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Adventures in the World of Matrices
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Authors: Paulus Gerdes (Director, Ethnomathematics Research Centre, Maputo, Mozambique) 
Book Description:
The purpose of the book is to give the reader a feeling for the beauty and the suprises of mathematical research by building up step by step a theory of cycle matrices. The notions of matrix and cycle are presented for those readers who do not yet know the concepts. Then, starting and experminenting with cycle matrices of low dimensions and engaging the readers in various activities, beautiful results are obtained with attractive geometrical interpretation. Gradually the results are extended to cycle matrices of higher dimensions and then generalized. A note is included for those readers who would like to use a computer in exporing cycle matrices. Two appendices give the possibility to further use the computer by exploring inverses matrices and determinants.

Table of Contents:
Preface

Presentation

Chapter 1 - The concept of matrix

Chapter 2 - Cycles of numbers

Chapter 3 - Some matrices of alternating cycles

Chapter 4 - Alternating cycle matrices of dimensions 4 by 4. First part

Chapter 5 - Alternating cycle matrices of dimensions 4 by 4. Second part

Chapter 6 - Alternating cycle matrices of dimensions 4 by 4. Third part: Multiplication tables

Chapter 7 - Some more properties of alternating cycle matrices of dimensions 4 by 4

Chapter 8 - Negative alternating cycle matrices of dimensions 6 by 6

Chapter 9 - Multiplication of negative alternating cycle matrices of dimensions 6 by 6

Chapter 10 - Multiplication of positive and negative alternating cycle matrices of dimensions 6 by 6

Chapter 11 - Alternating cycle matrices of even dimensions

Chapter 12 - General hypotheses concerning alternating cycle matrices of even dimensions

Chapter 13 - Alternating cycle matrices of dimensions 5 by 5

Chapter 14 - Multiplication of positive and negative alternating cycle matrices of dimensions 3 by 3

Chapter 15 - Alternating cycle matrices of dimensions 7 by 7

Chapter 16 - Multiplication tables of basic positive and negative alternating cycle matrices of dimensions 7 by 7

Chapter 17 - Cyclic structure of the multiplication tables

Chapter 18 - Multiplication tables of basic positive and negative alternating cycle matrices of dimensions 6 by 6

Cghapter 19 - Outline of a proof

Chapter 20 - Multiplication of basic positive alternating cycle matrices of even dimensions: Formulation of hypotheses

Chapter 21 - Multiplication of basic positive alternating cycle matrices of even dimensions: Some proofs

Chapter 22 - Proof activities

Chapter 23 - Cycle matrices of dimensions 6 by 6 and of period 3

Chapter 24 - Other periodic cycle matrices of dimensions 6 by 6

Chapter 25 - Periodic cycle matrices of odd dimensions

Chapter 26 - The world of periodic cycle matrices

Chapter 27 - Discovering the world of cycle matrices

Chapter 28 - Cycle matrices, genetic matrices and the golden section

Chapter 29 - Bibliography

Chapter 30 - Note about the use of a computer

Appendices

Chapter 31 - Inverse matrices

Chapter 32 - Determinants

Chapter 33 - Transformations of alternating cycle matrices. Permutations

Chapter 34 - Polygonal and circular representations

Index

   Series:
      Contemporary Mathematical Studies (Gaston M. N'Guerekata - Morgan State University - Series Editor)
   Binding: Hardcover
   Pub. Date: 2007
   ISBN: 1-60021-718-4
   Status: AV
  
Status Code Description
AN Announcing
FM Formatting
PP Page Proofs
FP Final Production
EP Editorial Production
PR At Prepress
AP At Press
AV Available
  
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Adventures in the World of Matrices