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for high school students:
Math Circle Saturday Workshops
January 14, 2012 - March 10, 2012
From January to March, come to campus to do math with friends, undergrads, and graduate students. In previous years we have explored chaos and combinatorics, tilings and number theory, linear programming and knot theory. This year we will explore the exciting topics of Mathematical Finance, Geometry and Quantum Information Theory!
Our former students have said of our program:
- "Excellent! Probably the only thing that could get me on my feet so early on a Saturday!"
- "A very fun experience!"
- "Before this, I had no idea there was so much to math."
Application Process
Applications only take 5 minutes and everyone is welcome!
Feel free to contact us if you have any questions.
Classes
"Math Circle makes math more enjoyable and interesting to all who participate. It changed the way I looked at and felt about math and Math Circle isn't just doing problems out of a book. It is people who teach and actually like math."
The classes for Math Circle 2012 are:- Mathematical Finance, taught by Jeff Anderson
- Geometry, taught by Yvonne Kemper
- Quantum Information Theory, taught by Amanda Back
Class descriptions:
(The following are Math Circle 2012 class descriptions.)
Mathematical Finance
Jeff Anderson
How can you learn to apply mathematics to model real world phenomena, understanding investing, and solve problems creatively? Where can you meet interesting people, express yourself and improve your ability to think critically? Answers to these questions are waiting for you to experience in Math Circle's six part series: Mathematical Finance: Understanding Options. Under the direction of Jeff Anderson, we will discover topics in mathematical finance including:- The Options Market: What are options and how do they work
- Options and Arbitrage: European Call and Put Options and Arbitrage
Examples
- The One Step Binomial Model: Pricing European Options using a one
period binomial model
- Multiperiod Binomial Model: Replication in the Multiperiod Binomial
Model
- Advanced Options Strategies: The Butterfly Spread
- Using Linear Programming to Detect Arbitrage: Optimization Applied to
Finance
Geometry
Yvonne Kemper
Despite being one of the oldest mathematical sciences, geometry is home to a large number of open problems which are easy to state...but difficult to prove! We will explore some of the open problems relating in particular to polyhedra, and discuss relevant notions and real-world applications, such as:- Triangulations
- Polynomials
- Lattice Points
- Voting Theory
- Graph Theory
Quantum Information Theory
Amanda Back
Quantum information processing refers to the science of communicating and computing through quantum systems. As a field of study it has developed rapidly in the last few decades and continues to do so today. We will learn the mathematical underpinnings of quantum information and computation along with some applications. Topics to be discussed include:
- Quantum Superposition
- Qubits and ways to represent them
- Measurements
- Single- and multi-qubit circuits
- Quantum entanglement and quantum teleportation
- Quantum Cryptography
Expectations
Our mission is to have fun doing great math.
To quote the Boston Math Circle: ``While the courses are mathematically rigorous, the atmosphere is friendly and relaxed. We want our students to feel free to express their ideas, to suggest their own approaches, and to make mistakes. We work in a spirit of friendship, cooperation, and enjoyment of one another.''
We expect students to maintain an atmosphere of respect and cooperation. Any students found severely disrupting such an atmosphere will not be allowed to return to the program.
2012 Schedule
Location: MSB 2112
| Jan. 14 | 9:30-10:20 | Guest Lecture: Owen Lewis |
| 10:35-11:25 | Mathematical Finance | |
| 11:25-11:40 | break | |
| 11:40-12:30 | Geometry |
| Jan. 21 | 9:30-10:20 | Geometry |
| 10:35-11:25 | Quantum Information Theory | |
| 11:25-11:40 | break | |
| 11:40-12:30 | Guest Lecture: Elizabeth Chen |
| Jan. 28 | 9:30-10:20 | Quantum Information Theory |
| 10:35-11:25 | Mathematical Finance | |
| 11:20-11:40 | break | |
| 11:40-12:30 | Mathematical Finance |
| Feb. 4 | 9:30-10:20 | Mathematical Finance |
| 10:35-11:25 | Geometry | |
| 11:25-11:40 | break | |
| 11:40-12:30 | Guest Lecture:Julian Gold |
| Feb. 11 | 9:30-10:20 | Geometry |
| 10:35-11:25 | Geometry | |
| 11:25-11:40 | break | |
| 11:40-12:30 | Quantum Information Theory |
| Feb. 18 | 9:30-10:20 | Quantum Information Theory |
| 10:35-11:25 | Mathematical Finance | |
| 11:25-11:40 | break | |
| 11:40-12:30 | Guest Lecture: Tim Lewis |
| Feb. 25 | 9:30-10:20 | Mathematical Finance |
| 10:35-11:25 | Guest Lecture: Steve Klee | |
| 11:25-11:40 | break | |
| 11:40-12:30 | Guest Lecture: Sven Bachmann |
| Mar. 3 | 9:30-10:20 | Geometry |
| 10:35-11:25 | Quantum Information Theory | |
| 11:25-11:40 | break | |
| 11:40-12:30 | Quantum Information Theory |
| Mar. 10 | All Session Puzzlemania (MSB 2112) |