Jeff Johannes
Communication:
- Paper mail:
Mathematics Department
South Hall
State University College
of Arts and Sciences
Geneseo, NY 14454-1401 - E-mail: johannes@geneseo.edu
/
permanent:
johannes@member.ams.org
- (aol)IM: JohannesOhrs
(link may not work, if not please try your chat client)
- Phone: (585) 245-5403
Department fax: (585) 245-5128
Monday 4-5p,
Tuesday 8-9p,
Wednesday 12N-1p,
Thursday 10-11a, 2:30 - 3:30p
and by appointment or visit
MATHEMATICS
101
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.
Calculus III
MTWF 10:30 - 11:20p: Sturges 105
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).
MATHEMATICS
233
Elementary Linear Algebra
MWF 1:30 - 2:20p: Sturges 208a
Prerequisite: 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.
MATHEMATICS 338
Topology
MF 2:30 - 3:45p: Sturges 103
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 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.
The Future
Among many other things, perhaps a
personal
web site.
Return to:
Mathematics Department, SUNY
Geneseo.