Jeff Johannes                    Head picture

Picture with Hopf Link     Picture at Bryce Canyon  

Communication:

Teaching (Day / Time Grid Schedule)

Monday 8-9p
Tuesday 2-3p
Wednesday 10-11a
Thursday 1-2p, 4:30 - 5:30p
and by appointment or visit
MATHEMATICS 228

Calculus II for Biologists
TR 11:20a - 1:00p:  Fraser 119
Prerequistes:  MATH 221

This course is defined, in many ways, by what it isn't.  It isn't the easy way out of calculus II - in fact, it will likely be more demanding than 222 would be.  It isn't merely the same topics from 222 with examples using biology.  It is a completely different experience than 222.  Some 222 topics will not be included, most notably infinite series.  We will learn many topics not studied in 222 - including probability and statistics, and many topics not studied in other mathematics courses - such as discrete dynamical systems.  You will be my experts on biology, and I will be the mathematics expert.  Along the way we will surely all learn something we never knew before.  Be prepared to work, to learn, and to see some new and different things.  Open your minds and hold on for a biology flavoured adventure in mathematics.
Topics in Secondary Mathematics
TR 9:55 - 11:10p:  South 336

This course, whch is intended for the mathematics major who is enrolled in the secondary education program, provides a bridge and establishes connections between the college level mathematics required of the mathematics major and the mathematics of the secondary school curriculum.

MATHEMATICS 348

Oral Presentation & Research Seminar
M 3:00 - 4:15p:  South 336

MATHEMATICS 470

History and Fundamental Concepts of Mathematics
MW 4:15 - 5:30p:  South 336

A graduate-level course in the history of mathematics connected to the secondary school curriculum.  As for all good graduate-level courses - it will be what the students make it.  

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

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

Prepared Talks

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.  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.