Architecture of Modern Mathematics: Essays in History and Philosophy

José Ferreirós Domínguez; Jeremy Gray

Oxford University Press, USA | 2006 | 204 páginas | PDF | 1,8 Mb

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Descrição: This edited volume, aimed at both students and researchers in philosophy, mathematics and history of science, highlights leading developments in the overlapping areas of philosophy and the history of modern mathematics. It is a coherent, wide ranging account of how a number of topics in the
philosophy of mathematics must be reconsidered in the light of the latest historical research and how a number of historical accounts can be deepened by embracing philosophical questions.

Figures of Thought: Mathematics and Mathematical Texts

David Reed

Routledge | 1994 | 208 páginas | 1,82 Mb

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Descrição: Figures of Thought looks at how mathematical works can be read as texts and examines their textual strategies. David Reed offers the first sustained and critical attempt to find a consistent argument or narrative thread in mathematical texts.

Reed selects mathematicians from a range of historical periods and compares their approaches to organizing and arguing texts, using an extended commentary on Euclid's Elements as a central structuring framework. He develops fascinating interpretations of mathematicians' work throughout history, from Descartes to Hilbert, Kronecker, Dedekind, Weil and Grothendieck. Reed traces the implications of this approach to the understanding of the history and development of mathematics.

A to Z of Mathematicians

(Notable Scientists)
McElroy Tucker

Facts on File | 2004 | 308 páginas | pdf | 3,35 Mb

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It is difficult to evaluate contemporary mathematicians without the benefit of a retrospective viewpoint, separated by several decades. This comprehensive single-volume A-to-Z reference covers both the past and present scientists who have significantly contributed to the field of mathematics. Including all of the central mathematicians, as well as other lesser-known persons in the field who made serious contributions, this inclusive reference covers the major areas of algebra, analysis, geometry, and foundational statisticians.

Special features include indexes by field of specialization, nationality, and subject area; a helpful bibliography; and appendixes listing the mathematicians covered by country of birth, country of work, field of specialization, nationality, and subject area. Covering notable mathematicians from antiquity to the present, this is an ideal reference for middle and high school students.

Entries include:

• Archimedes of Syracuse
• Georg Cantor
• René Descartes
• Euclid
• Leonhard Euler
• Fibonacci
• Carl Friedrich Gauss
• Kurt Gödel
• David Hilbert
• Pythagoras
• Srinivasa Aaiyangar Ramanujan
• (George Friedrich) Bernhard Riemann
• Brook Taylor
• John Von Neumann
• Zeno of Elea
• and more.

Houghton Mifflin Math, Grade 6

Houghton Mifflin Math, Grade 6
Student Textbook
Carole Greenes, Matt Larson, Miraim Leiva, Jean Shaw, Lee Stiff, Bruce Vogeli, Karol Yeatts

Houghton Mifflin | 2007 | 690 páginas | rar - pdf | 62,451 Mb

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Manual escolar para o 6.ºano de escolaridade

Site do manual: eduplace.com

Modern Geometries

(Essays in Public Policy)

James R. Smart

Thomson Brooks/Cole | 1973 | 371 páginas | pdf | 10 Mb

Faltam páginas 146, 147, 148, 149, 158, 159, 160, 161.

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Descrição: This comprehensive, best-selling text focuses on the study of many different geometries -- rather than a single geometry -- and is thoroughly modern in its approach. Each chapter is essentially a short course on one aspect of modern geometry, including finite geometries, the geometry of transformations, convexity, advanced Euclidian geometry, inversion, projective geometry, geometric aspects of topology, and non-Euclidean geometries. This edition reflects the recommendations of the COMAP proceedings on Geometry's Future, the NCTM standards, and the Professional Standards for Teaching Mathematics. References to a new companion text, Active Geometry by David A. Thomas encourage students to explore the geometry of motion through the use of computer software. Using Active Geometry at the beginning of various sections allows professors to give students a somewhat more intuitive introduction using current technology before moving on to more abstract concepts and theorems.

Mathematics the Man Made Universe

Sherman K. Stein

W H FREEMAN & CO | 1963 | djvu | 4,49 Mb

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Descrição: Developed from a course for students in a variety of fields, this highly readable volume covers a vast array of subjects, including number theory, topology, set theory, geometry, algebra, and analysis. Starting with questions on weighing, the primes, the fundamental theory of arithmetic, and rationals and irrationals, the text also surveys the representation of numbers, congruence, probability, much more. Several useful appendices, plus answers, comments for selected exercises.

