Ergodic Theory & Dynamical Systems
Full-year introductory course in Dynamical Systems
with emphasis on Ergodic theory
(studies measure-preserving maps of a space to itself)
and elementary Topological Dynamics
(studies continuous maps
of a compact metric-space to itself)
As time permits, Symbolic or Differential dynamics may be
studied, particularly in the 2nd
from Aut. 2000.)
Probability & Potential Theory 1
MWF2 in LIT217.
Probability & Potential Theory 2
Autumn 1997. Has elementary results on
connectedness, compactness and metric spaces; several were written by my students.
, the Spring 1998 continuation.
Introduction to Number Theory
Chinese Remainder Thm,
Fermat SoTS & Lagrange 4-square theorems,
basic cryptography (Diffie-Hellman, RSA)
Assumes no previous knowledge of Number Theory.
this ran as a full-year course
(using Special topics MAT4930 for the 2nd course-number).
The 2nd semester emphasized Cryptography.
Spring 2000 & Spring 2001,
was a two-semester course.
Number Theory 2
This course is a continuation of elementary algebraic number theory. It
assumes that the student is comfortable with the notion
n mod k
, what a prime number
is, the Chinese Remainder Theorem, and the Legendre symbol.
Roughly it assumes the first half of Strayer's
Elementary Number Theory
the first 3 chapters of
An Introduction to the Theory of Numbers
by Niven, Zuckerman and Montgomery.
NT & Mathematical Cryptography
[NT&Crypto] Spring 2016
Assumes only a basic knowledge of modular arithmetic, and the Euler
phi-function. Reading the first chapter or two of any standard text, e.g
Stayer's text, or Silverman's “Friendly” text.
NT&Crypto [Spring 2013, Spr. 2014]
Intro. to Elliptic Curves [Aut. 2007].
Combinatorics I & II
Autumn 2017, Spring 2018.
first semester, Autumn 2012.
, second semester, in Spring 2013.
See also the
Autumn 1994, Spring 1995
Abstract Algebra 1 [Spring 2008 and Aut. 2005]
Group theory, with some discussion of Fields and Rings.
Sets and Logic
(SeLo) [Aut. 2013]
Teaches students to read and produce
proofs, and learn the basic language of
(SeLo) [Spring. 2012]
(SeLo) [Aut. 2011]
which also has Autumn 2009
and Spring 2008
Numbers & Polynomials
(NaPo) [Spring 2006]
Text: Numbers & Polynomials
by Prof. Kermit Sigmon.
This course is run
, meaning that students prove
all theorems, with enlightened guidance from the Professor.
Computational Linear Algebra [Aut. 2007]
Introduces Matrices, determinants, the Gauss-Jordan algorithm... .
(theoretical) Linear Algebra [Aut. 2005]
MAS4105, which is a proof-based course.
A proof-based course covering a superset of: Theorems on Triangles
(centroid, in-center, circum-center, ortho-center, Euler-line,
circles (Central-angle thm, Power-of-a-point)
ruler/straightedge contructions and dissections of polygons.
Matrix multiplication will be introduced for easy descriptions of
transformations preserving Euclidean theorems. Time permitting,
elem. Projective Geometry will be introduced, since many PG thms are also EG thms.
(Advanced Calc for Engineers and Scientists)
Real Analysis in Euclidean spaces
(Advanced Calculus, Theoretical)
Real Analysis in metric spaces
This is the AdvCalc
for those intending graduate work in Mathematics.
Modern Analysis I
A full-year course in Real Analysis
It uses the highly-regarded
text, and covers some
Honors Calculus I [Aut. 2001]
Introductory calculus course requiring careful exposition by the students.
Calculus II [Spring 2010]
Careful treatment of 1-dimensional calculus, with emphasis on Taylor's
theorem and Taylor series.
(Also has notes from Autumn 1995, Calc2.)
Rigorous treatment of multi-dimensional calculus.
(Has notes from Autumn 2003&2002, and from Spring 2002&1999.)
Elementary Differential Equations [Autumn 2013]
for the bright, motivated, hard-working student.
Also has material from 3 other incarnations of the course.
Survey of Calculus 2 [Aut. 2000]
Has exams from Spring 2000
and Aut. 1999