Mathcamp 2000 -- Schedule for Week 3 -------------------------------------- Tuesday, July 25th ----------------------- 9:00 - 9:55 [160] Topology Track **** [166] Number Theory Track ** [260] Calculus 5 ** (Madeeha) 10:00 - 11:55 [166] Colloquium: Algorithmic problems (Mark S) 11:00 - 11:55 [256] More about complex numbers * (Mark K) 12:00 - 1:25 Lunch 1:30 - 2:25 [160] Projective Geometry 1 **-*** (Mira,Brenda) [166] Dimensional Physics ** (Sanjoy Mahajan) [256] Adding Things Up 3 * (Julian) [260] Diophantine Equations 1 *** (Dave) 2:30 - 3:25 [160] Virtual Ants 1 * (Evelyne) [166] Knots 1 ** (Chris) [256] Transcendental Numbers 1 **-*** (Aytek) [260] Differential Topology 1 **** (Noah) 3:30 - 4:25 PAUSE TO THINK [256] Problem Solving *-*** (Chris) 4:30 - 5:30 [160] Discrete Math Track * [166] Algebra Track *** [256] Combinatorics on Words Track **-*** (Mark S) [260] Problem Solving * - **** (Mark K) Wednesday, July 26th ----------------------- 9:00 - 9:55 [160] Discrete Math Track * [166] Algebra Track *** [256] Combinatorics on Words Track **-*** (Mark S) 10:00 - 11:55 [166] Colloquium: Lies, Damned Lies, and Proof: a Mathematician with a Newspaper Sanjoy Mahajan 12:00 - 1:25 Lunch 1:30 - 2:25 [160] Mental Calculation 1 ** (Sanjoy Mahajan) [166] Monster Equations 1 ** (Igor) [256] Non-Euclidean Geometry 7 * (Dr. Thomas) [260] Functions of a Complex Variable 1 *** (Mark K, Chris) 2:30 - 3:25 [160] Generating Functions 3 *** (Julian, Mark K) [166] Paradoxes 1 * (Meep) [256] Differential Equations 1 *** (Madeeha) [260] Diophantine Equations *** (Dave) 3:30 - 4:25 PAUSE TO THINK [256] Problem Solving *** (Aytek) 4:30 - 5:30 [160] Topology Track **** [166] Number Theory Track ** [256] Problem Solving *-** (Julian) Thursday, July 27th ----------------------- 9:00 - 9:55 [160] Topology Track **** [166] Number Theory Track ** [256] Calculus 6 ** (Madeeha) 10:00 - 11:55 [166] Transformations of the Plane Serge Lang 12:00 - 1:25 Lunch 1:30 - 2:25 [160] Projective GEometry 2 **-*** (Mira, Brenda) [166] Dimensional Physics ** (Sanjoy Mahajan) [256] Adding Things Up 4 * (Julian) [260] Diophantine Equations 3 *** (Dave) 2:30 - 3:25 [160] Virtual Ants 2 * (Evelyne) [166] Knots 2 ** (Chris) [256] Transcendental Numbers 2 **-*** (Aytek) [260] Differential Topology 2 **** (Noah) 3:30 - 4:25 PAUSE TO THINK [256] Problem Solving *-**** (Mark K) 4:30 - 5:30 [160] Discrete Math Track * [166] Algebra Track *** [256] Combinatorics on Words Track **-*** (Mark S) [260] Problem Solving ** (Igor) Friday, July 28th ----------------------- 9:00 - 9:55 [160] Discrete Math Track * [166] Algebra Track *** [256] Combinatorics on Words Track **-*** (Mark S) 10:00 - 11:55 [166] Colloquium: Mathematical Genetics David Reich 12:00 - 1:25 Lunch 1:30 - 2:25 [160] Functions of a Complex Variable 2 *** (Mark K, Chris) [166] Monster Equations 2 ** (Igor) [256] Non-Euclidean Geometry 8 * (Dr. Thomas) [260] ABC Conjecture *** (Serge Lang) 2:30 - 3:25 [160] Paradoxes 2 * (Meep) [166] Mental Calculation 2 ** (Sanjoy Mahajan) [256] Differential Equations 2 *** (Madeeha) [260] Generating functions 4 *** (Julian, Mark K) 3:30 - 4:25 PAUSE TO THINK [256] Problem Solving *** (Igor) 4:30 - 5:30 [160] Topology Track **** [166] Number Theory Track ** [256] Problem Solving * (Aytek) Saturday, July 29th ----------------------- 9:00 - 9:55 [160] Functions of a Complex Variable 3 *** (Mark K, Chris) [166] Monster Equations 3 ** (Igor) [256] Non-Euclidean Geometry 9 * (Dr. Thomas) [260] Knots 3 ** (Chris) 10:00 - 11:55 [166] Colloquium: Primes Serge Lang 12:00 - 1:25 Lunch 1:30 - 2:25 [160] BIG numbers: van der Waerden's Theorem * (Julian) [166] Mathematical Genetics 1 ** (David Reich) [256] Some sums ** (Igor) [260] Quadratic Reciprocity *** (Dave) 2:30 - 3:25 [160] Projective Geometry 3 **-*** (Brenda, Mira) [166] Dimensional Physics ** (Sanjoy Mahajan) [256] Virtual Ants 3 * (Evelyne) [260] TBA *** (Serge Lang) 3:30 - 5:30 [Shuswap, lounge] Relays! -------------------------------- TRACKS Discrete Math* is doing probability this week. If you haven't been going, but want to join, now is the time -- we're starting from scratch! NEW! Combinatorics on words ** - *** (Mark Sapir, new faculty). We'll start with a number theory problem, which will lead to words without squares, which will lead to avoidable patterns and symbolic dynamics, which will have some number theory applications (Furstenberg's results). Then we'll talk about geometry of Sturmian words, continued fractions, and again about avoidable patterns. I'm not sure I'll be able