| 09/30/2012 | When messages are being sent in every day life, errors could occur and affect the accuracies of the messages. In this session, we will look at the how one can mathematically detect and correct these errors automatically. ⊟Details |
| 10/07/2012 | In this session, we will continue to talk about particular examples of error-correcting codes and study their properties using matrices. ⊟Details |
| 10/14/2012 | In this session, we will explore different kinds of "shapes" one can obtain by "gluing" together polygons. ⊟Details |
| 10/21/2012 | This week we will attempt to explain what all the possible surfaces are, discussing the notions of orientation and Euler characteristic. ⊟Details |
| 10/28/2012 | This week we will investigate solving quadratic equations mod p, and the interesting questions that arise. ⊟Details |
| 11/4/2012 | This week we will continue last week's discussion of quadratic residues, and look at some problem-solving type exercises. ⊟Details |
| 11/11/2012 | |
| 11/18/2012 | This week we will investigate finding probabilities by comparing areas, discussing certain paradoxes that arise. ⊟Details |
| 11/25/2012 | |
| 12/2/2012 | In this talk, we will look at generating functions, lattices paths and random walks. ⊟Details |
| 12/9/2012 | We will have and end-of-quarter problem solving competition. There will be prizes for the top scoring teams. ⊟Details |
| 01/13/2013 | We will work on some interesting AMC problems from the past. ⊟Details |
| 01/20/2013 | We will work out some of the mathematics behind Einstein's theory of
relativity, including the concept of a spacetime diagram, the theory
of Doppler shifts, and Einstein's famous equation E=mc^2. Very little
prior knowledge of physics will be required (but we will assume some
familiarity with high school algebra). ⊟Details |
| 01/27/2013 | This week in the High School group we will investigate graphs colorings, planar graphs, and Eulerian and Hamiltonian circuits. ⊟Details |
| 02/03/2013 | |
| 02/10/2013 | We will go over the AMC 10/12A from this year. ⊟Details |
| 02/17/2013 | Happy President's long weekend. Math circle will resume the following week. ⊟Details |
| 02/24/2013 | We will introduce some probability theory and then we will discuss how these ideas can be used to study networks in real life. ⊟Details |
| 03/03/2013 | This week we will discuss the diagonalization of quadratic forms in order to draw quadratic curves in the plane, and their relationship with bilinear forms. ⊟Details |
| 03/10/2013 | In this lecture, we will take a look at the murky surroundings of Euclid's 5th Postulate, possibly the most controversial scientific statement of all times. The Great Theorem of Fermat, a proverbial symbol of mathematical complexity, stood open for 358 years. Conjectured by Pierre de Fermat in 1637, it was proven by Andrew_Wiles with the help of his former student Richard Taylor in 1995. The Poincare Conjecture, another very hard math problem made famous outside of the scientific community by its conqueror Gregory Perelman's rejection of the $1,000,000 prize money, was proven in less than 100 years. It took humanity over 2,000 years to realize that the 5th Postulate is indeed a postulate and cannot be derived from other axioms of Euclidean geometry. The breakthrough can only be compared to the Copernican Revolution in astronomy that replaced the geocentric model of the universe with the heliocentric one. Both discoveries broke the millennia-long paradigms. The Copernican Revolution brought about Newtonian mechanics. The discovery of non-Euclidean geometry paved the way to the Relativity Theory of Einstein.
In the lecture, we will derive from the axioms the formula for the sum of angles of a triangle in the Euclidean plane and on a sphere. We will see that the first formula, traditionally considered to be the more elementary of the two, is in fact much harder to prove. We will also visit a planet that has only one pole, figure out the shape of the Universe, and some more.
⊟Details |
| 03/17/2013 | Please join us for our last meeting of the Winter Quarter for a fun team problem-solving competition! ⊟Details |
| 04/07/2013 | Pick's Theorem relates the area of a lattice polygon to the number of lattice points on its boundary and the number of lattice points in its interior. We prove this theorem from the ground up, by starting with rectangles, building up to general triangles, and then using triangulations. This is the first of two weeks, the second of which will discuss generalizations of this theory to higher dimensions (Ehrhart Theory). ⊟Details |
| 04/14/2013 | |
