Welcome to the Mathematics Major
W 3:30 - 4:20p: Fraser 114
This course provides a welcoming and enthusiastic introduction
to the mathematics major. It exposes students to aspects
of mathematics typically not seen until later in their degree
program. Through presentations, discussions, and problem
solving the question “What is Mathematics?” will be examined.
MATHEMATICS 140
Mathematical Concepts for Elementary Education I
TR 12:30 - 1:45p: Fraser 108
In this course we develop an adult-level perspective
and insight into the nature of mathematics taught in
elementary school. In 140 we focus on number. Our
two themes for this course are the nature of mathematics and
the practice of problem solving (the act of doing
mathematics). Students often work together to develop
and deepen their understanding of the mathematical
concepts. Frequently this involves the use of
manipulatives to incorporate a tangible explanation for the
methods studied. This course is the next step toward a
career of explaining concepts (here mathematics) that
you have taken for granted before.
I will assume that university students do not need to be
taught elementary school mathematics. We will not be
reviewing, but rather justifying that material.
For a reference on the content of elementary school
mathematics, here are the New York State Standards for
Mathematics.
Calculus II
MWRF 10:30 - 11:20a: Fraser 116
Prerequisite: MATH 221
Calculus is the culmination of
high school mathematics and the entryway to higher level college
mathematics. The discovery of the calculus was a turning
point in the history of mathematics and society. As the
mathematics of change, calculus is widely applicable in all
fields of study that have quantifiable change. It is for
these reasons that we will be studying not only how to do
calculus, but why calculus is done the way it is, and why it is
done at all.
(Abstract) Algebra
MWF 2:30 - 3:20p: Welles 121
Prerequisites: MATH 233, 239
Algebra (mathematicians just call
it algebra, and what you did before is precalculus) is about
operations. We will explore what operations have in common
when working with the integers, the complex numbers, functions,
polynomials, matrices, and even transformations of geometric
objects. Understanding what we find in common is what
algebra is all about.
Past Classes Taught at Geneseo
Department
Professional Activities
I am an active member of the Mathematical Association of
America. In particular, I am the Member-at-Large, Chair of
the Seaway NExT commitee, liaison coordinator and the longtime
member of the Program Committee for the Seaway Section. I
was previously the Representative to the Congress. 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 project is translating an 1820 article by Simeon Poisson
about complex line integrals. I am also researching
the first 103 years of
history of mathematics at Geneseo.
Another project 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
- Game, SET - Math (mathematics of the card game SET)
- 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
- 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.
MAA national MathFest in Madison, WI, August 1 - 4, 2012
"The Flat Earth: The
Mathematics of Mapmaking", general contributed paper
session.
"Editing Episodes - Magazine, Chapter, and
More: Diverse Writing and Editing Projects",
contributed paper session on incorporating writing and
editing into mathematics classes.
MAA national MathFest in Hartford, CT, July 31 - August 3,
2013
"Tinkering with a
Mathematical Goldmine" about
this
website, contributed paper session on recreational
mathematics.
"Spherical Triangle Area and Angle Sum", contributed paper
session on geometry proofs.
MOVES conference at Museum of Mathematics, NYC, August 4 -
6, 2013
"Game: SET - Math"
talk
"Kaleidoscopic Mathematics" family activity
MAA national MathFest in Portland, OR, August 6 - 9, 2014
"On the Other Side of the
World, or Right Next Door?", general contributed
paper session.
"Geometry Knows Topology: The Gauß-Bonnet Theorem",
contributed paper session on geometry proofs.
MAA national MathFest in
Washington, DC, August 5 - 8, 2015
"Kaleidoscopic Journey", contributed paper session on
Mathematics and Art.
MAA national MathFest in Columbus, OH, August 4 - 6, 2016
"Take a Ride on the Parallel
Transport", general contributed paper session.
MAA national MathFest in Chicago, IL, July 27 - 29, 2017
"Galois Theory for High School Students", contributed paper
session on Exploring Zeroes of Polynomials.
MAA national MathFest in Denver, CO, August 2 - 4, 2018
"Writing Across the
Mathematics Curriculum", contributed paper session
Developing Mathematical Thinking and Communication Through
Writing.
Finger Lakes Master Teacher
Program, Geneseo, NY, February 9, 2019
MAA national MathFest in Cincinnati, OH, July 31 - August 3,
2019
Finger Lakes Master Teacher
Program, Geneseo, NY, January 11, 2020
"Mathematics
and Music" workshop.
MAA Seaway Section Panel,
October 8, 2021
"Coordinating
Groupwork Remotely" panelist.
MAA Seaway Section Panel,
February 24, 2021
"A Seaway
Conversation on the Course - History of Mathematics" panelist.
MAA national virtual MathFest,
August 4 - 7, 2021
"Needlepoint,
Toplogy, Geometry, and Beyond", contributed paper session
MathArt - ArtMath
MAA national MathFest in
Philadelphia, PA, August 3 - 6, 2022
"Poisson's
exploration of complex line integrals", contributed paper
session Complex Analysis: History, Pedagogy, Innovation, and
Research
MAA national MathFest in Tampa,
FL, August 2 - 5, 2023
"Analsis vs.
Algebra: What is Abstract?", contributed paper session
Analysis and Algebra: Convincing Students They Can Do It
MAA national MathFest in
Indianapolis, IN, August 7 - 10, 2024
"Mathematics
as a Human Creation", contributed paper session How My
Philosophy of Mathematics Affects My Teaching
The Future
Among many other things, perhaps a
personal web site.
Return to:
Mathematics Department, SUNY Geneseo.