Professor of Mathematics
Degrees, Specializations & Interests:
B.S., The Ohio State University; Ph.D., Princeton University;
(Combinatorial Low-dimensional Topology)
Courses offered in the past four years.
▲ indicates offered in the current term
▹ indicates offered in the upcoming term[s]
CSCI 1099 - C++ and the STL
C++ and the STL
In this course, we will work from students’ existing knowledge of Java to enter into the realm of the C++ language. Students will work on I/O and algorithm design in C++ through a combination of self-contained programming problems and larger projects. In the process, students will gain a core working knowledge of C++ and the Standard Template Library, including the Boost libraries if time permits. (CSCI 0101)
CSCI 1100 - Graphical Bots
FYSE 1380 - Information & Structure
Information & Structure
In this seminar we will study the relationship between raw information and the structures that are used to organize, translate, transmit, and make sense of it. We will consider information broadly, ranging from physical to virtual and from analog to digital, as it is acted upon by structures including physical, chemical, biological, physiological, and neurological phenomena, as well as by the human constructs of language, art, mathematics, engineering, and computer science. Along the way we will encounter the concepts of entropy, approximation, noise, and ambiguity that are inherent in the information that surrounds us in both our academics and daily lives. 3 hrs. sem.
INTD 0500 - Independent Study
MATH 0121 - Calculus I ▲
Introductory analytic geometry and calculus. Topics include limits, continuity, differential calculus of algebraic and trigonometric functions with applications to curve sketching, optimization problems and related rates, the indefinite and definite integral, area under a curve, and the fundamental theorem of calculus. Inverse functions and the logarithmic and exponential functions are also introduced along with applications to exponential growth and decay. 4 hrs. lect./disc.
Fall 2009, Spring 2010, Spring 2013, Fall 2013
MATH 0200 - Linear Algebra
Matrices and systems of linear equations, the Euclidean space of three dimensions and other real vector spaces, independence and dimensions, scalar products and orthogonality, linear transformations and matrix representations, eigenvalues and similarity, determinants, the inverse of a matrix and Cramer's rule. (MATH 0121 or by waiver) 3 hrs. lect./disc.
Fall 2011, Spring 2012
MATH 0247 - Graph Theory
A graph (or network) is a useful mathematical model when studying a set of discrete objects and the relationships among them. We often represent an object with a vertex (node) and a relation between a pair with an edge (line). With the graph in hand, we then ask questions, such as: Is it connected? Can one traverse each edge precisely once and return to a starting vertex? For a fixed k/, is it possible to “color” the vertices using /k colors so that no two vertices that share an edge receive the same color? More formally, we study the following topics: trees, distance, degree sequences, matchings, connectivity, coloring, and planarity. Proof writing is emphasized. (MATH 0122 or by waiver) 3 hrs. lect./disc.
MATH 0323 - Real Analysis
An axiomatic treatment of the topology of the real line, real analysis, and calculus. Topics include neighborhoods, compactness, limits, continuity, differentiation, Riemann integration, and uniform convergence. (MATH 0223) 3 hrs. lect./disc.
MATH 0325 - Complex Analysis
An introduction to functions of a complex variable. Mappings of the complex plane, analytic functions, Cauchy Integral Theorem and related topics. (MATH 0223 or by waiver) 3 hrs. lect./disc.
MATH 0423 - Topics in Analysis
Topics in Analysis
In this course we will study advanced topics in real analysis, starting from the fundamentals established in MA401. Topics may include: basic measure theory; Lebesgue measure on Euclidean space; the Lebesgue integral; total variation and absolute continuity; basic functional analysis; fractal measures. (MATH 0323 or by waiver) 3 hrs. lect./disc.
MATH 0432 - Elementary Topology
An introduction to the concepts of topology. Theory of sets, general topological spaces, topology of the real line, continuous functions and homomorphisms, compactness, connectedness, metric spaces, selected topics from the topology of Euclidean spaces including the Jordan curve theorem. (MATH 0122 or by waiver) 3 hrs. lect./disc.
MATH 0500 - Advanced Study ▲ ▹
Individual study for qualified students in more advanced topics in algebra, number theory, real or complex analysis, topology. Particularly suited for those who enter with advanced standing. (Approval required) 3 hrs. lect./disc.
Fall 2009, Winter 2010, Spring 2010, Winter 2011, Fall 2011, Winter 2012, Spring 2012, Fall 2012, Winter 2013, Spring 2013, Fall 2013, Spring 2014
MATH 0704 - Senior Seminar
Each student will explore in depth a topic in pure or applied mathematics, under one-on-one supervision by a faculty advisor. The course culminates with a major written paper and presentation. This experience emphasizes independent study, library research, expository writing, and oral presentation. The goal is to demonstrate the ability to internalize and organize a substantial piece of mathematics. Class meetings include attendance at a series of lectures designed to introduce and integrate ideas of mathematics not covered in the previous three years. Registration is by permission: Each student must have identified a topic, an advisor, and at least one principal reference source. 3 hrs. lect./disc.