Linear Algebra I
MWF 10:30 - 11:20a: Sturges 103
Prerequistes: MATH 221
Linear algebra is the algebra of
anything resembling straight lines. Therefore, linear algebra is
based on the most basic of algebraic fundamentals. And then
planes are like lines. And lines in three dimensions are like
lines in two dimensions. But they're a little more
complicated. And away we go. Linear algebra is about the
simplest geometry (linear) of higher dimensions. We will rely
upon visualisation in order to extend familiar concepts to unfamiliar
territory. Along the way we will also study vectors and matrices
as valuable notation for working in different dimensions.
Topics
in
Secondary Mathematics
TR 10:00 - 11:15a: South 336
This course, whch is intended for the
mathematics major who is enrolled in the secondary education program,
provides a bridge and establishes connections between the college level
mathematics required of the mathematics major and the mathematics of
the secondary school curriculum.
MATHEMATICS 348
Oral
Presentation & Research Seminar
M 2:30-3:45p: Sturges 208a
This is a most unusual mathematics
class, in that
you are not responsible for learning any mathematics. You will be
preparing a library research project on a topic in mathematics and
presenting several presenations to the class. We will also
discuss several issues related to these perfmance outcomes. These
may include some of the following: typesetting in mathematics,
bibliographic references in mathematics, and talk styles in
mathematics. This class is about producing products
(presentations and paper) and not about learning mathematics.
MATHEMATICS 380
Topics in Mathematics: Galois Theory
MWF 11:30a - 12:20p: ISC 136
Prerequisite: Math. 330 or 319
In this course we will explore the question of
solvability of polynomials. We will consider finding and
permuting roots from Galois’ original historical
perspective. Along the way we will settle some of the classical
construction problems and see the power of applying seemingly
theoretical ideas to the more practical question of finding roots of
polynomials.
- Past Courses Taught
at Geneseo
Department
Professional Activities
I am an active member of the Mathematical Association of
America.
In particular, I am the liaison coordinator and the chair
of the Seaway NExT Steering Committee. I am also a member of
the
American Mathematical Society.
Areas of research
- Low-dimensional Topology
- Knots, Links, and 3-manifolds
Current projects
I am currently pursuing
several research projects. The newest of the projects is an
exploration of the role of Euclid's Fourth Postulate: "All
right
angles are equal." The older of these projects
consists of investigating how the Casson-Walker-Lescop
3-manifold
invariant changes when modifying the presenting
link for a 3-manifold. This project has evolved into studying
questions of the Ohtsuki invariants of rational homology spheres, and
questions of the space of finite type
invariants for links of three or more components. Another
long-term project is to study
symmetries of links.
In particular I am examining a refinement of unlinking number
accounting for which components are involved in each of the
crossing changes, a so-called coloured unlinking number. Finally, I am
examining comparisons and connections between mathematician
Evariste Galois and composer Hector Berlioz.
Areas of interest
Prepared Talks
- Kaleidoscopic Mathematics
- The World That We See: Perspective and Projective
Geometry
- Mathematics and Music
- The Fourth Dimension and Science Fiction
- A Concise History of Calculus
- Mathematics of the Calendar
- An Introduction to Knot Theory
- Golden Rectangles Everywhere
- Evariste Galois and Hector Berlioz
- Evariste Galois and the Solution of Algebraic Equations
Publications
A Type 2 Polynomial Invariant of Links Derived from the
Casson-Walker Invariant, Journal of Knot Theory and Its
Ramifications, Vol. 8, No. 4 (1999) 491-504.
The
Casson-Walker-Lescop invariant and link invariants, Journal
of
Knot Theory and Its Ramifications, Vol. 14, No. 4 (2005) 425-433.
Bandpass
moves and the Casson-Walker-Lescop invariant, New
York Journal of Mathematics, Vol. 10 (2004), 231-247.
Modern Geometry
and the End of
Mathematics, in MAA notes #68 From
Calculus to Computers: Using
the Last 200 Years of Mathematics History in the Classroom,
2005.
Academic history
The Past
Project NExT
Seaway NExT Steering Committee Chair 2008-
Project
NExT
2000-2001 fellow (aka
"Gold Dot"
).
Co-organized "Creating and Teaching Interdisciplinary Courses" session
at Joint Meetings in New Orleans. January 11, 2001.
Conferences
AMS national meeting in New Orleans, January 10 - 13, 2001.
"Colored Unlinking",
special session on geometry and
topology of low dimensional manifolds.
"Temperament of Mind: Hector Berlioz and Evariste Galois",
contributed paper.
AMS sectional meeting in Las Vegas, April 21 - 22, 2001.
Co-organized special
session on the topology of
links.
MAA national MathFest in Madison, August 2 - 4, 2001.
"Infiltrating Preservice
Elementary School
Mathematics with
History", contributed paper session on the use of history in the
teaching of mathematics.
MAA national MathFest in Burlington, VT, July 31 - August 4,
2002
"Modern Geometry",
contributed paper session on the
use of
recent history of mathematics in teaching.
"Welcome to Mathematics: A Cornerstone Experience",
contributed
paper session on the role of proof in teaching mathematics.
MAA national MathFest in Boulder, CO, July 30 - August 2, 2003
"Days are Numbers:
The Mathematics of the
Calendar",
general contributed paper session.
"Honesty is the Best Philosophy", contributed paper session on
innovations in quantitative literacy.
MAA national MathFest in Providence, RI, August 11 - 15, 2004
Co-organised session on
"Extracurricular Mathematics"
MAA national MathFest in Albuquerque, NM, August 3 - 6, 2005
"Why Are We Math Majors?",
contributed
paper session on current issues in mathematics education courses.
"Greatest Hits of Mathematics",
general
contributed paper session.
MAA national MathFest in
Knoxville, TN,
August 9 - 12, 2006
"A Little Moore
Probability",
contributed
paper session on current issues in mathematics education courses.
"Kaleidoscope", general contributed paper session.
MAA national MathFest in San Jose, CA, August 2 - 5, 2007
"Where are we from? - An
entire class
project", contributed paper session on getting students to discuss and
to write about mathematics.
"Four dimensional tic-tac-toe on a torus - the game of SET", general
contributed paper session
5th annual Midwest Undergraduate Mathematics Symposium at Simpson
College, Indianola, IA. April 2008
"Game: SET -
Math", invited plenary address
MAA national MathFest in Madison, WI, July 30 - August 2, 2008
"Vedic Decimal Patterns",
contributed
paper session on interesting topics in history of mathematics that
enchance the teaching and learning of mathematics.
"Place Value Airthmetic via Polynomials", contributed paper session on
innovations in mathematics education.
MAA national MathFest in Portland, OR, August 5 - 8, 2009
"Counting Student
Groupings",
contributed paper session on fascinating examples from combinatorics,
number theory, and discrete mathematics.
"The Mathematical Fiction and Exposition of Rudy Rucker", general
contributed paper session
MAA national MathFest in Pittsburgh, PA, August 4 - 7, 2010
"Euclid's Neglected
Postulate", contributed paper session on history of mathematics uses in
the classroom.
"Four different experiences", contributed paper session on first year
seminar / experience mathematics courses.
MAA national MathFest in Lexington, KY, August 3 - 6, 2011
"A Mile Wide and an Inch Deep - 4000 BCE to 1950", general contributed paper session.
"Probability and Strategy in Farkle", contributed paper session on recreational mathematics.
The Future
Among many other things, perhaps a
personal
web site.
Return to:
Mathematics Department, SUNY
Geneseo.
