ESP Biography
JACOB STEINHARDT, MIT sophomore studying Mathematics
Major: Math College/Employer: MIT Year of Graduation: Not available. 

Brief Biographical Sketch:
I was born in Ithaca, NY but spend most of my precollege life in Virginia, near D.C. I went to Thomas Jefferson High School for Science and Technology for high school, where I was an officer for the math, physics, and computer science teams. I also attended various math and computer science summer programs  the Math Olympiad Summer Program, the USA Invitational Computing Olympiad, and Canada/USA MathCamp. Currently I am interested in mathematics (particularly graph theory and analysis), computer science (particularly algorithms), cognitive science, macroeconomics, and genetics. Past Classes(Look at the class archive for more.)Randomized Algorithms in Splash! 2010 (Nov. 20  21, 2010)
Is it okay if an algorithm works 'almost all' the time? In this class, we'll see how computers can use randomness to run faster. We'll give randomized algorithms for finding medians, for testing if a number is prime, and for finding structures in graphs. Along the way, we'll prove that the probability that our algorithms fail is less than the probability that the computer spontaneously bursts into flames.
Algorithms for Awesome in Splash! 2009 (Nov. 21  22, 2009)
Algorithms rock
But sometimes they don’t make sense
Segmentation fault
Topics: BigO (runtime analysis), sorting, searching, data structures (heaps, trees, lists), hashing, graph theory (Dijkstra’s algorithm, minimal spanning tree).
The Chernoff Bound in Splash! 2009 (Nov. 21  22, 2009)
Flip a coin 100 times, and you've got an 86% probability of getting between 40 and 60 heads. Find out how you can use this fact to calculate the volume of any convex body, and why succeeding is more important than trying.
Bayesian Inference in Splash! 2009 (Nov. 21  22, 2009)
We will study the behavior of a rational agent acting under uncertainty. As a result, we will develop Bayesian inference and use it as a model for human cognition. We will also demonstrate the Bayesian Occam's razor and investigate applications to modelfitting in statistics.
Introduction to Number Theory in Splash! 2008 (Nov. 22  23, 2008)
What is the remainder when you divide $$3999^4000$$ by 4001? What about if you divide 100! by 101? These questions have to do with an area of math called "modular arithmetic", and we will learn how to solve these and other problems.
Formal topics covered: modular arithmetic; arithmetic progressions in mods; inverses; Fermat's and Euler's theorems; Wilson's theorem.
HARDCORE GROUP THEORY in Splash! 2008 (Nov. 22  23, 2008)
Back in the day when things were more hardcore, we proved the OrbitStabilizer Theorem in our heads! And then Burnside's Lemma, and Sylow's First Theorem! Man, you kids have it so easy these days. We classified all groups of order 16, and we liked it! Now the only group you wimps ever deal with is the Dihedral group.
This class is going to be HARDCORE! Think you're up to the challenge?
Algorithms for Awesome in Splash! 2008 (Nov. 22  23, 2008)
Algorithms rock
But sometimes they don't make sense
Segmentation fault
Topics: BigO (runtime analysis), sorting, searching, data structures (heaps, trees, lists), hashing, graph theory (Dijkstra's algorithm, minimal spanning tree).
Game Theory and Mathematical Puzzles in HSSP Fall 2008 (Sep. 13, 2008)
We will look at various games and other mathematical puzzles and come up with methods for solving them. Along the way, we'll develop various mathematical tools, including an introduction to rigorous proof (for example, to show that a given strategy that we think is best is actually the best strategy). Topics to be covered: Nim and other "takeaway" games; proof by contradiction and strategystealing; introduction to graph theory; studentchosen topic.
Algebraic Combinatorics in HSSP (2008)
We will study various algebraic methods in combinatorics, with a focus on Algebraic Graph Theory. Topics to be covered: generating ...
