Sonia
Kovalevsky
Mathematics
Day

at

Hollins University
January 22, 2004

with support from the
Association for Women in Mathematics

Introduction
The Mathematics and Statistics Department (faculty and students) of Hollins University welcomed 64 young women to campus for our first Sonia Kovalevsky Mathematics Day.  We honored Sonia by sponsoring a day that encouraged young women to continue their study of mathematics and that allowed them a small glimpse into the exciting world of college mathematics.  All participants received a custom design t-shirt (design on right), dined on unlimited pizza and participated in many activities (listed below) that focused on the beauty, fun, and applicability  of mathematics as well as the importance of mathematics in a variety of careers.  For more information about these activities, simply click on the links below. 

Opening Remarks: Who is Sonia Kovalevsky?
Beauty in Mathematics?
Secret Codes
Mathematics in Sports
I Want Candy!
Scavenger Hunt
Career Panel

  

"It is impossible to be a mathematician without
being a poet in soul."
    Sonia Kovalevsky

 

Opening Remarks:  Who is Sonia Kovalevsky?

Our day carries the name of Sonia Kovalevsky, a famous Russian mathematician born in 1850.  Sonia's mathematical life began early as she studied her father's old calculus notes that were papered on her nursery as replacement for wallpaper.  Throughout her life, Sonia faced much personal and academic hardship, but she remained committed to the study of mathematics.  She was the first woman to earn a PhD in mathematics and her brilliant career included publication of ten papers in mathematics and mathematical physics.

For more information see:
www.agnesscott.edu/lriddle/women/kova.htm

 

Beauty in Mathematics ?

A fractal is an intricate geometric figure that contains infinitely many smaller copies of itself.  These images have long been appreciated for their striking beauty and mathematical complexity.  In this mini-class, students were introduced to many fractals including Sierpinski’s Triangle (above). They then used simple mathematical methods to generate fractals (see below). The deterministic methods (seed and rule) were carried out using MS PowerPoint. The random methods were carried out using //math.bu.edu/DYSYS/applets/fractalina.html. Students used both deterministic and random methods to generate Sierpinski's Triangle, Sierpinski's Hexagon, Fractal "X", Fractal Kite and Sierpinski's Carpet.  Nature’s fractals (e.g. ferns, snowflakes, clouds) were also discussed.

For more information see:

Fractal Class Handout

 



Sierpinski's Hexagon

 



Sierpinski's Carpet

 



Fractal "X"



Fractal Kite

 

Secret Codes

Cryptography is an important application of mathematics.  In this mini-class, students were introduced to cryptography and several simple mathematical cipher methods.  Working in groups students coded and decoded messages using transposition and monoalphabetic substitution.

For example, in the cryptogram on the right, students used Maple9 to generate a character frequency analysis as the first step in decryption.  Digraph and trigraph searches were also used.

For more examples see:

Secret Code Examples

 Coded Message
&  ?*--&<\   ;~   “)[*\#)<   )!   %&<)\#   +?$\{[%%~   )>\ ;!;\#)   )>\~   *\+&*\   )!   )?=\   #!    ;!$\    ;?)>\;?)&+< +![$<\<     )>\~    ;&@>)   }\   ?}%\   )!   >\?$    )>\   
“![#*   !{   +%!<&#@    *!!$<        
^\?$%  “   }[+=

Frequency Analysis
 & 07, ? 08, * 06, -- 01, < 08, \ 19, ; 07, ~ 04, " 03,
) 15, [ 05, # 06, ! 12, % 05, + 06, $ 06, { 02, > 07,
@ 02, } 03, = 02, ^ 01 

Decoded Message
“I advise my students to listen carefully the moment they decide to take no more mathematics courses.  They might be able to hear the sound of closing doors.” 
Pearl S. Buck

 

Mathematics in Sports

Mathematical formulas play an important role in the sports world today.  In this mini-class, students used linear models to explore the mathematics behind women's college basketball.  Using actual game results from the 2003-2004 Hollins, Virginia Tech, and Duke women's basketball seasons, student defined different dependent and independent variables (see below) and plotted the data.  Students then drew in best fit lines and interpreted slope and y intercept in the context of the application.  Using these linear models, students were able to make predictions for hypothetical match-ups between Hollins, Virginia Tech and Duke.

