Jeff Johannes                    Head picture

Picture with Hopf Link     Picture at Bryce Canyon  

Communication:

Teaching (Day / Time Grid Schedule)

Monday 9 -  9:50a, 2:30 - 3:30p
Wednesday 3:30 - 4:30p
Thursday 8 - 9p
Friday 11 - 11:50a, sometimes 3 - 4p
and by appointment or visit
MATHEMATICS 101 (188)
Welcome to the Mathematics Major
R 3:30 - 4:20p:  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 221
Calculus II
MWRF 1 - 1:50p:  Sturges 105
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 239
Introduction to Mathematical Proof
MWF 10 - 10:50a:  Sturges 103
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

MATHEMATICS 315
Combinatorics
MWF 12 - 12:50p:  Sturges 103
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. 

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.  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




The Future

Among many other things, perhaps a personal web site.

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