Jeff Johannes                    Head picture

Picture with Hopf Link     Picture at Bryce Canyon  

Communication:

Teaching (Day / Time Grid Schedule)

Monday 11:30a-12:20p S. 338
Monday 3:30-4:30p S. 336
Tuesday 1-2p Fr. 114
Wednesday 3-4p S. 336
Thursday 8-9p S. 336
MATHEMATICS 141

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 geometry, with probability and statistics.  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.


MATHEMATICS 239

Introduction to Mathematical Proof
MWF 12:30 - 1:20p:  South 328
TR 9:30 - 10:45a:  South 336
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.


MATHEMATICS 335

Geometry
MWF 1:30 - 2:20p:  South 336
Prerequisite:  MATH 239

The word geometry means measurement of the earth.  We will consider systems of geometry for measuring an idealised conception of the earth (Euclidean) the actual earth (spherical) and a possibility for measuring the universe (hyperbolic).  This course will take a more personal philosophical perspective on geometry rather than a computational or result-based perspective.  In this class we will use several different methods to analyse geometries.