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  • 1
    UID:
    almahu_BV012409016
    Format: X, 275 S. : Ill., graph. Darst.
    ISBN: 0-387-98434-8 , 0-387-98433-X
    Series Statement: Undergraduate texts in mathematics
    Note: Literaturverz. S. 259 - 267
    Language: German
    Subjects: Mathematics
    RVK:
    RVK:
    Keywords: Geometrie ; Geschichte ; Mengenlehre ; Geschichte ; Analysis ; Geschichte ; Zahlentheorie ; Geschichte ; Algebra ; Geschichte ; Quelle ; Quelle ; Quelle
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  • 2
    UID:
    almahu_9947362856902882
    Format: X, 278 p. , online resource.
    ISBN: 9781461205234
    Series Statement: Undergraduate Texts in Mathematics, Readings in Mathematics,
    Content: This book contains the stories of five mathematical journeys into new realms, told through the writings of the explorers themselves. Some were guided by mere curiosity and the thrill of adventure, while others had more practical motives. In each case the outcome was a vast expansion of the known mathematical world and the realization that still greater vistas remained to be explored. The authors tell these stories by guiding the reader through the very words of the mathematicians at the heart of these events, and thereby provide insight into the art of approaching mathematical problems. The book can be used in a variety of ways. The five chapters are completely independent, each with varying levels of mathematical sophistication. The book will be enticing to students, to instructors, and to the intellectually curious reader. By working through some of the original sources and supplemental exercises, which discuss and solve - or attempt to solve - a great problem, this book helps the reader discover the roots of modern problems, ideas, and concepts, even whole subjects. Students will also see the obstacles that earlier thinkers had to clear in order to make their respective contributions to five central themes in the evolution of mathematics.
    Note: 1 Geometry: The Parallel Postulate -- 1.1 Introduction -- 1.2 Euclid’s Parallel Postulate -- 1.3 Legendre’s Attempts to Prove the Parallel Postulate -- 1.4 Lobachevskian Geometry -- 1.5 Poincaré’s Euclidean Model for Non-Euclidean Geometry. -- 2 Set Theory: Taming the Infinite -- 2.1 Introduction -- 2.2 Bolzano’s Paradoxes of the Infinite -- 2.3 Cantor’s Infinite Numbers -- 2.4 Zermelo’s Axiomatization -- 3 Analysis: Calculating Areas and Volumes -- 3.1 Introduction -- 3.2 Archimedes’ Quadrature of the Parabola -- 3.3 Archimedes’ Method -- 3.4 Cavalieri Calculates Areas of Higher Parabolas -- 3.5 Leibniz’s Fundamental Theorem of Calculus -- 3.6 Cauchy’s Rigorization of Calculus -- 3.7 Robinson Resurrects Infinitesimals -- 3.8 Appendix on Infinite Series -- 4 Number Theory: Fermat’s Last Theorem -- 4.1 Introduction -- 4.2 Euclid’s Classification of Pythagorean Triples -- 4.3 Euler’s Solution for Exponent Four -- 4.4 Germain’s General Approach -- 4.5 Kummer and the Dawn of Algebraic Number Theory -- 4.6 Appendix on Congruences -- 5 Algebra: The Search for an Elusive Formula -- 5.1 Introduction -- 5.2 Euclid’s Application of Areas and Quadratic Equations -- 5.3 Cardano’s Solution of the Cubic -- 5.4 Lagrange’s Theory of Equations -- 5.5 Galois Ends the Story -- References -- Credits.
    In: Springer eBooks
    Additional Edition: Printed edition: ISBN 9780387984339
    Language: English
    Keywords: Quelle
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  • 3
    UID:
    gbv_242841767
    Format: X, 275 S , Ill., graph. Darst , 23.5 cm
    ISBN: 0387984348 , 038798433X
    Series Statement: Undergraduate texts in mathematics
    Note: Includes bibliographical references (p. - ) and index
    Language: English
    Subjects: Mathematics
    RVK:
    RVK:
    Keywords: Mathematik
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  • 4
    UID:
    almahu_9949405814302882
    Format: 1 online resource (1 online resource (ix, 216 pages) : illustrations, portrait.)
    Edition: Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2012
    ISBN: 9781470458461 (online)
    Series Statement: Spectrum, v. 6
    Content: Changing the way students learn calculus at New Mexico State University. In the Spring of 1988, Marcus Cohen, Edward D. Gaughan, Arthur Knoebel, Douglas S. Kurtz, and David Penegelley began work on a student project approach to calculus. For the next two years, most of their waking hours (and some of their dreams) would be devoted to writing projects for their students and discovering how to make the use of projects in calculus classes not only successful, but practical as well. A grant from the National Science Foundation made it possible for this experiment to go forward on a large scale. The enthusiasm of the original group of five faculty was contagious, and soon other members of the department were also writing and using projects in their calculus classes. At the present time, about 80% of the calculus students at New Mexico State University are doing projects in their Calculus courses. Teachers can use their methods in teaching their own calculus courses. Student Research Projects in Calculus provides teachers with over 100 projects ready to assign to students in single and multivariable calculus. The authors have designed these projects with one goal in mind: to get students to think for themselves. Each project is a multistep, take-home problem, allowing students to work both individually and in groups. The projects resemble mini research problems. Most of them require creative thought, and all of them engage the student's analytic and intuitive faculties. The projects often build from a specific example to the general case, and weave together ideas from many parts of the calculus. Project statements are clearly stated and contain a minimum of mathematical symbols. Students must draw their own diagrams, decide for themselves what the problem is about, and what tools from the calculus they will use to solve it. This approach elicits from students an amazing level of sincere questioning, energetic research, dogged persistence, and conscientious communication. Each project has accompanying notes to the instructors, reporting students' experiences. The notes contain helpful information on prerequisites, list the main topics the project explores, and suggests helpful hints. The authors have also provided several introductory chapters to help instructors use projects successfully in their classes and begin to create their own.--Publisher.
    Note: Includes index. , Introduction , Part I , History , Evaluation , Logistics: Ideas for Using Projects Successfully , Creating Projects , Part II , Guide to the Projects , List of Projects , Projects , Index , Mode of access : World Wide Web
    Additional Edition: Print version: Cohen, Marcus S., Student research prjects in calculus / ISSN 2638-6909 ISBN 9780883855034
    Language: English
    Keywords: Electronic books.
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