Mathematics: Frontiers and Perspectives

Mathematics: Frontiers and Perspectives PDF

Author: Vladimir Igorevich Arnolʹd

Publisher: American Mathematical Soc.

Published: 2000

Total Pages: 476

ISBN-13: 9780821826973

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A celebration of the state of mathematics at the end of the millennium. Produced under the auspices of the International Mathematical Union (IMU), the book was born as part of the activities of World Mathematical Year 2000. It consists of 28 articles written by influential mathematicians.

Theories of Mathematics Education

Theories of Mathematics Education PDF

Author: Bharath Sriraman

Publisher: Springer Science & Business Media

Published: 2009-10-13

Total Pages: 650

ISBN-13: 3642007422

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Advances in Mathematics Education is a new and innovative book series published by Springer that builds on the success and the rich history of ZDM—The Inter- tional Journal on Mathematics Education (formerly known as Zentralblatt für - daktik der Mathematik). One characteristic of ZDM since its inception in 1969 has been the publication of themed issues that aim to bring the state-of-the-art on c- tral sub-domains within mathematics education. The published issues include a rich variety of topics and contributions that continue to be of relevance today. The newly established monograph series aims to integrate, synthesize and extend papers from previously published themed issues of importance today, by orienting these issues towards the future state of the art. The main idea is to move the ?eld forward with a book series that looks to the future by building on the past by carefully choosing viable ideas that can fruitfully mutate and inspire the next generations. Taking ins- ration from Henri Poincaré (1854–1912), who said “To create consists precisely in not making useless combinations and in making those which are useful and which are only a small minority.

Mathematics Frontiers

Mathematics Frontiers PDF

Author: Facts On File, Incorporated

Publisher: Infobase Publishing

Published: 2006

Total Pages: 161

ISBN-13: 0791097196

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Tracing the development of mathematics from a biographical standpoint, Mathematics Frontiers: 1950 to the Present profiles innovators from the second half of the 20th century who made significant discoveries in both pure and applied mathematics. From John H. Conway, who helped complete the classification of all finite groups (and invented The Game of Life board game), to Stephen Hawking, who established the mathematical basis for black holes, to Fan Chung, who developed an encoding and decoding algorithm for cell phone calls, this lively survey of contemporary minds behind the math is ideal for middle and high school students seeking resources for research or general interest.

Mathematics Frontiers, Updated Edition

Mathematics Frontiers, Updated Edition PDF

Author: Michael Bradley

Publisher: Infobase Holdings, Inc

Published: 2019-11-01

Total Pages: 150

ISBN-13: 1438182309

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Tracing the development of mathematics from a biographical standpoint, Mathematics Frontiers, Updated Edition profiles innovators from the second half of the 20th century who made significant discoveries in both pure and applied mathematics. The 10 mathematicians in this updated edition exemplify a growing diversity within the mathematical community, drawing from the talents of individuals across all nationalities, races, and genders. From John H. Conway, who helped complete the classification of all finite groups (and invented "The Game of Life" board game), to Stephen Hawking, who established the mathematical basis for black holes, to Fan Chung, who developed an encoding and decoding algorithm for phone calls, this lively survey of contemporary minds behind the math is ideal for middle and high school students seeking resources for research or general interest.

Trick or Truth?

Trick or Truth? PDF

Author: Anthony Aguirre

Publisher: Springer

Published: 2016-02-20

Total Pages: 250

ISBN-13: 3319274953

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The prize-winning essays in this book address the fascinating but sometimes uncomfortable relationship between physics and mathematics. Is mathematics merely another natural science? Or is it the result of human creativity? Does physics simply wear mathematics like a costume, or is math the lifeblood of physical reality? The nineteen wide-ranging, highly imaginative and often entertaining essays are enhanced versions of the prize-winning entries to the FQXi essay competition “Trick or Truth”, which attracted over 200 submissions. The Foundational Questions Institute, FQXi, catalyzes, supports, and disseminates research on questions at the foundations of physics and cosmology, particularly new frontiers and innovative ideas integral to a deep understanding of reality, but unlikely to be supported by conventional funding sources.

Frontiers of Applied Mathematics

Frontiers of Applied Mathematics PDF

Author: Din-Yu Hsieh

Publisher: World Scientific

Published: 2007

Total Pages: 236

ISBN-13: 9812704566

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This volume brings together articles on the mathematical aspects of life sciences, astrophysics, and nonlinear wave problems. It covers theoretical problems associated with the nervous system, drosophila embryos, protein folding, biopolymers, protoplanetary disks and extrasolar planets, gaseous disks, spiral galaxies, dark matter dynamics, star formation, solitary waves, photonics, and nonlinear light propagation in periodic media. The contributions are written for a general audience, and the authors have included references for further reading.

Frontiers in Mathematical Biology

Frontiers in Mathematical Biology PDF

Author: Simon A. Levin

Publisher: Springer Science & Business Media

Published: 2013-03-13

Total Pages: 637

ISBN-13: 3642501249

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From a mathematical point of view, physiologically structured population models are an underdeveloped branch of the theory of infinite dimensional dynamical systems. We have called attention to four aspects: (i) A choice has to be made about the kind of equations one extracts from the predominantly verbal arguments about the basic assumptions, and subsequently uses as a starting point for a rigorous mathematical analysis. Though differential equations are easy to formulate (different mechanisms don't interact in infinites imal time intervals and so end up as separate terms in the equations) they may be hard to interpret rigorously as infinitesimal generators. Integral equations constitute an attractive alternative. (ii) The ability of physiologically structured population models to increase our un derstanding of the relation between mechanisms at the i-level and phenomena at the p-level will depend strongly on the development of dynamical systems lab facilities which are applicable to this class of models. (iii) Physiologically structured population models are ideally suited for the for mulation of evolutionary questions. Apart from the special case of age (see Charlesworth 1980, Yodzis 1989, Caswell 1989, and the references given there) hardly any theory exists at the moment. This will, hopefully, change rapidly in the coming years. Again the development of appropriate software may turn out to be crucial.

Mathematical Modeling in Optical Science

Mathematical Modeling in Optical Science PDF

Author: Gang Bao

Publisher: SIAM

Published: 2001-01-01

Total Pages: 344

ISBN-13: 0898714753

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This volume addresses recent developments in mathematical modeling in three areas of optical science: diffractive optics, photonic band gap structures, and waveguides. Particular emphasis is on the formulation of mathematical models and the design and analysis of new computational approaches. The book contains cutting-edge discourses on emerging technology in optics that provides significant challenges and opportunities for applied mathematicians, researchers, and engineers. Each of the three topics is presented through a series of survey papers to provide a broad overview focusing on the mathematical models. Chapters present model problems, physical principles, mathematical and computational approaches, and engineering applications corresponding to each of the three areas. Although some of the subject matter is classical, the topics presented are new and represent the latest developments in their respective fields.