Teaching

Courses Developed

Iona College

Demystifying Numbers: Over the 2016-2017 Academic Year, I worked with the other members of the Math department to develop MTH 125. This is a new core offering fulfilling the Mathematics Core requirement for those students not planning on majoring in Science or Business. The focus of this course is on introductory ideas from number theory, including modular arithmetic, prime numbers and the infinitude of primes, the irrationality of the square root of 2, and some basic recursive sequences and their properties. I played a significant role in the development of the syllabus and topics list of this course, and taught the inaugural section in Fall 2017. I have since taught this course 1-2 times per academic year.

Duke University

Tropical Geometry: This is intended to be an undergraduate seminar course on tropical geometry that would be accessible to students who have taken abstract algebra. While I have not had the opportunity to teach this course, I did use the designed syllabus as an outline when working on a research project with an undergraduate student on the properties of linear algebra under tropical addition and multiplication.

Courses Revised

Iona College

Discrete Mathematics: In Fall 2015, I worked to redesign the MTH 310 syllabus and topics list. This was done in close consultation with, and with significant feedback from, my colleagues in both the math department and those in the computer science department. The main purpose was to insure necessary topics for the computer science majors taking the course were included. The redesigned course, which is now cross-listed as a computer science course, is currently being taught.

Courses Taught

Iona College

Mathematical Thinking (9 sections): One of the core mathematics courses for students of business and the liberal arts, this course provides an overview of the mathematics used to solve problems which arise in modern society, business and science. The topics covered include probability, statistics, mathematics of finance, and other contemporary topics. The emphasis is on decision making, critical thinking and conceptual understanding.

Demystifying Numbers (1 section): One of the core mathematics courses for students of the liberal arts, this course provides an overview of numbers in their different formulations, interpretations and applications. Students will see numbers in new and unusual ways. They will see interesting numbers arising in nature, the arts and cyber security, among other applications. These topics will be approached from a problem solving as well as critical thinking point of view.

Brief Calculus (1 section): A basic introduction to selected topics from calculus. Topics include elementary functions, rates of change, the derivative, differentiation, and integration with special emphasis on a variety of applications.

Calculus I (1 section): Study of functions, continuity, limits, differentiation of algebraic and transcendental functions; mean value theorem, differentials, anti-derivatives, areas by integration, areas as limits of sums, the definite integral, fundamental theorem of the calculus, and differentiation and integration of trigonometric functions.

Calculus II (1 section): The continuation of Calculus I. Topics include area under the curve, antiderivatives, techniques of integration, applications of the definite integral, and numerical techniques, improper integration, and Taylor polynomials.

Applied Discrete Mathematics (1 section): An introduction to discrete mathematics and its applications. Topics selected from combinatorics, induction and recursion, logic and proof, algorithms and their analysis, discrete structures, and elements of modern applied algebra. Emphasis on the use of mathematics as a tool to model and solve applied problems from variety of disciplines. For students interested in computer science and modern applied mathematics.

Discrete Mathematics (3 sections): Set theory and mathematical logic, combinatorics, binomial and multinomial theorems, graph theory, digraphs and matrices, Boolean algebras, Boolean functions, and switching theory.

Linear Algebra (1 section UG, 1 section Grad IS): Introduction to vectors, vector fields, vector space Rn, bases of Rn, subspaces, projections, matrices and determinants, linear mappings, matrix representations of linear mappings, matrices and systems of linear equations, rank, existence and uniqueness of solutions, eigenvalues and eigenvectors.

Theory of Numbers (1 section): Study of the more important properties of the natural number system: divisibility, primes, recurring series, congruences, quadratic residues, Diophantine equations.

Mathematical Modeling (1 section IS): This course explores the process of constructing and implementing mathematical models for a large variety of situations. Models from the physical life and social sciences will be examined using deterministic and probabalistic methods, both continuous and discrete. A strong emphasis will be placed on independent and cooperative work and presentation of results in oral and written form. Capstone experience in applied mathematics.

Abstract Algebra (1 section Grad IS): Study of structures of groups, rings, fields, polynomial forms and functions. Appropriate applications to content of high school algebra course.

Duke University

Laboratory Calculus and Functions I (2 sections): A study of functions with applications, and an introduction to differential calculus, with a laboratory component. Topics include a review of algebra and functions, mathematical modeling with elementary functions, rates of change, inverse functions, logarithms and exponential functions, the derivative, graphical interpretations of the derivative, optimization, related rates.

Laboratory Calculus and Functions II (1 section): A continuation of Laboratory Calculus and Functions I. Topics include zeros of functions, antidifferentiation, initial value problems, differential equations, Euler's method, slope fields, review of trigonometry, modeling with trigonometric functions, Riemann sums, the Fundamental Theorem of Calculus, integration by substitution, integration by parts, separation of variables, systems of differential equations.

Multivariable Calculus (1 section): Partial differentiation, multiple integrals, and topics in differential and integral vector calculus, including Green's theorem, the divergence theorem, and Stokes's theorem.