Sonia at 



Introduction 
"It is
impossible to be a mathematician without 
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: 
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 miniclass, 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: 




Cryptography is an important application of mathematics. In this miniclass, 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: 
Coded
Message
&
?*&<\ ;~ “)[*\#)<
)! %&<)\# +?$\{[%%~ )>\
;!;\#) )>\~ *\+&*\ )!
)?=\ #! ;!$\
;?)>\;?)&+< +![$<\<
)>\~ ;&@>) }\
?}%\ )! >\?$ )>\
“![#*
!{ +%!<&#@ *!!$<
^\?$% “ }[+= 
Frequency Analysis 

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 
Mathematical formulas play an important role in the sports world today. In this miniclass, students used linear models to explore the mathematics behind women's college basketball. Using actual game results from the 20032004 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 matchups between Hollins, Virginia Tech and Duke. For
more examples (Virginia Tech and Duke) see :
Sports Examples (under construction) 

In this miniclass, 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 ( 5player) 

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 
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.

