Conjecture and Proof

(Classroom Resource Materials)
Miklós Laczkovich

The Mathematical Association of America | 2001 | 140 páginas | djvu | 2, 9 Mb

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Descrição: The Budapest semesters in mathematics were initiated with the aim of offering undergraduate courses that convey the tradition of Hungarian mathematics to English-speaking students. This book is an elaborate version of the course on 'Conjecture and Proof'. It gives miniature introductions to various areas of mathematics by presenting some interesting and important, but easily accessible results and methods. The text contains complete proofs of deep results such as the transcendence of e, the Banach-Tarski paradox and the existence of Borel sets of arbitrary (finite) class. One of the purposes is to demonstrate how far one can get from the first principles in just a couple of steps. Prerequisites are kept to a minimum, and any introductory calculus course provides the necessary background for understanding the book. Exercises are included for the benefit of students. However, this book should prove fascinating for any mathematically literate reader.

Ancient Egyptian Mathematics

Ancient Egyptian Science, A Source Book.
Volume Three
Marshall Clagett

DIANE Publishing | 1999 | 462 páginas

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Descrição: This volume continues Marshall Clagett's studies of the various aspects of the science of Ancient Egypt. The volume gives a discourse on the nature and accomplishments of Egyptian mathematics and also informs the reader as to how our knowledge of Egyptian mathematics has grown since the publication of the Rhind Mathematical Papyrus toward the end of the 19th century. The author quotes and discusses interpretations of such authors as Eisenlohr, Griffith, Hultsch, Peet, Struce, Neugebauer, Chace, Glanville, van der Waerden, Bruins, Gillings, and others. He also also considers studies of more recent authors such as Couchoud, Caveing, and Guillemot.

Ancient Egyptian Science: Calendars, clocks, and astronomy

Volume II
Marshall Clagett

DIANE Publishing | 1995 | 575 páginas

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Descrição: This volume is part of Marshall Clagett's three-volume study of the various aspects of science of Ancient Egypt. Volume Two covers calendars, clocks, and astonomical monuments. Within each area of treatment there is a fair chronology evident as benefits a historical work covering three millenia of activity. Includes more than 100 illustrations of documents and scientific objects.

Navigating Through Algebra in Grades 3-5

Navigating Through Algebra in Grades 3-5
(Principles and Standards for School Mathematics Navigations Series)
Gilbert J. Cuevas, Karol L. Yeatts

National Council of Teachers of Mathematics | 2001 | 90 páginas | rar -pdf | 51,2 Mb

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Descrição: The important ideas of algebra, including patterns, variables, equations, and functions, are the focus of this book. Student activities that introduce and promote familiarity with these ideas include constructing growing patterns using isosceles triangles, analyzing situations with constant or varying rates of change, and observing and representing various patterns in an array. The supplemental CD-ROM features interactive electronic activities, master copies of activity pages for students, and additional readings for teachers (only the additional readings for teachers are included in the link).

Dreams of Calculus: Perspectives on Mathematics Education

Johan Hoffman, Claes Johnson, Anders Logg

Springer | 2004 | 158 páginas | pdf | 5,6 Mb

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Descrição: What is the relationship between modern mathematics - more precisely computational mathematics - and mathematical education? It is this controversal topic that the authors address with an in-depth analysis. In fact, what they present in an extremely well-reasoned account of the development of mathematics and its culture giving concrete recommendation for a much-needed reform of the teaching of mathematics. The book is essential reading for everybody involved in mathematics and science, and mathematics teaching.

Number theory and its history

Oystein Ore

McGraw Hill Publishing | 1948 | 370 páginas |

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Descrição: Unusually clear, accessible introduction covers counting, properties of numbers, prime numbers, Aliquot parts, Diophantine problems, congruences, much more.

Graph Theory 1736-1936

Norman L. Biggs, E. Keith Lloyd, Robin J. Wilson

Oxford University Press, USA | 240 páginas | 1999 |

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Descrição: First published in 1976, this book has been widely acclaimed as a major and enlivening contribution to the history of mathematics. The updated and corrected paperback contains extracts from the original writings of mathematicians who contributed to the foundations of graph theory. The author's commentary links each piece historically and frames the whole with explanations of the relevant mathematical terminology and notation.