Interests

  • Low-dimensional Topology 
  • Knots, Links, and 3-manifolds 
  • History of Mathematics
  • Mathematics and Music
  • Teacher Training in Mathematics
 

Jeff Johannes

Associate Professor of

Mathematics

South 326A
1 College Circle
Geneseo, NY 14454
585-245-5403
johannes@geneseo.edu

Jeff Johannes has been a member of the Geneseo faculty since 2001.

 

I will not update this page.  My actual website is here:  

 

 

Please visit me there.  

Faculty Information

Education

  • Ph. D, Indiana University, 1998
  • B. A., Cornell University, 1992

Research Interests

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.

Publications and Professional Activities

  • 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.

Affiliations

  • 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.
Spring 2015 Classes

MATH 239:
Intro to Mathematical Proof

    The course will provide an introduction to the language of advanced mathematics and to mathematical proof. It will emphasize rigorous argument and the practice of proof in various mathematical contex
    ts. Topics will include logic, set theory, cardinality, methods of proof, and induction. Other mathematical topics chosen at the discretion of the instructor will be included as material through which proving skills will be honed. Prerequisites: MATH 222 or permission of the department. Offered every semester
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MATH 335:
Foundations of Geometry

    This course presents an investigation of the axiomatic foundations for several approaches to the study of modern geometry. Euclidean geometry, geometric transformations, and non-Euclidean geometries w
    ill be discussed. Prerequisites: MATH 222 and MATH 239. Offered every spring
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MATH 350:
Vector Analysis

    The course develops and expands upon certain topics in multivariate calculus. This includes the algebra and geometry of vectors, real and vector functions of one and several variables, curves, scalar
    and vector fields, vector differential and integral calculus, applications to geometry. Prerequisites: Math 223. Offered spring, odd years
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