I am teaching two courses this semester (Fall 2017): Calculus II and Advanced Calculus. Here are links to the course pages:
I have taught a 300-level Dynamical Systems course on four occasions. The course is at an introductory level — suitable for students coming right out of Linear Algebra with ODE's, and has a heavy focus on the computational and experimental aspects of the subject. Students in the course spend much of their time learning to use Mathematica
to explore dynamical systems. Here is my web page for the last time I taught the course:
I taught an advanced calculus course in the fall of 2016. The course focused on the derivative as a linear transformation, parameterization of manifolds, and integration on manifolds. Here is the web page for the course:
I taught a mathematical modeling course in the fall of 2016. The course focused on modeling with ordinary differential equations and difference equations, and we explored applications to growth of organisms and allometric laws, population dynamics, HIV modeling, and climate modeling. Here is the web page for the course:
I taught a 300-level topology course on two occasions. This course serves as an introduction to both point-set and algebraic topology, and typically most of the students in the class are junior and senior math majors. Here are my old course pages:
I taught a 300-level differential geometry course on two occasions. The course requires only multivariable calculus as a prerequisite, and most of the students who take the course are junior or senior math or physics majors. I used Pressley's Elementary Differential Geometry
as a textbook the first time I taught the course, and Banchoff and Lovett's Differential Geometry of Curves and Surfaces
the second time. Here are my old course pages for this course:
I taught a cryptology course for non-majors (Math 108: Secret Codes) in the spring of 2015. Students in the course make heavy use of computers, specifically Microsoft Excel, to decode encrypted messages. Here is the course page:
I taught first-year seminar (FYSEM) in the spring of 2017. The students read works by Emerson, Aristotle, Neitzsche, Augustine, Malcolm X, Aeschylys, Mary Shelley, Sor Juana Inés de la Cruz, and James Joyce. Here is my course page:
I have taught Bard's one-semester Abstract Algebra on three occasions. I use Gallian's book for this course,
but I sometimes add additional material (e.g. automorphisms of graphs, matrix representations
of groups, etc.). Here are my old course pages:
I taught a number theory course in the spring of spring of 2016. The course had a mix of theoretical content and computational applications.
I taught Bard's one-semester Real Analysis course in the spring of 2012.
I also taught an advanced analysis course in the spring of 2015. This mostly concentrated on measure theory and related topics, with some material on rigorous multivariable calculus towards the end.
Calculus & Linear Algebra
I taught my first calculus class at Binghamton University in the spring of 1999, and I have since taught calculus and linear algebra courses at Cornell University, Texas A&M University, and Bard College. Here are links to some of my old course pages here at Bard:
I have twice taught the second-semester introductory physics course here at Bard. The course covers electricity, magnetism, and optics:
Proofs & Fundamentals
I taught Proofs & Fundamentals in the fall of 2010. This course is an introduction to formal proofs, logic, and set theory, and is usually taken by sophomore math majors. Here is the old course page:
I supervised the 2-credit mathematics problem-solving seminar in the fall of 2009. Here is the course page: