Calculus: Concepts and Contexts

James Stewart

Brooks Cole | 2000 | 1184 páginas | pdf | 17 Mb

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James Stewart's well-received CALCULUS: CONCEPTS AND CONTEXTS, Second Edition follows in the path of the other best-selling books by this remarkable author. The First Edition of this book was highly successful because it reconciled two schools of thought: it skillfully merged the best of traditional calculus with the best of the reform movement. This new edition continues to offer the balanced approach along with Stewart's hallmark features: meticulous accuracy, patient explanations, and carefully graded problems. The content has been refined and the examples and exercises have been updated. In addition, CALCULUS: CONCEPTS AND CONTEXTS, Second Edition now includes a free CD-ROM for students that contains animations, activities, andhomework hints. The book integrates the use of the CD throughout by using icons that show students when to use the CD to deepen their understanding of a difficult concept. In CALCULUS: CONCEPTS AND CONTEXTS, this well respected author emphasizes conceptual understanding - motivating students with real world applications and stressing the Rule of Four in numerical, visual, algebraic, and verbal interpretations. All concepts are presented in the classic Stewart style: with simplicity, character, and attention to detail. In addition to his clear exposition, Stewart also creates well thought-out problems and exercises. The definitions are precise and the problems create an ideal balance between conceptual understanding and algebraic skills.

Perspectives on the History of Mathematical Logic

Thomas Drucker

Birkhäuser Boston | 2008 | 196 páginas |

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Descrição: This volume offers insights into the development of mathematical logic over the last century. Arising from a special session of the history of logic at an American Mathematical Society meeting, the chapters explore technical innovations, the philosophical consequences of work during the period, and the historical and social context in which the logicians worked. The discussions herein will appeal to mathematical logicians and historians of mathematics, as well as philosophers and historians of science
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The Roles of Representation in School Mathematics

2001 Yearbook
Albert A. Cuoco, Frances R. Curcio

National Council of Teachers of Mathematics (NCTM) | 2001 | 282 páginas | PDF | 3,6 Mb

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Descrição: The focus of NCTM's 2001 Yearbook is one aspect of how students learn mathematics–in particular, how they learn to form abstractions and build mathematical representations of phenomena. It explains how students come to develop mathematical habits of mind, and even how they develop misunderstandings about mathematics. Discussions on the nature and roles of representation, the use of representation tools for gaining insights, various symbol systems used in mathematics, and the role of context in the interplay between modeling and representation make this an excellent resource for teachers who want to make smart decisions about content and pedagogy.
Conteúdospt. 1. Roles for representations.
Systems of representations and the development of mathematical concepts / Gerald Goldin, Nina Shteingold
Representation and abstraction in young children's numerical reasoning / Constance Kamii, Lynn Kirkland, Barbara A. Lewis
Algebra : what are we teaching / Mark Saul
Attending to transparent features of opaque representations of natural numbers / Rina Zazkis, Karen Gadowsky
pt. 2. Tools for thinking.
The influence of language on mathematical representations / Irene T. Miura
The role of tools in supporting students' development measuring conceptions / Michelle Stephan ... [et al.] Promoting the use of diagrams as tools for thinking / Carmel Diezmann, Lyn English
Constructing a foundation for the fundamental theorem of calculus / Mary J. Schnepp, Ricardo Nemirovsky
Mapping diagrams : another view of functions / Mark Bridger, Maxine Bridger
A multirepresentational journey through the law of cosines / Daniel Scher
Representations of reversal : an exploration of Simpson's paradox / Lawrence Mark Lesser
pt. 3. Symbols and symbol systems.
Presenting and representing : from fractions to rational numbers / Susan J. Lamon
Representations of patterns and functions : tools for learning / Wendy N. Coulombe, Sarah B. Berenson
Promoting multiple representations in algebra / Alex Friedlander, Michal Tabach
From Fibonacci numbers to fractals : recursive patterns and subscript notation / Deborah S. Franzblau, Lisa B. Warner
Tracing the origins and extensions of Michael's representation / Regina D. Kiczek, Carolyn A. Maher, Robert Speiser
pt. 4. The role of context.
Listen to their pictures : an investigation of children's mathematical drawings / Kristine Reed Woleck
Using literature to invite mathematical representations / Phyllis Whitin, David Whitin
Representation in realistic mathematics education / Margaret R. Meyer
Charting a visual course to the concept of function / Michal Yerushalmy, Beba Shternberg
Teaching mathematical modeling and the skills of representation / Joshua Paul Abrams.

