (802) 443-5417
Fax: (802) 443-2080
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. 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)
“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.
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
to 75 minutes
Bob Rosenfeld
Phone: (802) 454-8497
E-mail: rosenfeld@vtlink.net
"The Hopping
Bug—an Introduction to Random Walks"
Typified as the journey
taken by a drunk stumbling randomly away from a lamp post: Where will he end
up? The same mathematics applies to the paths of atomic particles subject to
random collisions. The presentation uses some basic ideas on probability, infinite
series, and computer simulations.
Prerequisite:
Multiplication of matrices and some familiarity with the sum of infinite
series.
“What Does
“MEAN” Mean?”
A small
survey of various kinds of means and what they are good for. (Example: Geometric, harmonic, etc.)
Tony Trono
Phone: (802) 863-4363
E-mail: tonytrono@aol.com
"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 to 80 minutes
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