D. Phil. (Doctorate), University of Oxford, 2002
Dr. Raines received his doctorate in mathematics from Oxford University where he was a member of St. Edmund's Hall. He travels extensively to work with collaborators in the UK, Italy, and Croatia. He was born and raised in Texas. He is married with two children, and loves to cook and play games of all sorts.
Academic Interests and Research:
Dr. Raines research is in the topology of pathological spaces that arise in dynamical systems. He is also interested in applications of topology to non-deterministic dynamical systems that arise in mathematical economics.
"A compact metric space that is universal for orbit spectra of homeomorphisms," joint with C. Good, S. Greenwood and C. Sherman, Advances in Mathematics (2011) to appear 1�14.
"Fixed points imply chaos for a class of differential inclusions that arise in economic models," joint with D. Stockman, Transactions of the AMS (2011) to appear 1--18.
"Basins of measures on inverse limit spaces for the induced homeomorphism," joint with J. Kennedy and D. Stockman, Ergodic Theory and Dynamical Systems 30 (2010) 1119--1130.
"A Characterization of Omega-limit sets in shift spaces," joint with A. Barwell, C. Good and R.W. Knight, Ergodic Theory and Dynamical Systems 30 (2010), 21--31.
"A Classification of inverse limit spaces of tent maps with a non-recurrent critical point," joint with S. Stimac, Algebraic and Geometric Topology (2009), 1--34.
NSF Grant DMS 0604958: "Classifying a model for the Henon Attractor: a U.S. - Croatia Collaboration"
Former Ph.D. Students:
Courses taught at Baylor:
- MTH 1309 - Calculus for Business Students
- MTH 1321 - Calculus I
- MTH 1322 - Calculus II
- MTH 3312 - Foundations of Combinatorics and Algebra
- MTH 3323 - Introduction to Analysis
- MTH 4326 - Advanced Calculus I
- MTH 4327 - Advanced Calculus II
- MTH 5323 - Theory of Functions of Real Variables I
- MTH 5324 - Theory of Functions of Real Variables II
- MTH 5330 - Topology
- MTH 5331 - Algebraic Topology I
- MTH 5332 - Algebraic Topology II
- MTH 6V30 - Advanced topics in Topology
- MTH 6V23 - Advanced topics in Analysis
- MTH 5V23 - Special topics in Analysis
- MTH 6V99 - Dissertation