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Jeff Johannes

Associate Professor of Mathematics
South 326A
585-245-5403
johannes@geneseo.edu
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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.

Curriculum Vitae

Education

  • Ph. D, Indiana University, 1998

  • B. A., Cornell University, 1992

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.

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.

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.

Interests

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

Classes

  • MATH 101: Welcome Mathematics Majors

    An introductory course for entering mathematics majors. Through presentations, discussions and problem solving the question "What is Mathematics?".

  • MATH 141: R/Math Concepts for Elem Ed II

    This course is intended for education majors and is designed to provide a mathematical treatment of the fundamental concepts of probability, statistics, and elementary geometry as they relate to the elementary school mathematics curriculum.

  • 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 contexts. 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.

  • MATH 324: Real Analysis I

    A study of the underlying theory of elementary calculus. Topics include the structure and properties of the real numbers, sequences, functions, limits, continuity, the derivative, the Riemann integral, and Taylor's theorems.