Biography

I am an incoming graduate student in the mathematics department at the University of Pennsylvania. I obtained a B.S. in Mathematics and a minor in Philosophy at the Massachusetts Institute of Technology in June 2008. This page includes links to my academic coursework over the past four years, as well as some published material and any related or un-related research. I might actually maintain the following:

Blog - A Mental Space Odyssey

Published

Soliton Solutions of Integrable Systems and Hirota's Method (HCMR, Research with Aliaa Barakat)

Godel, Escher, Bach: A Mental Space Odyssey (MIT OCW, with Curran Kelleher)

A Formal Treatment of Deterministic Fractals (MIT OCW, 18.100C with Dan Ciubotaru)

Academic Coursework 

Spring 2008 

18.952 - Theory of Differential Forms - Victor Guillemin

Problem Sets 1, 2, 3, 4, 5, 6, 7-8, 9, 10, 11

18.821 - Project Laboratory in Mathematics - Paul Seidel

Coloring Knots (with Matt Gordon and Michael Forbes)

Generating Matrices (with Matt Gordon and Michael Forbes)

Polynomial Images of Circles (with Matt Gordon and Michael Forbes)

24.260 - Topics in Philosophy: David Lewis - Agustin Rayo

Complex Systems and Folk Physics 2.0: The Utility of Causation

STS.002 - Toward the Scientific Revolution - Robb Eason

An Analysis of Plato's Timaeus

The Condemnation of 1277 and its Interpretation

Bacon and Kuhn: A Paradigm Analysis of the Scientific Revolution

Fall 2007

18.904 - Seminar in Topology: Algebraic Topology - Pokman Cheung 

Introductory Lecture

De Rham Cohomology

18.101 - Analysis on Manifolds - Brett Parker

24.111 - Philosophy of Quantum Mechanics - Brad Skow 

Homeworks 1, 2, 3, 4, 5, 6, 7 

21W.775 - Writing About Nature and the Environment - Karen Boiko

How I Learned to Stop Worrying and Love Writing

A Naturalist's Notebook: A Truly Holey Terrace

Kudzu

Transcending and Descending into Nature

A Metaphysical Pilgrim

Science and Green Buddhism

On the Written Road

Fall 2006 - Spring 2007

Part IB Mathematical Tripos at Cambridge University 

Linear Algebra, Quantum Mechanics, Mathematical Methods, Analysis II, Markov Chains, Groups-Rings-Modules, Geometry, Complex Analysis/Methods, Fluid Dynamics, Metric and Topological Spaces  

CATAM

Project 1.1 - Ordinary Differential Equations

Project 1.2 - Public Key Cryptography

Project 2.3 - Chaos in ABC Flows

Project 2.4 - The Diffusion Equation 

Spring 2006

18.100C - Analysis - Dan Ciubotaru

Musings on Compactness

Completion of a Metric Space

A Formal Treatment of Deterministic Fractals: Paper

A Formal Treatment of Deterministic Fractals: Presentation - PDF

A Formal Treatment of Deterministic Fractals: Presentation - PPT

18.354J - Nonlinear Dynamics and Chaos II: Continuum Mechanics - Matthew Hancock

Diffusion on Fractals: Paper

Diffusion on Fractals: Presentation - PDF

Diffusion on Fractals: Presentation - PPT

8.044 - Statistical Physics

24.251 - Philosophy of Language - Agustin Rayo

Kripke and Intuitions of Natural Languages

Giving Up Metaphysical Glue 

SP.258 - Godel, Escher, Bach - Rob Speer

Independent Activities Period 2006

New England Complex Systems Intensive Course - Yaneer Bar-Yam

Information Theoretic and Complexity Considerations in Four Classes of Cellular Automata (with A. Alavizadeh, C. Kelleher, C. Lewiston, A. Resnick, E. Solis, Y. Bar-Yam)

Presentation

Fall 2005

6.001 - Structure and Interpretation of Computer Programs

6.041 - Probabilistic Systems Analysis

18.353J - Nonlinear Dynamics and Chaos I

18.511 - Mathematical Logic and Recursion Theory

24.118 - Paradox and Infinity

Spring 2005

18.03 - Ordinary Differential Equations

8.022 - Honors Electricity and Magnetism

24.00 - Problems of Philosophy

1.016 - Communicating Complex Environmental Issues - Terrascope

Fall 2004

18.02 - Multivariable Calculus

8.012 - Honors Classical Mechanics

3.091 - Introduction to Solid State Chemistry 

24.04J - Justice

12.000 - Solving Complex Problems - Terrascope