- Paper mail:
State University College of Arts and Sciences
Geneseo, NY 14454-1401
email@example.com / permanent:
- Phone: (585) 245-5403
Department fax: (585) 245-5128
Welcome to the Mathematics Major
R 4:00 - 4:50p: Newton 203
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.
MTWF 11:30a - 12:20p: Sturges 103
Prerequisite: MATH 222
Calculus III is not really a continuation of Calculus I and
II. It takes both of them to a whole new dimension - the third
dimension. We will learn calculus that can be applied to the three
dimensional world in which we live (but which we frequently ignore because
it cannot be completely reproduced on paper or on screens).
Introduction to Mathematical Proof
MWF 1:30 - 2:20p: Sturges 105
Prerequisite: MATH 222
It is often said that mathematics is a language. In this class you
will begin to learn to speak this language. Just like in an
introductory language course, we will start with the most fundamental
concepts and grammar rules. After we have some familiarity with the
language of formal mathematics, we will practice this language in the
setting of counting problems of different types. More like an
advanced language class, it will not suffice just memorizing the
vocabulary (in fact, hopefully we can keep vocabulary to a minimum), but
rather you will be required to understand and speak clearly in this
language. The material learned here will help you understand the
mathematics you read and clarify the mathematics you write. Because
we are learning how to write mathematics, exposition will also be a
component in your evaluation.
Past Classes Taught at Geneseo
MF 2:30 - 3:45p:
This is not truth tables, Philosophy 101, or a gentle continuation of
Introduction to Proofs. In this course we will tell the tale of
Gödel's theorems, one of the most amazing stories inside of mathematics,
and about mathematics as well. Come join us for a wild ride and a
trip and a half into the surprising world of vast abstraction.
101: First Semester Seminar - Does Anybody Really Know
What Time, Day, Month or Year It Is?
INTERDEPARTMENTAL 101: First Semester
Seminar - Infinity, the Fourth Dimension and Geneseo
INTERDEPARTMENTAL 101: First Semester
Seminar - Reality Bites
INTERDEPARTMENTAL 301: Topics in
MATHEMATICS 101: Welcome to the Math Major
MATHEMATICS 104: Mathematical Ideas
MATHEMATICS 140: Mathematical Concepts
for Elementary Education I
MATHEMATICS 141: Mathematical Concepts
for Elementary Education II
MATHEMATICS 160: Elements of Chance
MATHEMATICS 221: Calculus I
MATHEMATICS 222: Calculus II
MATHEMATICS 223: Calculus III
MATHEMATICS 228: Calculus II for
MATHEMATICS 233: Elementary Linear
MATHEMATICS 239: Introduction to
MATHEMATICS 301: Mathematical Logic
MATHEMATICS 315: Combinatorics
MATHEMATICS 330: Abstract Algebra
MATHEMATICS 335: Foundations of Geometry
MATHEMATICS 338: Topology
MATHEMATICS 348: Oral Presentation &
MATHEMATICS 350: Vector Analysis
MATHEMATICS 371: Complex Analysis
MATHEMATICS 380/381: Galois Theory
MATHEMATICS 380: Differential Geometry
MATHEMATICS 380: Visual Mathematics
MATHEMATICS 390: History of Mathematics
MATHEMATICS 470: History and Fundamental
Concepts of Mathematics
I am currently chair of the department's curriculum committee. This
lingers, but I'm happy to keep it here in case anyone wishes: here are
some mathematics GRE subject exam preparations #2
#2and#4answers #3 #4
I am an active member of the Mathematical Association of America. In
particular, I am the liaison coordinator and the co-chair of the Program
Committee for the Seaway Section. I am also a member of the American
Areas of research
- Low-dimensional Topology
- Knots, Links, and 3-manifolds
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
- 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
A Type 2 Polynomial Invariant of Links Derived from the Casson-Walker
Invariant, Journal of Knot Theory and Its Ramifications, Vol. 8, No. 4
Casson-Walker-Lescop invariant and link invariants, Journal
of Knot Theory and Its Ramifications, Vol. 14, No. 4 (2005) 425-433.
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
to Computers: Using the Last
200 Years of Mathematics History in the Classroom, 2005.
Seaway NExT Steering Committee Chair 2008-2012
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.
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
AMS sectional meeting in Las Vegas, April 21 - 22, 2001.
Co-organized special session on the topology
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
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"
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
"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
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
enhance 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
"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
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
, contributed paper session on recreational
"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
MAA national MathFest in Columbus, OH, August 4 - 6, 2016
"Take a Ride on the Parallel Transport",
general contributed paper session.
Among many other things, perhaps a personal web
Return to: Mathematics
Department, SUNY Geneseo.