Mathcamp 2000 -- Schedule for Week 5 -------------------------------------- Tuesday, Aug 8th ----------------------- 9:00 - 9:55 [160] Topology Track **** [166] Number Theory Track ** 10:00 - 11:55 [166] Colloquium: "Integer Sequences -- online!" Neil Sloane 12:00 - 1:25 Lunch 1:30 - 2:25 [160] Gaussian Elimination * (Julian) [166] Information Theory 1 ** (Mira) [256] Differential Equations 5 *** (Madeeha) [260] Differential Topology 5 **** (Noah) 2:30 - 3:25 [160] Don't leave camp without this: integers and their friends * (Aytek) [166] More about Nim and other games 1 ** (Mira) [256] Functions of a complex variable 7 *** (Mark,Chris) [260] Linear Programming and Fractional Graph Theory 1 *** (Ari) 3:30 - 4:25 PAUSE TO THINK [256] Problem Solving **-**** (Mark S) 4:30 - 5:30 [160] Discrete Math Track * [166] Algebra Track *** [256] Combinatorics on Words Track **-*** (Mark S) [260] Problem Solving *** (Aytek) Wednesday, Aug 9th ----------------------- 9:00 - 9:55 [160] Discrete Math Track * [166] Algebra Track *** [256] Combinatorics on Words Track **-*** (Mark S) 10:00 - 11:55 [166] Colloquium: "Codes, Sphere Packing, and Integer Sequences" Neil Sloane 12:00 - 1:25 Lunch 1:30 - 2:25 [160] More Cryptography 1 * [166] COOL STUFF! ** (Mystery Mentor) [256] Elliptic Curves 5 *** (Dave) [260] Projective and Algebraic Geometry 7 *** (Mira) 2:30 - 3:25 [160] Don't leave camp without this: mathematical induction * (Aytek) [166] Unique factorization and the simplest cases of Fermat's Last Theorem 1 *** (Ravi Vakil) [256] Determinants 3 ** (Mark K) [260] Analytic Geometry * (Dr. Thomas) 3:30 - 4:25 PAUSE TO THINK [256] Problem Solving *-*** (Chris) 4:30 - 5:30 [160] Topology Track **** [166] Number Theory Track ** [256] Aytek's Farewell Problem Solving *** Thursday, Aug 10th ----------------------- 9:00 - 9:55 [160] Topology Track **** [166] Number Theory Track ** 10:00 - 11:55 [166] You can't there from here: non-constructibility proofs Ravi Vakil 12:00 - 1:25 Lunch 1:30 - 2:25 [160] indigo: the return! ** (guess who?) [166] Some unsolved problems *** (Neil Sloane) [256] Problems on geometric inversion **-*** (Aytek) [260] Analytic Geometry * (Dr. Thomas) 2:30 - 3:25 [160] Don't leave camp without this: pigeonhole principle * (Aytek) [166] More Nim and other games 2 ** (Mira) [256] Functions of a Complex Variable 8 *** (Mark K, Chris) [260] Unique factorization and Fermat's Last Theorem 2 *** (Ravi Vakil) 3:30 - 4:25 PAUSE TO THINK [256] Problem Solving **-**** (Mark S) 4:30 - 5:30 [160] Discrete Math Track * [166] Algebra Track *** [256] Combinatorics on Words Track **-*** (Mark S) [260] Problem Solving *-**** (Mark K) Friday, Aug 11th ----------------------- 9:00 - 9:55 [160] Discrete Math Track * [166] Algebra Track *** [256] Combinatorics on Words Track **-*** (Mark S) 10:00 - 11:55 [166] CAMP ASSEMBLY -- REQUIRED! 12:00 - 1:25 Lunch 1:30 - 2:25 [160] Information Theory 2 ** (Mira) [166] Fun with Fibonacci * (Ravi Vakil) [256] Differential Equations 6 *** (Madeeha) [260] Differential Topology 6 **** (Noah) 2:30 - 3:25 [160] Don't leave camp without this: do you know how to count? * (Aytek) [166] COOL STUFF ** (Mystery Mentor) [256] Functions of a complex variable 9 *** (Chris, Mark K) [260] Linear programming and fractional graph theory 2 *** (Ari) 3:30 - 4:25 PAUSE TO THINK [256] Chris's Farewell Problem Solving 4:30 - 5:30 [160] Topology Track **** [166] Number Theory Track ** [256] Julian's Farewell Problem Solving ------------------------------ TRACKS Discrete Math * will be covering some theoretical computer science such as Turing machines and thoughts on computability. The last day will likely be a grand debate on whether we'll ever be able to make machines that think, whatever that means.... If you haven't been before, you can still join! VISITORS We have two excellent visitors coming this week, Neil Sloane and Ravi Vakil. Both of them are incredibly