LAMC Calendar // 2009-2010 Academic Year. Jump to: September October November December January February March April May

Fermat's Last Theorem has been baffling and intriguing mathematicians for over 350 years. We are going to trace the work of some of the amazing men and women who worked on this problem, and even prove the Theorem in a few cases ourselves! ⊟Details

Handouts: Fermat\'s Last Theorem

We will discuss the continued fraction expansion and talk a little bit about the golden ratio and its occurrence in arts and nature. Then we will calculate the continued fraction expansion of roots of small integers and discover some interesting structure in these expansions. This will lead to the understanding of a beautiful theorem named after Fermat but proven by Euler, that characterizes the primes that can be written as the sum of two squares.⊟Details

Handouts: Continued Fractions and a theorem by Fermat

We will continue with the topic started last time. ⊟Details

Going from real numbers (ordinary numbers) to complex numbers is like coming out of a tunnel. You can see much more of the mathematical landscape than you thought possible. Even some properties of real numbers that were mysterious before become clearer. This session will be an introduction to complex numbers, their basic properties, and some things you can do with them. In future sessions we'll discuss more applications, ranging from number theory to cell phones.⊟Details

Handouts: Unit circle | Complex plane | Geoboard

This is the second part of the meeting (from 3 p.m. to 5 p.m.). We will start reviewing the material for AMC 10 and AMC 12. ⊟Details

This is the first part of the meeting (2-3 p.m.): Some thoughts on using math and science thinking and math and science knowledge far outside math and the sciences, from Eugene Volokh, who’s a professor at UCLA School of Law. Eugene started as a math buff, shifted to computer programming, and eventually turned to law as well as popular writing about the law (he’s the founder of The Volokh Conspiracy weblog, http://volokh.com). Before going into teaching, he clerked for Justice Sandra Day O’Connor at the U.S. Supreme Court. ⊟Details

We will begin with a review of basic number theory/abstract algebra, discussing the "integers modulo N." We will move on to discussions of how to determine if a number is a "quadratic residue" modulo N, introducing the Legendre and Jacobi symbols. We'll conclude by using these tools to build an encryption scheme, which we'll play around with at the end.⊟Details

Handouts: Problem Set | Handout