Jeff JohannesAssociate Professor of Mathematics
Jeff Johannes has been a member of the Geneseo faculty since 2001. I will not update this page. My actual website is here: http://www.geneseo.edu/~johannes/ Please visit me there.
Ph. D, Indiana University, 1998
B. A., Cornell University, 1992
I am an active member of the Mathematical Association of America.
I am the liaison coordinator and the chair of the Seaway NExT Steering Committee.
I am also a member of the American Mathematical Society.
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.
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.
- Low-dimensional Topology
- Knots, Links, and 3-manifolds
- History of Mathematics
- Mathematics and Music
- Teacher Training in Mathematics
MATH 101: Welcome Mathematics Majors
An introductory course for entering mathematics majors. Through presentations, discussions and problem solving the question "What is Mathematics?".
MATH 140: Math Concepts for Elem Educ I
This course is intended for education majors and is designed to provide a mathematical treatment of the fundamental concepts of arithmetic, algebra, and number theory as they relate to the elementary school mathematics curriculum.
MATH 315: Combinatorics
As calculus seeks to develop proficiency in analysis problem solving, the aim of this course is to develop proficiency in basic combinatorial problem solving and reasoning. Topics include: Enumeration, generating functions, sieve formulas, recurrence relations, graph theory, network analysis, trees, search theory, and block designs. Prerequisites: MATH 222, MATH 233 and either MATH 237 or MATH 239. Offered fall, even years
MATH 338: Topology
detailed examination of topological spaces and mappings. The properties of compactness, connectedness, and separation are studied. Further topics from general, geometric, or algebraic topology will also be discussed. Prerequisites: MATH 223 and MATH 239. Offered fall, even years