to cover all that, but I'll try. NEW CLASSES, SHORT TERM (just Week 3): Virtual Ants* (Evelyne). This class will be an easy-paced introduction to cellular automata. Most of our time will be spent in getting acquainted with virtual ants: observing the nice patterns they create, understanding their behavior and wondering whether marriage really exists in their world. No background is required; the less you know, the more you'll learn! Adding things up* (Julian). We will continue to look at different ways of adding the first n squares. These sessions will be mostly independent of last week's sessions. Big numbers: van der Waerden's Theorem* (Julian). Color the whole numbers red, green, and blue, with one color per number. Is it always possible to find four numbers in an arithmetic progression which are the same color? (Arithmetic progressions are things like 1,4,7,10... or 8,18,28,38,....) Be warned: the numbers in this session are going to be REALLY BIG! If you are scared by incomprehensively humongous numbers, then this session is not for you! Mathematical Paradoxes* (Meep). Inductive paradoxes, Russell's paradox, and others. Things to keep you awake at night! Some Sums **(Igor). Some interesting summations involving binomial coefficients (so, not surprisingly, there'll be some combinatorics as well). Monster Equations ** (Igor). Sure, everyone knows how to solve quadratic equations! But imagine a suspicious-looking 6-th degree polynomial. Or the sum of a 4th and 5th degree roots of two polynomials. Believe it or not, we will solve such monsters -- and beautifully! The class will culminate in deriving formulas (or at least methods) for solutions of the general cubic and quartic polynomial equations. Quintics? Talk to Galois (or Madeeha) about those. Knots ** (Chris). What exactly is a knot? Can we classify knots? How do we tell different knots apart? Can we even tell a square knot from a granny knot? Transcendental Numbers **-*** (Aytek). You probably know that e and pi are irrational, but you may have also heard that they are "transcendental". So what are transcendental numbers, and how can we tell whether a number is transcendental? We will quickly review the notions of countable and uncountable sets, and then proceed to our main goal: to prove that transcendental numbers exist and give some explicit examples. (not e or pi, unfortunately -- that's too hard to prove -- but as we'll see, finding any example at all is not so simple.) Quadratic Reciprocity *** (Dave). A beautiful result from elementary number theory, which is also a prerequisite for an advanced class that Ken Ribet (of Fermat's Last Theorem fame) will give in Week 4. Accessible to anyone who has been following the Number Theory Track. LONG TERM (continuing into Weeks 4 and 5): Projective and Analytic Geometry **-*** (Mira, Brenda the JC). Parallel lines don't meet? You can't see to infinity? That's what =you= think! When you work on the projective plane, you can literally see what happens at infinity; lines and points become (in some sense) interchangeable; ellipses are no different from hyperbolas; and lots of other interesting things happen. We will introduce you to homogeneous coordinates on the projective plane, and prove the theorems of Pappus, Desargues, and Pascal. Prerequisites: the first session has no prerequisites; after that, you'll need some linear algebra, though we'll try to define as much as we can from scratch. Ordinary Differential Equations*** (Madeeha). We will use techniques from calculus and linear algebra to model the behavior and evolution of complicated systems over time. Prerequisites: basic calculus; basic linear algebra (know what it means to multiply matrices and apply them to vectors). Diophantine Equations and Other Topics in Advanced Number Theory*** (Dave). Diophantine equations are equations with integer coefficients whose solutions are also required to be integers. For example, Fermat's Last Theorem states that a certain diophantine equation has no non-trivial solutions. We will explore some of the known techniques for solving such equations. We will not be using anything from the first two weeks of Advanced Number Theory. Functions of a Complex Variable***(Mark K, Chris). Find out how different -- and in many ways beautiful -- calculus is over C than over R. Prerequisites: very solid calculus, basic knowledge of complex numbers. Differential Topology**** (Noah). Manifolds, Differentiable Structures, Intersection Theory. Prerequisites: calculus a must, multivariate calculus a plus.