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

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 “What is a number?” 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.

Goals

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

· Texts

· Life by the Numbers by Keith Devlin (Wiley, 1998) and

· Numbers, the Universal Language by Denis Guedj (Abrams , 1998)

Syllabus

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 “7 Bridges of Konisgsberg”

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

Hand in Two: Assignment on uses of mathematics

Class Seven Extending the Number System

April 7 Reading: Numbers, the Universal Language, Chapters 5 and 6

Handout on the history of fractions

Part Three: Mathematics in the Modern World

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

May 26, June 2

Hand in Four: Updated mathematical autobiography

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