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 “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

 

Š      Texts

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

Š       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