The Bard College Clemente Bridge Course in the Humanities

Codman Square Health Center, Spring 2005

**Mathematics in History and
Culture**

Dr. Joan Lukas, Professor Emerita of Mathematics

University of Massachusetts Boston

Email: joan.lukas@umb.edu

Telephone: Office 617 287 6454 Home 781 321 0681

Mathematics
plays an integral role in human intellectual development, both for individuals
and societies, but traditional mathematics teaching often leaves the impression
that mathematics is an unchanging and isolated system. In reality,
mathematical concepts, such as the idea of number, have developed over many
centuries, often with much disagreement and confusion among the mathematicians
who developed them. Learners struggling with mathematical concepts, as we
all do at some time, can benefit from an understanding of the difficulties
these concepts have posed historically and the ways in which these difficulties
have been approached.

This course will examine the development of mathematical ideas, the
interaction of these ideas with other cultural forces, and historical struggles
over changing mathematical concepts. We will consider the question ÒWhat is a
number?Ó and answers given to this question by various cultures at various
times. We will then look at the interaction of mathematics with
other areas of life and culture.

- to develop an appreciation of the process through which mathematical ideas have developed and the historical and cultural contexts of this process.
- to investigate connections between mathematics and other aspects of culture and ways in which mathematical ideas can be used to understand the world around us.
- to become more comfortable with mathematics in our own thinking

** **

á
**Texts**

á
__Life by the
Numbers__ by Keith Devlin (Wiley, 1998) and

á
__Numbers, the
Universal Language__ by Denis Guedj (Abrams , 1998)

**Part One: What is mathematics about? What is it good for?**

** **

Class One Introduction and overview. Our relationships to mathematics.

February 10

Class Two Mathematical problems and solutions. Mathematical ways of reasoning

February
17 Reading:
__Life by the Numbers__, Chapter 1

Handout from Euler on Ò7 Bridges of KonisgsbergÓ

**Hand in One: Mathematical autobiography**

**February
24 Public School Vacation No class**

The Bard College Clemente BridgeCourse in the Humanities

**Mathematics in History and
Culture**

Dr. Joan Lukas

**Part
Two:**** Evolution of the Concept of Number**

Class Three Biological and cultural origins of mathematics

March
3 Reading:
__Numbers, the Universal Language__, Chapter 1

__The Number Sense__ by Stanislas Dehaene
Chapter 2

(will be handed out February 17)

Class Four Numeration systems

March
10 Reading:
__Numbers, the Universal Language__, Chapter 2

** **

**March
17 Evacuation Day No class**

Class Five Positional notation and the Hindu-Arabic system of numeration

March
24 Reading:
__Numbers, the Universal Language__, Chapter 3

Class Six The wonders of arithmetic: Natural Numbers

March
31 Reading:
__Numbers, the Universal Language__, Chapter 4

Class Seven Extending the Number System

April
7 Reading:
__Numbers, the Universal Language__, Chapters 5 and 6

Handout on the history of fractions

** **

Class Eight The role of mathematics in human knowledge

April
14 Reading:
__Life by the Numbers__, Chapters 3 and 5

** **

**April
21 Public School
Vacation No class**

Class Nine Mathematics and Art

April
28 Reading:
__Life by the Numbers__, Chapter 2

Class Ten Mathematics and Sports

May
5 Reading:
__Life by the Numbers__, Chapter 4

**Hand in
Three: Assignment on mathematics and culture**

** **

Class Eleven The idea of chance: Probability and Statistics

May
12 Reading__:
Life by the Numbers__, Chapter 6

Class Twelve Computers and computation

May
19 Reading__:
Life by the Numbers__, Chapter 7

**Optional
Classes on Mathematics Topics **

This syllabus is available online at http://www.math.umb.edu/~joan/BardClemente