Exploring, Investigating and Discovering in Mathematics

Exploring, Investigating and Discovering in Mathematics PDF

Author: Vasile Berinde

Publisher: Springer Science & Business Media

Published: 2003-12-17

Total Pages: 272

ISBN-13: 9783764370190

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This book offers creative problem solving techniques designed to develop and inspire inventive skills in students. It presents an array of selected elementary themes from arithmetic, algebra, geometry, analysis and applied mathematics. Includes solutions to over 100 problems and hints for over 150 further problems and exercises.

Exploring, Investigating and Discovering in Mathematics

Exploring, Investigating and Discovering in Mathematics PDF

Author: Vasile Berinde

Publisher: Birkhäuser

Published: 2012-12-06

Total Pages: 250

ISBN-13: 3034878893

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This book offers creative problem solving techniques designed to develop and inspire inventive skills in students. It presents an array of selected elementary themes from arithmetic, algebra, geometry, analysis and applied mathematics. Includes solutions to over 100 problems and hints for over 150 further problems and exercises.

Discovering Mathematics

Discovering Mathematics PDF

Author: A. Gardiner

Publisher: Courier Corporation

Published: 2006-01-26

Total Pages: 226

ISBN-13: 0486452999

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The term "mathematics" usually suggests an array of familiar problems with solutions derived from well-known techniques. Discovering Mathematics: The Art of Investigation takes a different approach, exploring how new ideas and chance observations can be pursued, and focusing on how the process invariably leads to interesting questions that would never have otherwise arisen. With puzzles involving coins, postage stamps, and other commonplace items, students are challenged to account for the simple explanations behind perplexing mathematical phenomena. Elementary methods and solutions allow readers to concentrate on the way in which the material is explored, as well as on strategies for answers that aren't immediately obvious. The problems don't require the kind of sophistication that would put them out of reach of ordinary students, but they're sufficiently complex to capture the essential features of mathematical discovery. Complete solutions appear at the end.

Exploring Mathematics

Exploring Mathematics PDF

Author: John Meier

Publisher: Cambridge University Press

Published: 2017-08-07

Total Pages: 341

ISBN-13: 1107128986

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With exercises and projects, Exploring Mathematics supports an active approach to the transition to upper-level theoretical math courses.

Creative Investigations in Early Math

Creative Investigations in Early Math PDF

Author: Angela Eckhoff

Publisher: Gryphon House Incorporated

Published: 2017

Total Pages: 0

ISBN-13: 9780876597293

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Encourages teachers to explore play , imagination deep involvement and risk taking all I the mathematical context.

Investigations

Investigations PDF

Author: Stuart A. Kauffman

Publisher: Oxford University Press

Published: 2002-09-19

Total Pages: 469

ISBN-13: 0190283858

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"It may be that I have stumbled upon an adequate description of life itself." These modest yet profound words trumpet an imminent paradigm shift in scientific, economic, and technological thinking. In the tradition of Schrödinger's classic What Is Life?, Kauffman's Investigations is a tour-de-force exploration of the very essence of life itself, with conclusions that radically undermine the scientific approaches on which modern science rests--the approaches of Newton, Boltzman, Bohr, and Einstein. Building on his pivotal ideas about order and evolution in complex life systems, Kauffman finds that classical science does not take into account that physical systems--such as people in a biosphere--effect their dynamic environments in addition to being affected by them. These systems act on their own behalf as autonomous agents, but what defines them as such? In other words, what is life? Kauffman supplies a novel answer that goes beyond traditional scientific thinking by defining and explaining autonomous agents and work in the contexts of thermodynamics and of information theory. Much of Investigations unpacks the progressively surprising implications of his definition. Significantly, he sets the stages for a technological revolution in the coming decades. Scientists and engineers may soon seek to create autonomous agents--both organic and mechanical--that can not only construct things and work, but also reproduce themselves! Kauffman also lays out a foundation for a new concept of organization, and explores the requirements for the emergence of a general biology that will transcend terrestrial biology to seek laws governing biospheres anywhere in the cosmos. Moreover, he presents four candidate laws to explain how autonomous agents co-create their biosphere and the startling idea of a "co-creating" cosmos. A showcase of Kauffman's most fundamental and significant ideas, Investigations presents a new way of thinking about the fundamentals of general biology that will change the way we understand life itself--on this planet and anywhere else in the cosmos.

Discovering Algebra

Discovering Algebra PDF

Author: Jerald Murdock

Publisher:

Published: 2007

Total Pages:

ISBN-13: 9781559538619

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Discovering Algebra provides a balance between skill development and mathematical exploration, between individual work and group work, between teacher directed activity and student led activity, and between the study of mathematics per se and the study of mathematics as it relates to the world and other disciplines.

Exploring Mathematics

Exploring Mathematics PDF

Author: Daniel Grieser

Publisher: Springer

Published: 2018-05-21

Total Pages: 308

ISBN-13: 3319903217

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Have you ever faced a mathematical problem and had no idea how to approach it? Or perhaps you had an idea but got stuck halfway through? This book guides you in developing your creativity, as it takes you on a voyage of discovery into mathematics. Readers will not only learn strategies for solving problems and logical reasoning, but they will also learn about the importance of proofs and various proof techniques. Other topics covered include recursion, mathematical induction, graphs, counting, elementary number theory, and the pigeonhole, extremal and invariance principles. Designed to help students make the transition from secondary school to university level, this book provides readers with a refreshing look at mathematics and deep insights into universal principles that are valuable far beyond the scope of this book. Aimed especially at undergraduate and secondary school students as well as teachers, this book will appeal to anyone interested in mathematics. Only basic secondary school mathematics is required, including an understanding of numbers and elementary geometry, but no calculus. Including numerous exercises, with hints provided, this textbook is suitable for self-study and use alongside lecture courses.