Professor of Mathematics
Degrees, Specializations & Interests:
A.B., University of Michigan; M.A., Ph.D., University of Wisconsin;
Spring 2010 Courses:
Courses offered in the past four years.
▲ indicates offered in the current term
▹ indicates offered in the upcoming term[s]
FYSE 1229 - Discovering Infinity
"Infinity" has intrigued poets, artists, philosophers, musicians, religious thinkers, physicists, astronomers, and mathematicians throughout the ages. Beginning with puzzles and paradoxes that show the need for careful definition and rigorous thinking, we will examine the idea of infinity within mathematics, discovering and presenting our own theorems and proofs about the infinite. Our central focus will be the evolution of the mathematician’s approach to infinity, for it is here that the concept has its deepest roots and where our greatest understanding lies. In the final portion of the course, we will consider representation of the infinite in literature and the arts. (four years of secondary school mathematics) 3 hrs. sem.
INTD 1065 / FYSE 1280 - Breaking the Code: Alan Turing
Breaking the Code: The Enigma of Alan Turing
British mathematician Alan Turing broke the Nazis prized Enigma cipher, created the foundations of modern computer science, and pioneered the fields of artificial intelligence (“Can Machines Think?”) and neural networks. Turing was arrested for homosexuality and forced to undergo hormone treatments perhaps leading to his apparent suicide by cyanide poisoning. The British government only recently apologized for its "appalling" treatment of Turing. His brilliant achievements and tragic death are the subject of biographies, essays, plays, novels, and films. We will explore the life and works of this remarkable individual which will be celebrated throughout 2012, the centennial of his birth. (This course is not open to students who have taken FYSE 1280)
Fall 2009, Winter 2010, Winter 2012
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.
MATH 0122 - Calculus II
A continuation of MATH 0121, may be elected by first-year students who have had an introduction to analytic geometry and calculus in secondary school. Topics include a brief review of natural logarithm and exponential functions, calculus of the elementary transcendental functions, techniques of integration, improper integrals, applications of integrals including problems of finding volumes, infinite series and Taylor's theorem, polar coordinates, ordinary differential equations. (MATH 0121 or by waiver) 4 hrs. lect./disc.
Fall 2010, Fall 2012
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 2010, Fall 2012
MATH 0223 - Multivariable Calculus
The calculus of functions of more than one variable. Introductory vector analysis, analytic geometry of three dimensions, partial differentiation, multiple integration, line integrals, elementary vector field theory, and applications. (MATH 0122 or MATH 0200 or by waiver) 3 hrs. lect./disc.
MATH 0225 - Topics in Linear Alg & Diff Eq ▲
Topics in Linear Algebra and Differential Equations
Topics may include diagonalization of matrices, quadratic forms, inner product spaces, canonical forms, the spectral theorem, positive matrices, the Cayley-Hamilton theorem, ordinary differential equations of arbitrary order, systems of first-order differential equations, power series, and eigenvalue methods of solution, applications. (MATH 0200 or by waiver) 3 hrs. lect./disc.
Spring 2011, Fall 2013
MATH 0315 - Mathematical Models
Mathematical Models in the Social and Life Sciences
An introduction to the role of mathematics as a modeling tool and an examination of some mathematical models of proven usefulness in problems arising in the social and life sciences. Topics will be selected from the following: axiom systems as used in model building, optimization techniques, linear and integer programming, theory of games, systems of differential equations, computer simulation, stochastic process. Specific models in political science, ecology, sociology, anthropology, psychology, and economics will be explored. (MATH 0200 or waiver) 3 hrs. lect./disc.
Spring 2011, Spring 2013
MATH 0318 - Operations Research ▲
Operations research is the utilization of quantitative methods as an aid to managerial decisions. In the course, several of these methods will be introduced and studied in both a mathematical context and a physical context. Topics included will be selected from the following: classification of problems and the formulation of models, linear programming, network optimization, transportation problems, assignment problems, integer programming, nonlinear programming, inventory theory, and game theory. (MATH 0200 or waiver)
Spring 2012, Fall 2013
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.
Fall 2011, Spring 2012
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, Fall 2010, Winter 2011, Spring 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.
Spring 2010, Spring 2012