Professor: Jeff Johannes
Section 1 MWF 2:30-3:20p Sturgis 113
Office: South
326A
Telephone: 245-5403
Office Hours: Monday 10:30 - 11:20a, 1:30 - 2:20p;
Tuesday 2 - 3p, 4 - 5p; Wednesday 8 - 9p and by appointment or visit
Email Address: Johannes@Geneseo.edu
Web-page:
http://www.geneseo.edu/~johannes
Textbooks
The Heart of Mathematics: An invitation to
effective thinking, Burger & Starbird
What is Mathematics Really? Reuben
Hersh
Purposes
To develop an understanding of the nature of
mathematics and its relevance in daily life.
Overview
In this course we will examine the question "What is
mathematics and what is it good for?". We will learn
by exploring mathematics that is not frequently studied in high school
or undergraduate mathematics courses. We will come to the
(perhaps
surprising) conclusion that mathematics is not primarily about
computing
or measuring, but rather about a style of thought. The important
applications of mathematics are more about making life decisions and
solving
problems than paying mortgage, finding the area of fabric, or
determining
the speed of a cannonball. We will also directly explore the
philosophy
and history of mathematics. Why does mathematics exist at all?
Reading
We have two very different books for this
course. The Heart of Mathematics is a fun coffee-table
type book. The book is about as easy to read as a light magazine.
The main point of this book is that mathematics helps us to think
about our daily life and the world around us. This will be the
source
of our mathematical content and most of the projects. Homework
will
primarily come from this book. The exams will cover material in
this book.
What is Mathematics Really? is much more a
philosophy book than a mathematics book. Occasionally
the reading is rough, but the mathematics is almost always very simple.
The references and discussions may feel obscure at times.
Hersh
addresses this eventually, saying something like "If a reference is
unfamiliar, it's probably not important." We will discuss Hersh's
book for 30-45 minutes occasionally. For those days you are
required to bring reading reactions to class. These reading
reactions must include reactions (items you particularly identified
with, disagreed with, or do not understand but would like to discuss)
to at least five topics in the reading. They must be written in
intelligible English. Each one will be evaluated out of 5 points,
with points deducted for fewer than five points being
addressed.
Course Content
We will begin the course by reading Chapter One of Heart
of Mathematics. We will also read Chapters 1 - 5 and 13 of What
is Mathematics, Really? The remaining course content will be
determined based on student preference indicated on forms distributed
on the first day. The most popular sections will be discussed in
class January 31 - March 11 and April 4 - 15. Other sections will
be assigned to paired students as projects. I will also present
Hersh's brief summary of calculus to give a different perspective on
material that is commonly presented in mathematics courses.
Grading
Your grade in this course will be based upon your
performance on these items:
In-class exams
15% each
Reading
Reactions 10%
Homework
15%
Colloquium
Report 10%
Project
15%
Final Exam
20%
Colloquium Report
Attend one of the department colloquium talks.
Write a report. In the report, describe the content of
the talk (you do not need to explain all the details, but it is
necessary to include the main points that the speaker was attempting to
convey).
In addition to your description of the talk, also write how this
talk added to your understanding of the nature of mathematics.
Projects
Each student is responsible for completing a project
as part of a pair. A project will consist of reading a section of
one of our textbooks and completing all the exercises in the chosen
part (there may be supplemental exercises for projects chosen from
Hersh). Projects will be presented during the last two weeks of
class. Writeups are due on the last day of class.
Homework Exercises
There will be homework exercises assigned from each
section that we cover in class. The first homework
assignment will be finalised after we decide on the course content.
Following that each homework assignment will be announced on the
day that the previous assignment is due. You are encouraged to
consult with me outside of class on any questions toward completing
the homework. You are also encouraged to work together on
homework
assignments, but each must write up their own well-written solutions (a
simple rule - discuss homework, but do not look at each other's
writing).
Each question will be counted in the following manner:
0 – missing or copied question
1 – question copied
2 – partial question
3 – completed question (with some solution)
4 – completed question correctly and well-written
Each entire homework set will then be graded on a 90-80-70-60% (decile)
scale. Late items will not be accepted. Homework will be
returned on the following class day.
In-class Exams
In class exams will check your understanding of the
mathematical content of the course. They will have questions
directly from the "Solidifying Ideas" questions pertaining to the
sections we have discussed.
Final Exam
Half of the final exam will be in the same form as
the in-class exams. A quarter of the exam will require
you to state the main idea of several projects other than your own.
The last quarter of the exam will require you to summarise your
understanding of Hersh's book and to explain your reaction to his
ideas.
Feedback
Occasionally you will be given
anonymous feedback forms. Please use them to share any thoughts
or concerns for how the course is running. Remember, the sooner
you tell me your concerns, the more I can do about them. I have
also created a web-site
which accepts anonymous comments.
If we have not yet discussed this in class, please encourage me to
create a class code. This site may also be accessed via our
course
page on a link entitled anonymous
feedback. Of
course, you are always welcome to approach me outside of class to
discuss these issues as well.
Religious Holidays
It is my policy to give students who miss class
because of observance of religious holidays the opportunity to make up
missed work. You are responsible for notifying me no
later than January 28 of plans to observe the holiday.
Schedule
January 19 Course Introduction
January 21 Burger & Starbird - Fun and Games
January 24 Fun and Games / Course Plan and Projects Assigned
January 26 Hersh Preface
January 28 2.4
January 31 2.4
February 2 2.5
February 4 2.5
February 7 Hersh 1
February 9 4.3 / HW1 due
Febuary 11 4.3
February 14 4.3 / 4.7
February 16 4.7
February 18 4.7
February 21 Hersh 2 / HW2 due
February 23 review
February 25 XM1
February 28 6.5
March 2 6.5
March 4 6.5 / Hersh 3
March 7 7.6
March 9 7.6
March 11 7.6 / HW3 due
March 21 Hersh Calc
March 23 Hersh Calc
March 25 Hersh Calc
March 28 Hersh 4 / HW4 due
March 30 review
April 1 XM2
April 4 7.2
April 6 7.2
April 8 7.2 / Hersh 5
April 11 7.3
April 13 7.3
April 15 7.3
April 18 Hersh 13 / HW5 due
April 20 Projects
April 22 Projects
April 25 Projects
April 27 Projects
April 29 Projects
May 2 Review / Project writeups due
Friday, May 6 3:30 - 6;30p Final XM
HW1:
Complete 4 of Chapter 1 Mindscapes (follow all directions
and answer all particular questions in section 1.4). Select one
each from these groups: 1 - 3, 4 - 6, 7 - 9, 10 - 15
2.4 31, 35, 37, 38
2.5 4 of 16 - 20
HW2:
4.3 16, 17, 19, 20, 22
4.7 16, 20, 21, 24
HW3:
6.5 26, 28, 29, 32, 36
HW4:
7.6 21, 23, 26, (29 or 30), (one of 31,
33, 35).
Calculus 1. Why does 6 / 3 = 2?
Why does 3 / 0 have no answer? Why does 0 / 0 have any
answer?
2. Following Hersh's discussion, consider a
stone traveling by the equation
h(t) = -16t^2 + 10t + 5, compute the speed at time t by computing the
distance
change in a moment H near time t divided that by moment H.
3. What is the slope of a curve at a point where it reaches
a maximum or
a minimum?
HW5:
7.2 26, 27, 35, (one
of 36, 38, 39)
7.3 27, 31, 34, (one of 37, 39, 40)