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

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.

Course Content

We will begin the course by reading Chapter One of

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 - 15HW2:

2.4 31, 35, 37, 38

2.5 4 of 16 - 20

4.3 16, 17, 19, 20, 22HW3:

4.7 16, 20, 21, 24

6.5 26, 28, 29, 32, 36HW4:

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 haveanyanswer?

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)

7.3 27, 31, 34, (one of 37, 39, 40)