Mathematics and Cultures

    Ethnomathematics

Marcia Ascher, Ethnomathematics: A multicultural View of Mathematical Ideas, Chapman & Hall / CRC, 1998.

Ascher introduces the mathematical ideas of people in traditional cultures often omitted from discussion of mathematics: North American Indians; the Inca of South America; Polynesian islanders, and the Tshokwe, Bushoong, and Kpelle of Africa.

Marcia Ascher, Mathematics Elsewhere: An Exploration of Ideas Across Cultures, Princeton University Press, 2002.

This scholarly work describes the anthropology of mathematical ideas in traditional societies and shows how the same ideas might be expressed by standard mathematical expressions. Examples include traditional calendars, fortune-telling devices, systems of family and societal relationships, stick-charts used as navigation maps by Polynesian cultures, and "kolam" sand paintings made by Tamil Nadu women in India.

Gary Urton, with the collaboration of Primitivo Nina Llanos, The Social Life of Numbers: A Quechua Ontology of Numbers and Philosophy of Arithmetic, University of Texas Press, 1997.

The book is based too a large extent on fieldwork in communities near Sucre, south-central Bolivia. This is a study of the origin, meaning, and significance of numbers. For example in Quechua there is no symbol for zero. It was represented by not making a knot on a string.


    Favorite Mathematics Texts

My favorite set of exercises for advanced undergraduate and beginning graduate students can be found in the book, Berkeley Problems in Mathematics, Springer, third edition, 2004, by Jorge-Nuno Silva (Contributor) and Paulo Ney De Souza. The book contains approximately nine hundred problems which have appeared in preliminary exams in Berkeley over the last twenty years. It is an invaluable source of problems and solutions for every mathematics student who plans to enter a Ph.D. program.
For supplementary reading, I recommend the book, Calculus Made Easy Being a Very-Simplest Introduction to Those Beautiful Methods of Reckoning Which Are Generally Called by the Terrifying Names of, by Silvanus P. Thompson and Martin Gardner. This book will help you learn calculus. It will develop your intuition, You will see that calculus is EASY! You can find more comments about Calculus Made Easy on Amazon.com.
For a more advanced level of calculus, my favorite book is Principles of Mathematical Analysis by Walter Rudin. This book is a classic. I learned calculus from this book a long time ago. Now my students use it to study advanced calculus.

CONTENTS: The Real and Complex Number System, Basic Topology, Numerical Sequences and Series, Continuity, Differentiation, The Riemann-Stieltjes Integral, Sequences and Series of Functions, Some Special Functions, Functions of Several Variables, Integration of Differential Forms, The Lebesgue Theory, Bibliography, List of Special Symbols, Index.

This is a very elegant introduction to differential forms and to Stokes' theorem. I used this book to teach a vector calculus course.

Proofs from THE BOOK, Springer, third edition, 2003, by Martin Aigler and Gunter M. Ziegler is a wonderful book inspired by Paul Erdos. It presents a collection of "perfect" proofs. Everything in this book should be accessible to readers whose backgrounds include only a modest amount of techniques from undergraduate mathematics.

CONTENTS: Preface, Number Theory, Geometry, Analysis, Combinatorics, Graph Theory, About the Illustrations, Index.