Jeff Johannes                    Head picture

Picture with Hopf Link     Picture at Bryce Canyon  


Teaching (Day / Time Grid Schedule)

Monday 2:30 - 4p
Tuesday 8-9p (staying as long as there is interest)
Wednesday 2:30 - 4p
Thursday 11:30a-1p,
and by appointment or visit.

In this course we develop an adult-level perspective and insight into the nature of mathematics taught in elementary school.  In 141 we focus on probability, statistics and geometry.  Our two themes for this course are the nature of mathematics and the practice of problem solving (the act of doing mathematics).  Students often work together to develop and deepen their understanding of the mathematical concepts.  Frequently this involves the use of manipulatives to incorporate a tangible explanation for the methods studied.  This course is the next step toward a career of explaining concepts (here mathematics) that you have taken for granted before.  

I will assume that university students do not need to be taught elementary school mathematics.  We will not be reviewing, but rather justifying that material.  For a reference on the content of elementary school mathematics, here are the New York State Standards for Mathematics.


Vector Analysis
Asynchronous online. 
Prerequisite:  MATH 223

In this course we will formalise and view the mathematics of Calculus III from a more advanced perspective, while establishing and highlighting the historical connections with physics.

History of Mathematics
Asynchronous online. 
Prerequisite:  MATH 222

The first main goal of this course is to connect the mathematics you have learned (and some you haven't) with the history you have learned (and some you haven't).  The second main goal is to connect the mathematics you have learned together.

  • Past Classes Taught at Geneseo

    INTERDEPARTMENTAL 101:  First Semester Seminar - Does Anybody Really Know What Time, Day, Month or Year It Is?
    INTERDEPARTMENTAL 101:  First Semester Seminar - Infinity, the Fourth Dimension and Geneseo
    INTERDEPARTMENTAL 101:  First Semester Seminar - Reality Bites
    INTERDEPARTMENTAL 301:  Topics in Secondary Mathematics
    MATHEMATICS 101: Welcome to the Math Major
    MATHEMATICS 104: Mathematical Ideas
    MATHEMATICS 113:  Finite Mathematics
    MATHEMATICS 140:  Mathematical Concepts for Elementary Education I
    MATHEMATICS 141:  Mathematical Concepts for Elementary Education II
    MATHEMATICS 160:  Elements of Chance
    MATHEMATICS 221:  Calculus I
    MATHEMATICS 222:  Calculus II
    MATHEMATICS 223:  Calculus III
    MATHEMATICS 228:  Calculus II for Biologists
    MATHEMATICS 233:  Elementary Linear Algebra
    MATHEMATICS 239:  Introduction to Mathematical Proof
    MATHEMATICS 301:  Mathematical Logic
    MATHEMATICS 315:  Combinatorics
    MATHEMATICS 330:  Abstract Algebra
    MATHEMATICS 333:  Linear Algebra II
    MATHEMATICS 335:  Foundations of Geometry
    MATHEMATICS 338:  Topology
    MATHEMATICS 348:  Oral Presentation & Research Seminar
    MATHEMATICS 350:  Vector Analysis
    MATHEMATICS 371:  Complex Analysis
    MATHEMATICS 381 (380):  Galois Theory
    MATHEMATICS 380:  Differential Geometry
    MATHEMATICS 380:  Symmetry
    MATHEMATICS 380:  Visual Mathematics
    MATHEMATICS 390:  History of Mathematics
    MATHEMATICS 470:  History and Fundamental Concepts of Mathematics


    I am currently chair of the department's curriculum committee.  I am also happy to rejoin the departments' colloquium committee.  This lingers, but I'm happy to keep it here in case anyone wishes:  here are some mathematics GRE subject exam preparations #2 #2and#4answers #3 #4 (practice). 

    Professional Activities

    I am an active member of the Mathematical Association of America.  In particular, I am the liaison coordinator and the co-chair of the Program Committee for the Seaway Section.  I am also a member of the American Mathematical Society. 

    Areas of research

    Current projects

    I am currently pursuing several research projects.  The newest project is researching the history of mathematics at Geneseo.  I am hoping to work my way through the first 103 years in time for our sesquicentennial in September, 2021.  Another 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.  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


    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 2008-2012
    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.


    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 enhance 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

    MAA national MathFest in Pittsburgh, PA, August 4 - 7, 2010

    "Euclid's Neglected Postulate", contributed paper session on history of mathematics uses in the classroom.
    "Four different experiences", contributed paper session on first year seminar / experience mathematics courses.

    MAA national MathFest in Lexington, KY, August 3 - 6, 2011

    "A Mile Wide and an Inch Deep - 4000 BCE to 1950", general contributed paper session.
    "Probability and Strategy in Farkle", contributed paper session on recreational mathematics.  

    MAA national MathFest in Madison, WI, August 1 - 4, 2012

    "The Flat Earth: The Mathematics of Mapmaking", general contributed paper session.
    "Editing Episodes -  Magazine, Chapter, and More:  Diverse Writing and Editing Projects", contributed paper session on incorporating writing and editing into mathematics classes. 

    MAA national MathFest in Hartford, CT, July 31 - August 3, 2013

    "Tinkering with a Mathematical Goldmine" about this website, contributed paper session on recreational mathematics.
    "Spherical Triangle Area and Angle Sum", contributed paper session on geometry proofs.
    MOVES conference at Museum of Mathematics, NYC, August 4 - 6, 2013

    "Game:  SET - Math" talk
    "Kaleidoscopic Mathematics" family activity

    MAA national MathFest in Portland, OR, August 6 - 9, 2014

    "On the Other Side of the World, or Right Next Door?",  general contributed paper session.
    "Geometry Knows Topology:  The Gauß-Bonnet Theorem", contributed paper session on geometry proofs.

    MAA national MathFest in Washington, DC, August 5 - 8, 2015

    "Kaleidoscopic Journey", contributed paper session on Mathematics and Art.

    MAA national MathFest in Columbus, OH, August 4 - 6, 2016

    "Take a Ride on the Parallel Transport", general contributed paper session.

    MAA national MathFest in Chicago, IL, July 27 - 29, 2017

    "Galois Theory for High School Students", contributed paper session on Exploring Zeroes of Polynomials.

    MAA national MathFest in Denver, CO, August 2 - 4, 2018

    "Writing Across the Mathematics Curriculum", contributed paper session Developing Mathematical Thinking and Communication Through Writing.

    Finger Lakes Master Teacher Program, Geneseo, NY, February 9, 2019

    MAA national MathFest in Cincinnati, OH, July 31 - August 3, 2019

    "Enhancing Classes with In-Class Group Work and Presentations" panel presentation for Project NExT.
    "19th Century Normal Mathematics", contributed poster.

    Finger Lakes Master Teacher Program, Geneseo, NY, January 11, 2020

    "Mathematics and Music" workshop.

    The Future

    Among many other things, perhaps a personal web site.

    Return to:  Mathematics Department,   SUNY Geneseo.