High School Math Night: Difference between revisions

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=What is it?=
This academic year the High School Math Nights are being combined with the [[Madison Math Circle]]. In addition to the usual Math Night Talks, the department will also host Math Circle activities, so there's something fun and educational each Monday!
The UW-Madison math department organizes a series of talks aimed at high school students throughout the semester. Our goal is to present fun talks that give students a taste of interesting ideas in math and science. In the past we've had talks about plasma and weather in outer space, the way images are shaded in video games, and how credit card numbers are securely transmitted over the internet.


'''Important:''' After each talk we'll have '''pizza''' provided by the department, and students will have an opportunity to mingle and chat with the speaker to ask questions about college, careers in science, etc.
Please click [[Madison Math Circle]] for a schedule of Math Night talks and Math Circle activities.
 
=Alright, I want to come!=
Great! If you're a high school teacher, we hope you'll tell your students about these talks and organize a car pool to the UW (all talks take place in Van Vleck Hall on the UW campus). '''We'd also appreciate if you [mailto:math-night@math.wisc.edu email] us the dates that your group will be attending''', so we can purchase the appropriate amount of pizza.
 
If you're a high school student, speak with your high school teacher about organizing a car pool to the math night (and tell us how many people are coming!)
 
=Questions?=
If you have any questions, suggestions for topics, or so on, just email the Math Night organizers: [mailto:math-night@math.wisc.edu math-night@math.wisc.edu].
 
==Talks this semester==
More details about each talk to follow. All talks are at 7pm in Van Vleck Hall B231.
 
<center>
 
{| style="color:black; font-size:120%" border="1" cellpadding="14" cellspacing="0"
|-
! Date !! Speaker !! Talk (click for more info)
|-
| February 17th, 2011 '''still being held''' || Andrew Bridy || [[#Cryptography|Cryptography]]
|-
| March 10th, 2011 || Ed Dewey || [[#The 0.5th Dimension|The 0.5th Dimension]]
|-
| March 24th, 2011 || Lalit Jain || [[#Cutting & Pasting|Cutting & Pasting]]
|-
| April 7th, 2011 || Balazs Strenner || [[#Tilings|Tilings]]
|-
| April 28th, 2011 || Prof. Nigel Boston || [[#Face Recognition|Face Recognition]]
|}
 
</center>
----
===Cryptography===
<span style="background:#00FF00">February 17th, 2011</span> '''Update 2/16/11: still being held'''
 
'''The science of code making and code breaking'''
 
Sending information securely over the internet is an enormous practical problem.  How can you be sure that no one is reading your email, or worse, stealing your credit card number when you buy something online?  Cryptography is the art of encoding a message so it looks like a string of random letters or numbers, and decoding it on the other side to get the original message back.  In this talk I'll show you some simple ways you can use math to encode and decode information, and how the same techniques can be used to attack codes and try to break them.  The branch of math used is called number theory, and the problems that come up are very simple to state and very hard to solve, leading right to current research that mathematicians are working on today.
 
====Speaker: [http://www.math.wisc.edu/~bridy Andrew Bridy]====
Andrew is a third year math Ph. D. student studying algebra and computer science. Before coming to graduate school, he taught high school math for a year and was deployed with the Peace Corps to Honduras. Andrew is an avid video game fan - you should ask him to tell you about his favorite PC video games of the late 1990's.
----
===The 0.5th Dimension===
<span style="background:#00FF00">March 10th, 2011</span>
 
'''A Harrowing Journey to the 0.5th Dimension'''
 
We frequently think about two dimensional spaces, like a map of a country, or three dimensional spaces, like the Holodeck from Star Trek. But what exactly is "dimension", anyway? This turns out to be a surprisingly deep question, without a unique answer.  But asking it is still useful, and leads us to the strange and beautiful notion of Hassdorf dimension, one of the fndamentals of fractal geometry, which gives a meaning to non-integer dimensions.  We will discuss Haussdorf dimension and its motivation, and see an application to psychology.   
 
====Speaker: [http://www.math.wisc.edu/~dewey Ed Dewey]====
Ed is a first year Ph. D. student in mathematics. He used to be in a ska band. 
 
----
===Cutting & Pasting===
<span style="background:#00FF00">March 24th, 2011</span>
 
 
The Bolyai-Gerwein theorem says that any two polygons of the same area have an "equi-dissection". In other words, there is a way to cut up one of the polygons into pieces (using straight line cuts) that can be rearranged to form the other. This deep theorem is surprisingly recent compared to much of classical geometry and has many interesting generalizations. During this weeks talk we will prove the theorem as a group using little more then argument by "scissors and glue."
 