Table of Contents 

Map; Guide; Preface

1. Questions on weighing
Weighing with a two-pan balance and two measures—Problems raised—Their algebraic phrasing

2. The primes
The Greek prime-manufacturing machine—Gaps between primes—Average gap and 1/1 + 1/2 + 1/3 + . . . + 1/N—Twin primes

3. The Fundamental Theorem of Arithmetic
Special natural numbers—Every special number is prime—"Unique factorization" and "every prime is special" compared—Euclidean algorithm—Every prime number is special—The concealed theorem

4. Rationals and Irrationals
The Pythagorean Theorem-—he square root of 2—Natural numbers whose square root is irrational—Rational numbers and repeating decimals

5. Tiling
The rationals and tiling a rectangle with equal squares—Tiles of various shapes—use of algebra—Filling a box with cubes

6. Tiling and electricity
Current—The role of the rationals—Applications to tiling—Isomorphic structures

7. The highway inspector and the salesman
A problem in topology—Routes passing once over each section of highway—Routes passing once through each town

8. Memory Wheels
A problem raised by an ancient word—Overlapping n-tuplets—Solution—History and applications

9. The Representation of numbers
Representing natural numbers—The decimal system (base ten)—Base two—Base three—Representing numbers between 0 and 1—Arithmetic in base three—The Egyptian system—The decimal system and the metric system

10. Congruence
Two integers congruent modulo a natural number—Relation to earlier chapters—Congruence and remainders—Properties of congruence—Casting out nines—Theorems for later use

11. Strange algebras
Miniature algebras—Tables satisfying rules—Commutative and idempotent tables—Associativity and parentheses—Groups

12. Orthogonal tables
Problem of the 36 officers—Some experiments—A conjecture generalized—Its fate—Tournaments—Application to magic squares

13. Chance
Probability—Dice—The multiplication rule—The addition rule—The subtraction rule—Roulette—Expectation—Odds—Baseball—Risk in making decisions

14. The fifteen puzzle
The fifteen puzzle—A problem in switching cords—Even and odd arrangements—Explanation of the Fifteen puzzle—Clockwise and counterclockwise

15. Map coloring
The two-color theorem—Two three-color theorems—The five-color theorem—The four-color conjecture

16. Types of numbers
Equations—Roots—Arithmetic of polynomials—Algebraic and transcendental numbers—Root r and factor X—r—Complex numbers—Complex numbers applied to alternating current—The limits of number systems

17. Construction by straightedge and compass
Bisection of line segment-Bisection of angle-Trisection of line segment—Trisection of 90° angle—Construction of regular pentagon—Impossibility of constructing regular 9-gon and trisecting 60°

18. Infinite sets
A conversation from the year 1638—Sets and one-to-one correspondence—Contrast of the finite with the infinite—Three letters of Cantor—Cantor's Theorem—Existence of transcendentals

19. A general view
The branches of mathematics—Topology and set theory as geometries—The four "shadow" geometries—Combinatorics—Algebra—Analysis—Probability—Types of proof—Cohen's theorem—Truth and proof—Gödel's theorem

Appendix A. Review of arithmetic
A quick tour of the basic ideas of arithmetic

Appendix B. Writing mathematics
Some words of advice and caution

Appendix C. The rudiments of algebra
A review of algebra, which is reduced to eleven rules

Appendix D. Teaching mathematics
Suggestions to prospective and practicing teachers

Appendix E. The geometric and harmonic series
Their properties—Applications of geometric series to probability

Appendix F. Space of any dimension
Definition of space of any dimension

Appendix G. Update
Answers and comments for selected exercises

Index

Conceptions, croyances et représentations en maths, sciences et technos

Louise Lafortune, Colette Deaudelin, Pierre-André Doudin, Daniel Marti

Presses de l'Université du Québec | 2005 | 297 páginas | pdf | 3,74 Mb

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Descrição: En éducation, les conceptions, croyances et les représentations des élèves, des étudiants et étudiantes en formation à l’enseignement, des enseignants et enseignantes et des parents côtoient très souvent les connaissances, le savoir et les pratiques. Comment définir ces perceptions? Quelle est leur influence sur l’apprentissage scolaire et plus particulièrement sur celui des mathématiques, des sciences et des technologies?

À partir des résultats de recherche, cet ouvrage propose des pistes d’interventions multidimensionnelles visant à modifier les croyances aussi bien des spécialistes de l’enseignement que des élèves à l’égard des mathématiques, des sciences et des technologies. Des réflexions sur le rapport au savoir des étudiants et étudiantes en formation à l’enseignement et sur les principes pouvant guider la construction des pratiques professionnelles du personnel scolaire sont également au coeur de cet ouvrage.