Jeff Johannes

Communication:

Paper mail:

E-mail: johannes@geneseo.edu / permanent: johannes@member.ams.org
Phone: (585) 245-5403

Teaching (Day / Time Grid Schedule)

Office Hours

Monday 1:30 - 2:30p
Tuesday 8:00 - 9:00p
Wednesday 11:30a - 12:20p
Thursday 8:00 - 9:00p
Friday 1:30 - 2:30p

Classes - Fall 2008

MATHEMATICS 188 (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.

MATHEMATICS 160

Elements of Chance
MWF 10:30 - 11:20: Sturges 105

This course will help you think about statistics and probability, how to identify the tools needed to study a particular problem, and how to read and critically evaluate quantitative information presented in the media. The course format involves extensive reading and discussion of newspaper and journal articles, writing assignments, and student projects.

MATHEMATICS 222

Calculus II
M(T)WF 3:00 - 3:50p (2:10 3:00p) : Sturges 113

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.

MATHEMATICS 380

Topics in Mathematics: Differential Geometry
MWF 12:30 - 1:20p: Sturgees 114

Differential geometry is the study of geometric figures using the methods of calculus. Most of our work will be focused on characteristics of curves and surfaces.

Past Courses 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 104: Mathematical Ideas
MATHEMATICS 140: Mathematical Concepts for Elementary Education I
MATHEMATICS 141: Mathematical Concepts for Elementary Education II
MATHEMATICS 221: Calculus I
MATHEMATICS 222: Calculus II
MATHEMATICS 223: Calculus III
MATHEMATICS 228: Calculus II for Biologists
MATHEMATICS 239: Introduction to Mathematical Proof
MATHEMATICS 315: Combinatorics
MATHEMATICS 335: Foundations of Geometry
MATHEMATICS 338: Topology
MATHEMATICS 348: Oral Presentation & Research Seminar
MATHEMATICS 350: Vector Analysis
MATHEMATICS 380: Visual Mathemaitcs

Department

I am the chair of the colloquium committee for 2002-2007 and 2008-. Please visit our schedule of colloquium talks for this year.

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 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 with Thang Le at SUNY Buffalo, and questions of the space of finite type invariants for links of three or more components with Lorenzo Traldi at Lafayette College. 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

History of Mathematics
Mathematics and Music
Teacher Training in Mathematics

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

Ph. D, Indiana University , 1998

Advisor: Charles Livingston

B. A., Cornell University , 1992

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. Thursday, January 11, 11:00a - 12:00N.

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

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 mathemaitcs.
"Place Value Airthmetic via Polynomials", contributed paper session on innovations in mathematics education.

The Future

Among many other things, perhaps a personal web site.

Return to: Mathematics Department, SUNY Geneseo.