- Paper mail: Mathematics Department
- E-mail: johannes@geneseo.edu / permanent: johannes@member.ams.org
- (aol)IM: JohannesOhrs (link may not work, if not please try your chat client; if you want to send text messages, please tell me)
- Phone: (585) 245-5403 Department fax: (585) 245-5128

South Hall

State University College of Arts and Sciences

Geneseo, NY 14454-1401

- Office Hours

to be determined in classes

- Classes - Spring 2014

Calculus II

MWF 10:30 - 11:20a, R 11:30a - 12:30p: Sturges 105

Prerequisite: MATH 221

MWF 10:30 - 11:20a, R 11:30a - 12:30p: Sturges 105

Prerequisite: MATH 221

Calculus is the culmination of high
school mathematics and the entryway to higher level college
mathematics. The discovery of the calculus was a turning point in
the history of mathematics and society. As the mathematics of
change, calculus is widely applicable in all fields of study that have
quantifiable change. It is for these reasons that we will be
studying not only how to do calculus, but why calculus is done the way
it is, and why it is done at all.

MATHEMATICS 239

Introduction to Mathematical Proof

MWF 1:30 - 2:20p: Sturges 113

Prerequisite: MATH 222

MWF 1:30 - 2:20p: Sturges 113

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, hopefully 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.

Topology

MWF 11:30a - 12:30p: Sturges 105

Prerequisites: MATH 223, MATH 239

MWF 11:30a - 12:30p: Sturges 105

Prerequisites: MATH 223, MATH 239

Topology can be divided into three main
areas: general, geometric, and algebraic. General topology
is the study of sets with a defined “closeness”. Geometric
topology is the study of the shapes that are unchanged under
stretching. Algebraic topology is the study of algebraic objects
that arise from topological objects, or the study of topological objects
using algebra.

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).

- Low-dimensional Topology
- Knots, Links, and 3-manifolds

- History of Mathematics
- Mathematics and Music
- Teacher Training in Mathematics

- Game, SET - Math (mathematics of the card game SET)
- Kaleidoscopic Mathematics

- The World That We See: Perspective and Projective Geometry

- Mathematics and Music
- The Fourth Dimension and Science Fiction
- A Concise History of Calculus
- Mathematics of the Calendar
- An Introduction to Knot Theory
- Evariste Galois and Hector Berlioz
- Evariste Galois and the Solution of Algebraic Equations

* 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.

- Ph. D, Indiana University , 1998
- Advisor: Charles Livingston
- B. A., Cornell University , 1992

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.

**Conferences**

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."Temperament of Mind: Hector Berlioz and Evariste Galois", contributed paper.

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"Welcome to Mathematics: A Cornerstone Experience", contributed paper session on the role of proof in teaching mathematics.

"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"Honesty is the Best Philosophy", contributed paper session on innovations in quantitative literacy.

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.

"Greatest Hits of Mathematics", general contributed paper session.

MAA national MathFest in Knoxville, TN,
August 9 - 12, 2006

MAA national MathFest in San Jose, CA, August 2 - 5, 2007

MAA national MathFest in Madison, WI, July 30 - August 2, 2008

MAA national MathFest in Portland, OR, August 5 - 8, 2009

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

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

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

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

"A Little Moore Probability",
contributed paper session on current issues in mathematics education
courses.

"Kaleidoscope", general contributed paper session.

"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"Four dimensional tic-tac-toe on a torus - the game of SET", general contributed paper session

"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.

"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

"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.

"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"Probability and Strategy in Farkle", contributed paper session on recreational mathematics.

"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.

"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"Spherical Triangle Area and Angle Sum", contributed paper session on geometry proofs.

"Game: SET - Math" talk

"Kaleidoscopic Mathematics" family activity

"Kaleidoscopic Mathematics" family activity

"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.

"Geometry Knows Topology: The Gauß-Bonnet Theorem", contributed paper session on geometry proofs.

Return to: Mathematics Department, SUNY Geneseo.