Here are some fun applets to see this in action:
 
http://demonstrations.wolfram.com/AnExampleOfTheBolyaiGerwienTheorem/
 
http://www.cut-the-knot.org/Curriculum/Geometry/TwoRectangles.shtml
 
 
An example of dissecting a square into pieces that form a triangle of the same area.
[[Image:TriangleSquare.jpg|200px]]
 
 
====Speaker: [http://www.math.wisc.edu/~jain Lalit Jain]====
Lalit is a first year Ph. D. student in mathematics interested in number theory and computer science. Before coming to graduate school, Lalit was a high school math teacher with [http://en.wikipedia.org/wiki/Teach_for_america Teach For America] in San Francisco. You should ask Lalit about who shot Frances in the video game Left 4 Dead.
----
 
===Tilings===
<span style="background:#00FF00">April 7th, 2011</span>
 
'''Tilings'''
 
Tilings in the mathematical sense mean non-overlapping, gap-free coverings of the plane by certain shapes. For instance, one can take (infinitely many) squares and place them on the infinite plane as they are on a chessboard, nicely fitting next to each other. This is maybe the simplest example. But if one takes regular pentagons, it is impossible to form a tiling using only them.
 
The first class of interesting tilings we will discuss are the Penrose tilings. These involve two different shapes, the "kite" and the "dart". Not only it is fun to play with them and to try to make different arrangements, but these tilings have really interesting mathematical properties. Just to mention one of these: the ratio of the number of kites and darts - which I'll make precise - in all the possible arrangements is always the same, and it is the golden ratio!
 
Tilings have an artistic nature as well. The Dutch graphic artist M. C. Escher is famous for his math-connected drawings, and in fact many of these are tilings with funny shapes, birds for example. Another series of masterpieces by him are the woodcuts Circle Limit I-IV which picture hyperbolic tilings of the disk using funny graphics again. We will talk about their mathematical background, and also about how to write a program that makes a hyperbolic tiling out of an arbitrary image file.
 
[[Image:LW434.jpg]]
[[Image:LW361A.jpg]]
[[Image:kite and dart.gif]]
 
 
====Speaker: [http://www.math.wisc.edu/~strenner/balazs/Home.html Balazs Strenner]====
Balazs is a first year PhD student originally from Hungary, land of [http://en.wikipedia.org/wiki/Paul_Erd%C5%91s many] [http://en.wikipedia.org/wiki/Leo_Szilard fantastic] [http://en.wikipedia.org/wiki/John_von_Neumann mathematicians and scientists]. Balazs is quite merciless as the Deputy Sheriff in the card game [http://en.wikipedia.org/wiki/Bang! Bang!]
 
----
 
===Face Recognition===
<span style="background:#00FF00">April 28th, 2011</span>
 
'''Invariant-Based Face Recognition'''
 
I shall describe the main difficulties with automated face recognition and how our team of mathematicians, engineers, and computer scientists overcame some of them by using mathematical invariants.
 
What are invariants? Invariants are mathematical properties that can help you tell the difference between two objects you're interested in studying. For instance, if you're studying polygons, a good invariant might be the number of vertices on a polygon: all triangles have 3 vertices, all squares have 4 vertices, and so on. Also observe that this relationship goes the other way - if you have a polygon with exactly 3 vertices, it must be a triangle.
 
Why do mathematicians care about invariants? They can be used to filter out mathematical objects you're interested in studying from larger and more complicated collections. For instance, say you're studying a database with 10 trillion different polygons, but you're really only interested in the triangles in this database. Since the number of vertices is an invariant of a polygon, we can restrict our attention to the polygons in the database with exactly 3 vertices and (hopefully) simplify our problem.
 
Facial recognition is an example of a very complicated real-world problem that invariants can help simplify. In fact invariants have been rejected in the past for recognizing faces because they were not robust to measurement error, so we had to come up with a new family of robust invariants. Our implementation of this won us 2nd place in the 3D section of the national Face Recognition Grand Challenge.
 
====Speaker: [http://www.math.wisc.edu/~boston Professor Nigel Boston]====
Nigel Boston is a professor in the departments of mathematics and electrical & computer engineering at UW-Madison. Nigel works in many interesting areas, including applying research from algebra and number theory to real world problems in engineering.

Latest revision as of 14:07, 13 October 2011

This academic year the High School Math Nights are being combined with the Madison Math Circle. In addition to the usual Math Night Talks, the department will also host Math Circle activities, so there's something fun and educational each Monday!

Please click Madison Math Circle for a schedule of Math Night talks and Math Circle activities.

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