Euclidean & Non-Euclidean Geometries: Development and History

Marvin Jay Greenberg

W. H. Freeman | 1993 | 512 páginas | djvu | 4,16 Mb

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This is the definitive presentation of the history, development and philosophical significance of non-Euclidean geometry as well as of the rigorous foundations for it and for elementary Euclidean geometry, essentially according to Hilbert. Appropriate for liberal arts students, prospective high school teachers, math. majors, and even bright high school students. The first eight chapters are mostly accessible to any educated reader; the last two chapters and the two appendices contain more advanced material, such as the classification of motions, hyperbolic trigonometry, hyperbolic constructions, classification of Hilbert planes and an introduction to Riemannian geometry.

An Essay on the Foundations of Geometry

Bertrand Russell

Dover | 1956 | Djvu | 2,4 Mb

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Descrição: This is Russell's first philosophical work published in 1897. The book provides an insight into his earliest analytical and critical thought, as well as an introduction to the philosophical and logistical foundations of non-Euclidean geometry, a version of which is central to Einstein's theory of relativity.

Foundations of Geometry

David Hilbert

Open Court Publishing Company | 1971 | 226 páginas


on-line: gutenberg.org
on-line: archive.org

Geometry and the Imagination

David Hilbert, Stephan Cohn-Vossen

Chelsea Pub Co| 1952 | 357 páginas | Djvu | 4,16 Mb

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Descrição:

This remarkable book has endured as a true masterpiece of mathematical exposition. There are few mathematics books that are still so widely read and continue to have so much to offer--after more than half a century! The book is overflowing with mathematical ideas, which are always explained clearly and elegantly, and above all, with penetrating insight. It is a joy to read, both for beginners and experienced mathematicians.

"Hilbert and Cohn-Vossen" is full of interesting facts, many of which you wish you had known before, or had wondered where they could be found. The book begins with examples of the simplest curves and surfaces, including thread constructions of certain quadrics and other surfaces. The chapter on regular systems of points leads to the crystallographic groups and the regular polyhedra in $\mathbb{R}^3$. In this chapter, they also discuss plane lattices. By considering unit lattices, and throwing in a small amount of number theory when necessary, they effortlessly derive Leibniz's series: $\pi/4 = 1 - 1/3 + 1/5 - 1/7 + - \ldots$. In the section on lattices in three and more dimensions, the authors consider sphere-packing problems, including the famous Kepler problem.

One of the most remarkable chapters is "Projective Configurations". In a short introductory section, Hilbert and Cohn-Vossen give perhaps the most concise and lucid description of why a general geometer would care about projective geometry and why such an ostensibly plain setup is truly rich in structure and ideas. Here, we see regular polyhedra again, from a different perspective. One of the high points of the chapter is the discussion of Schlafli's Double-Six, which leads to the description of the 27 lines on the general smooth cubic surface. As is true throughout the book, the magnificent drawings in this chapter immeasurably help the reader.

A particularly intriguing section in the chapter on differential geometry is Eleven Properties of the Sphere. Which eleven properties of such a ubiquitous mathematical object caught their discerning eye and why? Many mathematicians are familiar with the plaster models of surfaces found in many mathematics departments. The book includes pictures of some of the models that are found in the Göttingen collection. Furthermore, the mysterious lines that mark these surfaces are finally explained!

The chapter on kinematics includes a nice discussion of linkages and the geometry of configurations of points and rods that are connected and, perhaps, constrained in some way. This topic in geometry has become increasingly important in recent times, especially in applications to robotics. This is another example of a simple situation that leads to a rich geometry.

It would be hard to overestimate the continuing influence Hilbert-Cohn-Vossen's book has had on mathematicians of this century. It surely belongs in the "pantheon" of great mathematics books.