Saturday Morning Math Group
 



Here is a list of talks and relevant links given in years past.

Spring 2003 Schedule:

Organizer: Kelly McKinnie

Queen Dido's Problem came from a story described in Virgil's Aneid. Queen Dido is on the run from her evil brother and flees to North Africa. She arrives at what becomes known as Carthage (nowadays Tunisia). Queen Dido wants to buy some land from the local ruler, King Jambas, so they agree that she can buy all the land that she could enclose with a bull's hide. Queen Dido has the bull's hide cut into small strips and stitches the strips together. Queen Dido wants as much land as possible,  and since she knows her geometry, she outlines the shape with the biggest area possible. The city is on the sea, and she is very clever, we found out how she outsmarted King Jambas!

See the poster, pictures, and the handout from the meeting.


Symmetrical patterns surround us - on our clothes, our floors, our architecture, even our gift-wrap! For over 20,000 years people have been inventing such decorative patterns, but mathematicians began to understand them well just within the last century. The correct mathematical perspective is less than twenty years old, and surprisingly, comes from the branch of mathematics known as Topology ("rubber sheet geometry").

Click for the poster or some pictures.

Perhaps the greatest logician of all times, he [Kurt Gödel] brought a revolution to mathematical thought with his Incompleteness Theorem which states, in simple terms, that our axioms for the natural numbers do not guarantee that all conceivable statements are decidable (true or false). More astonishingly, it is impossible to create such a "complete" axiomatic system. There will always remain statements that are neither true nor false i.e impossible to be proved or refuted.

Godel's Incompleteness Theorem states that in any consistent formal system which is adequate for arithmetic there is a true but unprovable sentence. What did this mean for mathematics? Well as Gregory Chaitin put it:

"At the time of its discovery, Kurt Gödel's incompleteness theorem was a great shock and caused much uncertainty and depression among mathematicians sensitive to foundational issues, since it seemed to pull the rug out from under mathematical certainty, objectivity, and rigor."

Russell's Paradox is an example of an incomplete system. A description of it can be found at the "Russell's Paradox" web site http://users.forthnet.gr/ath/kimon/Russells_pdx.html.

Here are pictures,  the handout, and the poster.


During World War II, the German Air Force, Army, and Navy all used similar code machines that the Allies called ``Enigma''. Battles were won, and convoys saved, partly because the Allies could read much of the German radio messages to airplanes, submarines, and armies fighting in the war. The first achievements were due to a very small group of Polish mathematicians, and after the defeat of Poland their successes were magnified and improved by a huge effort of British mathematicians, engineers, and code breakers including Alan Turing. The underlying mathematics of Enigma is itself fascinating, relying on studying permutations and other basic mathematical objects. We talked about codes and ciphers in general, and specifically about the Enigma machine. We tried our hand at ``breaking'' easy codes, and got some idea how to break very hard codes like Enigma. We even talked a bit about how this mathematics was so very important in the war.
 
Click http://www.mtholyoke.edu/~adurfee/cryptology/enigma_j.html to go to a website that has an Applet of an Enigma machine.
Or try this one, it has a great explanation of the Enigma machine:http://www.ugrad.cs.jhu.edu/~russell/classes/enigma/

See pictures and the poster.


Fall 2004 Schedule:

Organizer: Kelly McKinnie


Dr. Marcotte presented the role that mathematics had in Renaissance art, discussed proportion and helped the crowd draw in perspective.  Here are the poster  and some  photos of the program.  Click here to see the prospective drawings from the handout:
Perspective drawing exercise,  perspective room with grid, perspective room with grid and cube.
In 1997, Robert Merton and Myron Scholes won the Nobel Prize in Economics for inventing a method of calculating the fair prices of financial securites called derivatives. This talk explained their method and explored the connections with the seeminlgy unrelated problem of heat conduction. During this SMMG program we explored some of the driving forces behind the stock market. One of them is the "Central Limit Theorem". To see an example of the Central Limit Theorem click on one of the links below.

http://www.stat.sc.edu/~west/javahtml/CLT.html Roll 2 or more dice many times, and you should start to get a bell shaped curve.

http://www.rand.org/methodology/stat/applets/clt.html Click on this page to see a "Price is Right" type of illustration of the Central Limit Theorem.

http://www.ifa.tv/12steps/Step3/Step3Page3.html For some information on how the Central Limit Theorem applies to the theory behind the stock market, check out this page.

http://mathworld.wolfram.com/CentralLimitTheorem.html Click on this webpage to find out more technical information about the Central Limit Theorem.

See photos,  the handout, or the powerpoint file for the meeting.


Spring 2003 Schedule:

Organizer: Heather Lehr

Fall 2002 Schedule:

Organizer: Heather Lehr

Spring 2002 Schedule:

Organizer: Melissa Macasieb