Ryan Lance

Ryan Lance

email: rjl@math.umd.edu

phone: 301-405-8842

office: CSS 4364 (that's in the old wing of CSS - look for the number above the door)
new office: CSS 4100

office hours: Monday 4-6 in CSS 4100. If this time is inconvenient email me to set up another time.

Mathematical interests: dynamical systems, chaos, nonlinear time series analysis

My advisors: Dr. Hunt and Dr. Yorke

Also collaborating on research with Dr. Ott and Ian Frommer

A bit about my current research:
Transmission Control Protocol (TCP) is the mechanism responsible for controlling the rate of internet connections. There are many mathematical models which describe how this rate changes, some models are stochastic, others are deterministic. We are developing and evaluating deterministic models in terms of their ability to predict network traffic over short time spans. Our models are aimed at capturing the dynamics of an Internet connection which experiences congestion. We are comparing our results to those of other models, focusing on cases of irregular network behavior. An important step in evaluating such models is to analyze actual network traffic data. This is not only to understand what behaviors are present, but also to facilitate new empirical models. Analyzing this type of data is difficult because certain key rate-controlling variables are not directly recorded and must be inferred. We have novel methods of reconstructing such variables leading to a greater understanding of TCP dynamics and perhaps new types of models.

Semester	GA/TA/RA assignments	Classes
Spring 2004	Research, and MATH 411, Advanced Calc with Dr. Yorke	zippy
Fall 2003	Research	Dr. Rudolph's RIT MATH 648D, One-Dimensional Dynamics with Dr. Jakobson
Spring 2003	Research, and Chaos with Dr. Yorke	Dr. Rudolph's RIT
Fall 2002	Research only	Research only, although I am frequenting Dr. Rudolph's RIT
Spring 2002	TA for ENEE 241/MATH 242, Numerical Techniques with Dr. Li	STAT 610, Stochastic Processes with Dr. Lee MATH 648, Wavelets with Dr. Healy
Fall 2001	TA for MATH 141, Calc II with Dr. Boyle	MATH 630, Real Analysis with Dr. Warner AMSC 607 , Advanced Optimization with Dr.O'Leary MATH 730, Topology with Dr. Millson
Spring 2001	Grader/TA for MATH 452, Chaos with Dr. Yorke	MATH 643, Dynamics with Dr. Brin STAT 600, Probability with Dr. Lee STAT 650, Stochastic Processes with Dr. Yang
Fall 2000	Grader for MAPL/MATH 666, Numerical Analysis with Dr. Li Math department tutor for Mathematica (mainly DiffEq and Calc3 stuff)	MATH 642, Dynamics with Dr. Rudolph STAT 600, Probability with Dr. Lee MAPL 660, Scientific Computing with Dr. Liu
Spring 2000		MATH 671, Differential Equations with Dr. Berg MAPL/MATH 667, Numerical Analysis with Dr. Stewart MATH 452, Chaos with Dr. Yorke
Fall 1999		MATH 670, Differential Equations with Dr. Berg MAPL/MATH 666, Numerical Analysis with Dr. O'Leary STAT 420, Probability with Dr. Slud

Other schools I've attended and math programs I've participated in

Summer 1999: DSP (Director's Summer Program) at the NSA (National Security Agency)
1997-1999: Hillsdale College (math major)
Summers 1996 and 97: Summer Mathematics Institute at Oakland University
1993-1997: Kimball High School

Other crap

henon
chaos
chaos2
chaos3
chaos4
occasionally chaotic systems page
occasionally chaotic systems paper
girls=evil
through the trees

2/27/05