Jeff Johannes                    Head picture

Picture with Hopf Link     Picture at Bryce Canyon  


Teaching (Day / Time Grid Schedule)

Monday 4:15 - 5:15p
Tuesday 8:00-9:00p
Wednesday 12:30 - 1:20p
Thursday 11:30 - 2:00p

Topics in Secondary Mathematics
TR 10:00 - 11:15a:  South 336

This course, which is intended for the mathematics major who is enrolled in the secondary education program, provides a bridge and establishes connections between the college level mathematics required of the mathematics major and the mathematics of the secondary school curriculum.


Introduction to Mathematical Proof
MWF 1:30 - 2:20p:  Sturges 104
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, I hope 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.


History of Mathematics
MWF 11:30a - 12:20p:  Sturges 208a
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 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 335:  Foundations of Geometry
    MATHEMATICS 338:  Topology
    MATHEMATICS 348:  Oral Presentation & Research Seminar
    MATHEMATICS 350:  Vector Analysis
    MATHEMATICS 371:  Complex Analysis
    MATHEMATICS 380:  Galois Theory
    MATHEMATICS 380:  Differential Geometry
    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.  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 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.  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 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

    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 - August 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.

    The Future

    Among many other things, perhaps a personal web site.

    Return to:  Mathematics Department,   SUNY Geneseo.