Statement on Teaching
and Other Non-Research Activities
Since 1996 I have been working with Dr. Michael Poliakoff, Deputy
Secretary of Education in the Commonwealth of Pennsylvania, on a
variety of projects to improve mathematics teaching in Pennsylvania.
I have served as a resource person for the Governor's Institute for
Mathematics Education and other panels and boards.
I have done a lot to bring my research area, mathematical logic and
foundations of mathematics, to the public. My expository article
intended for the general reader and will soon be published by the
Book-of-the-Month Club. My recently published book
Subsystems of Second Order
regarded as a milestone in foundations of mathematics. I run
the Penn State Logic
1997 I have been running the FOM
list, an important scholarly
resource in foundations of mathematics. This mailing list is very
active, with more than 400 subscribers including some of the best
known researchers. In March 2000 I did a talk-radio interview on
Gödel's theorem for the Prodos radio
in Melbourne, Australia.
On the Penn State Mathematics Department computer system, I maintain
some important user software including
and foreign language
software. I have also
helped to develop an extensive on-line User's
I am a committed and dedicated teacher of mathematics. I especially
enjoy teaching calculus classes, and I believe I am successful in
communicating my high enthusiasm for the subject. For several years I
was the coordinator of approximately 10 sections of one of our
calculus courses, Math 230.
I routinely make my lecture notes and other class materials
available on the
web. Over the last few
years I have developed a graph theory course, wherein I use the Maple
symbolic mathematics package for demonstrations and projects in our
web-enabled classrooms. I have also used a web-enabled classroom to
teach an advanced graduate topics course on lambda calculus and the
theory of programming languages.
Because the Department of Mathematics at Penn State University is very
large and diverse, the majority of my advanced undergraduate teaching
and all of my graduate teaching has been in the area of my research
specialty, mathematical logic and foundations of mathematics.
However, I am also quite able and happy to teach courses in many other
areas of mathematics, including any standard undergraduate and
beginning graduate course. I would particularly welcome opportunities
to teach courses in calculus, ordinary and partial differential
equations, differential geometry, algebra, combinatorics,
computational complexity, and formal languages.
- Math 140. Calculus with Analytic Geometry I (4 credits).
Functions; limits; analytic geometry; derivatives, differentials,
applications; integrals, applications.
- Math 141. Calculus with Analytic Geometry II (4 credits).
Derivatives, integrals, applications; sequences and series; analytic
geometry; polar coordinates. Prerequisite: Math 140.
- Math 230. Calculus and Vector Analysis (4 credits).
Three-dimensional analytic geometry; vectors in space; partial
differentiation; double and triple integrals; integral vector
calculus. Prerequisite: Math 141.
- Math 250. Ordinary Differential Equations (3 credits). First-
and second-order equations; numerical methods; special functions;
Laplace transform solutions; higher order equations. Prerequisite:
- Math 251. Ordinary and Partial Differential Equations (4
credits). First- and second-order equations; special functions;
Laplace transform solutions; higher order equations; Fourier series;
partial differential equations. Prerequisite: Math 141.
- Math 411. Ordinary Differential Equations (3 credits). Linear
ordinary differential equations; existence and uniqueness questions;
series solutions; special functions; eigenvalue problems; Laplace
transforms; additional topics and applications. Prerequisites: Math
230; Math 250 or 251.
- Math 412. Fourier Series and Partial Differential Equations (3
credits). Orthogonal systems and Fourier series; derivation and
classification of partial differential equations; eigenvalue
function method and its applications; additional topics.
Prerequisites: Math 230; Math 250 or 251.
- Math 421. Complex Analysis (3 credits). Infinite sequences
and series; algebra and geometry of complex numbers; analytic
functions; integration; power series; residue calculus; conformal
mapping, applications. Prerequisites: Math 230; Math 401 or 403.
- Math 457. Introduction to Mathematical Logic (3 credits).
Propositional logic, first-order predicate logic, axioms and rule of
inference, structures, models, definability, completeness,
compactness. Prerequisites: Math 311.
- Math 459. Computability and Unsolvability (3 credits). An
introduction to the theory of recursive functions; solvable and
unsolvable decision problems; applications. Prerequisite: Math 311.
- Math 485. Graph Theory (3 credits). Introduction to the
theory and applications of graphs and directed graphs. Emphasis on
the fundamental theorems and their proofs. Prerequisite: Math 311.
- Math 557. Mathematical Logic (3 credits). The predicate
calculus. Completeness and compactness. Gödel's first and second
incompleteness theorems. Introduction to model theory. Introduction
to proof theory. Prerequisite: Math 435 or 457 or equivalent.
- Math 558. Foundations of Mathematics I (3 credits).
Decidability of the real numbers. Computability. Undecidability of
the natural numbers. Models of set theory. Axiom of choice.
Continuum hypothesis. Prerequisite: any 400-level Math course or
- Math 559-560. Recursion Theory I, II (3 credits each).
Recursive functions; degrees of unsolvability. Hyperarithmetic
theory; applications to Borel combinatorics. Computational
complexity. Combinatory logic and the lambda calculus.
Prerequisite: Math 459 or 557 or 558.
- Math 561-562. Set Theory I, II (3 credits each). Models of
set theory. Inner models, forcing, large cardinals, determinacy.
Descriptive set theory. Applications to analysis. Prerequisite:
Math 557 or 558.
- Math 563-564. Model Theory I, II (3 credits each).
Interpolation and definability. Prime and saturated models.
Stability. Additional topics. Applications to algebra.
Prerequisite: Math 557.
- Math 565. Foundations of Mathematics II (3 credits).
Subsystems of second order arithmetic. Set existence axioms.
Reverse mathematics. Foundations of analysis and algebra.
Prerequisite: Math 557 and 558.
- Math 574. Topics in Logic and Foundations (3-6 credits; may be
taken repeatedly). Topics in mathematical logic and the foundations
of mathematics. Prerequisite: Math 558.
Statement on Teaching
and Other Non-Research Activities
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