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 is the Common
Core Standards for Mathematics.
MATHEMATICS 315
Combinatorics
MWF 10:30 - 11:20a: Sturges 104
Prerequisites: MATH 222, 233, and either 237 or 239
The purpose of this class is to solve a variety of
diverse discrete and counting problems.
MATHEMATICS 338
Topology
MW 4:00 - 5:15p: Sturges 105
Prerequisites: MATH 223, MATH 239
Topology can be divided into three main
areas: general, geometric, and algebraic. General topology
is the study of sets with a defined “closeness”. Geometric
topology is the study of the shapes that are unchanged under
stretching. Algebraic topology is the study of algebraic objects
that arise from topological objects, or the study of topological objects
using algebra.
Past Classes Taught at Geneseo
INTERDEPARTMENTAL
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
Secondary Mathematics
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
Biologists
MATHEMATICS 233: Elementary Linear
Algebra
MATHEMATICS 239: Introduction to
Mathematical Proof
MATHEMATICS 301: Mathematical Logic
MATHEMATICS 315: Combinatorics
MATHEMATICS 330: Abstract Algebra
MATHEMATICS 335: Foundations of
Geometry
MATHEMATICS 338: Topology
MATHEMATICS 348: Oral Presentation
& Research Seminar
MATHEMATICS 350: Vector Analysis
MATHEMATICS 371: Complex Analysis
MATHEMATICS 380: Galois Theory
MATHEMATICS 380: Differential
Geometry
MATHEMATICS 380: Visual Mathematics
MATHEMATICS 390: History of Mathematics
MATHEMATICS 470: History and
Fundamental Concepts of Mathematics
Department
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 (
practice).
Professional Activities
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
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
- 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 2008-2012
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.
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
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
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.
The Future
Among many other things, perhaps a
personal web
site.
Return to: Mathematics
Department, SUNY
Geneseo.