full of cool mathematical facts and ideas and really fun to talk to -- so don't miss the opportunity! Here's what Neil Sloane says about his talks: "I will organize these lectures around my Online Encyclopedia of Integer Sequences (http://www.research.att.com/~njas/sequences). Some of the topic to be discussed are: - sequences from combinatorics - puzzle sequences - techniques for guessing the next term - some interesting sequences that need extending - some famous open problems - sequences arising from error-correcting codes and sphere packing There will be many examples and stories." Ravi Vakil will be talking about problems that people had been trying to solve for thousands of years, but in the last century were proved to be unsolvable: trisecting an angle with ruler and compass, squaring the circle, and more. He'll also teach a class on unique factorization (or lack thereof!), where he hopes to get to the proof of Fermat's Last Theorem for exponents 3 and 4. NEW CLASSES Gaussian elimination * (Julian). Have you ever had difficulties solving simultaneous linear equations? (Things like "x + 3y = 5 and 2x - 4y = 2".) In this session, we will learn a general technique for solving problems like this, which will make such difficulties a thing of the past. More Cryptography * (Julian). This week we will look at some more algorithms and techniques for encrypting messages, including unbreakable encryption and the long-awaited coin-tossing-over-the-phone. Attendance at last week's lectures is not really mandatory. Don't leave Camp without this! * (Aytek). Essential mathematical techniques and ideas that you may have come across in your classes this summer - but maybe you didn't? Or maybe you would like a more systematic review? There will be four independent session -- you can come to all or just some. The classes will be followed by a problem session during the Pause to Think. Fun with Fibonacci * (Ravi Vakil). You've probably already met the Fibonacci numbers: 0,1,1,2,3,5,8,13,21,34,etc. If all you know about them is that each next one is the sum of the previous two, then come find what you've been missing -- there's some very beautiful stuff going on with this sequence! More about Nim and other games ** (Mira). Didn't get enough games at Cathy O'Neill's colloquium? In the first class we'll derive a really nice closed formula for Nim losing positions. In the second, we'll talk about non-Nim-like games, where the two players don't have the same moves available to them. You have to have gone to Cathy's colloquium, but otherwise the classes will be more or less independent of each other. Information Theory ** (Mira). We'll define a mathematical concept of information and see how it relates to coding and data compression. At the end we'll calculate the redundancy of English speech -- how much less information you transmit when talking than you (in theory) could. Lots of silly sentences will arise in between! Elliptic Curves *** (Dave). Elliptic Curves 5 will require knowledge from Cathy O'Neil's p-adics class. Elliptic Curves 6 will require knowledge from Mark K. and Chris's Functions of a Complex Variable class. These two classes will be independent from one another, so you can go to Elliptic Curves 6 without having gone to Elliptic Curves 5. Linear Programming and Fractional Graph Theory *** (Ari). How can linear algebra be used to define concepts of graph theory -- without having to do actual nasty calculations? What happens to graph theory when we relax the requirement of integer values in said definitions? We will find out how to fix scheduling problems, why the four-color theorem might be easier if we allowed eight half-colors, and more. Recommended: bits of linear algebra and graph theory, although we'll go over it all quickly. (Academic Coordinator's Note: attendance at this class is mandatory for all members of the Committee for a Conflict-Free Schedule!)