For more examples (Virginia Tech and Duke) see :      Sports Examples (under construction)

 

 

I Want Candy !

In this mini-class, students participated in several math experiments outlined in "Candy Sharing," by Iba and Tanton in The American Mathematical Monthly, January 2003.  Students, sitting in a circle, were given a certain amount of candy and were asked to trade pieces of candy according to a presribed set of guidelines.  Did the number of pieces in everyone's pile stabilize? Oscillate? Or did the process show no pattern?  The students experimented (right) with different beginning amounts of candy and different amounts to pass. 

For more information see:

Candy Class Handouts (under construction)

Rules and Results ( 5-player)
player A B C D E
fraction passed 1/3 2/5 1 1/2 3/4
round UP multiple 3 5 1 2 4
initial Amount 12 10 3 4 8
round 1 amount 15 10 3 6 4
round 2 amount 15 10 4 8 4
round 3 amount 15 15 4 8 8
round 4 amount 18 15 6 10 8
round 5 amount 18 15 6 12 8
round 6 amount 18 15 6 12 8

 

Scavenger Hunt

Students "hunted" through Dana Science Building to uncover mathematical clues (see example below) and to solve challenging geometry and algebra tasks (see example below), which involved similar triangles, volume, calories in a cheeseburger and sales commissions.  Working in groups of three, students competed for correct answers and fast times.  For the complete scavenger hunt (clues and tasks) see:  More Clues and Tasks (under construction)

Clue #4

To find the number of milligrams of cholesterol per ounce in cheddar cheese for  Task #4, find the office (on the second floor) with a picture of Sonia Kovalevsky.  Using this door's number, add the first two digits to get the ten's place of the number you're looking for.  Use the third digit of the door number as the one's place of the number you are looking for.

Task #4

Cheddar cheese has x milligrams of cholesterol per ounce and lean ground beef has 27 milligrams of cholesterol per ounce.  A cheeseburger made with 1/2 ounce of cheese that contains a total of 123 mg of cholesterol has how many ounces of lean ground beef?  In other words, if y is the ounces of ground beef, then 0.5x + 27y = 123.  Solve for y.

 

 

 

Career Panel
Students were surprised to learn of the many uses of mathematics in a variety of careers, some of which seem nonmathematical.  Professionals (see below) from the Roanoke Valley discussed the importance of mathematics in their careers and then answered many follow-up questions.

David Dvorscak
In addition to his job as associate professor of theatre at Hollins, David is a freelance director, stage combat choreographer and actor whose work is frequently seen on the Mill Mountain Theatre stage.  Since college, David has always tried to balance his love of performance with his fascination with physics.  In 1996, his work applying chaos and fractal theory to theatre production earned him acceptance in the prestigious Saratoga International Theatre Institute.

Susan Gring
Susan is the executive director of Carilion Foundation, which funds programs dedicated to enhancing the health of communities.  Her background includes degrees in nursing, long term care and healthcare administration.  Susan admits to suffereing from "math anxiety" as a young adult but has certainly overcome it.  She says "...math is something I use every day in every fadcet of my life -- my advice to others is to learn as much as you are able and enjoy math.  It is a critical skill, enhances your thinking abilities and can be richly rewarding.

Karen Harvey
Karen is currently in her ninth year as head basketball coach and physical education instructor at Hollins.  She also serves as the sports information director.  Karen played basketball at Roanoke College where she was named Kodak All-American in 1991.  Her background includes a BS degree in Physical Education from Roanoke College and  a MS degree in Exercise Science from Virginia Tech.  Karen's players use math skills almost daily in weight training, nutrition, drills and in determinig team and player statistics.

Paul Kaiser
Paul is currently an orthodontist in private practice.  His background includes a BS in chemistry from Roanoke College and a DDS from the Medical College of Virginia.  He completed his specialization in Orthodontics and Dentofacial Orthopedics from University of Missouri in Kansas City just 3 days before joining the practice of O.W. Clifton in Roanoke.  Paul says "..orthodontics is one of those rare careers that combines ideas from many different disciplines - art, science, and mathematics."