Dark and Bright Mathematics
Dark and Bright Mathematics

Author: Dirk Huylebrouck

Publisher: Springer Nature

Published: 2023-11-20

Total Pages: 244

ISBN-13: 3031362551

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Was it necessary for a 17th century painter to know principles of optics to hide a skull in one of his masterpieces? Is it possible the violent deaths of Roman emperors obey a statistical law? Are there connections between market trends and geometry? How did Islamic artists draw almost perfectly regular nine-sided polygons, when these cannot be traced with the use of compasses? Dirk Huylebrouk asks these and other exciting questions in this collection of essays, originally written for the science magazine EOS, a Dutch equivalent of Scientific American, distributed in Belgium and in The Netherlands. Every chapter can be read independently, as some subjects are repeated, and not strictly interconnected. Such is the case for instance of the golden section, an often-recurring topic in general mathematics. The reader will appreciate the original point of view expressed through each chapter, which makes this book stand out against the general information one can find by browsing the general media. The subtly provocative character of some parts is meant to stimulate the reader for further exploration. The book's title itself may already generate surprise. Sure, to many, mathematics seems to come from hell, but the darkness in the title in fact refers to the lugubrious stories about math and skulls, murders or World War II. There is also a more down-to-earth part is about math and maps, money, Facebook, folding paper, shapes in ice and the most earthly yet unsolved math problems. ‘Bright mathematics’ alludes to Vedic, Islam, New Age, a meta-divine section, and is concluded by an interview with a top mathematician who also wrote about the existence of God.

Bright Galaxies, Dark Matters
Bright Galaxies, Dark Matters

Author: Vera Rubin

Publisher: Springer Science & Business Media

Published: 1996-11-22

Total Pages: 270

ISBN-13: 9781563962318

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In 1965, Vera Rubin was the first woman permitted to observe at Palomar Observatory. In the intervening years, she has become one of the world's finest and most respected astronomers. This particular collection of essays is compiled from work written over the past 15 years and deals with a variety of subjects in astronomy and astrophysics, specifically galaxies and dark matter. The book also contains biographical sketches of astronomers who have been colleagues and friends, providing a stimulating view of a woman in science. About the Author Since 1965 Vera Rubin has been a staff member at the Department of Terrestrial Magnetism of the Carnegie Institution of Washington. Dr. Rubin has authored nearly 200 papers on the structure of our galaxy, motions within other galaxies, and large scale motions in the universe. She has been a distinguished visiting astronomer at the Cerro Tololo Inter American Observatory in Chile; a Chancellor's Distinguished Professor at the University of California, Berkeley; a President's Distinguished Visitor at Vassar College; and a Beatrice Tinsley visiting professor at the University of Texas, Austin.

Math with Bad Drawings
Math with Bad Drawings

Author: Ben Orlin

Publisher: Black Dog & Leventhal

Published: 2018-09-18

Total Pages: 556

ISBN-13: 0316509027

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A hilarious reeducation in mathematics-full of joy, jokes, and stick figures-that sheds light on the countless practical and wonderful ways that math structures and shapes our world. In Math With Bad Drawings, Ben Orlin reveals to us what math actually is; its myriad uses, its strange symbols, and the wild leaps of logic and faith that define the usually impenetrable work of the mathematician. Truth and knowledge come in multiple forms: colorful drawings, encouraging jokes, and the stories and insights of an empathetic teacher who believes that math should belong to everyone. Orlin shows us how to think like a mathematician by teaching us a brand-new game of tic-tac-toe, how to understand an economic crises by rolling a pair of dice, and the mathematical headache that ensues when attempting to build a spherical Death Star. Every discussion in the book is illustrated with Orlin's trademark "bad drawings," which convey his message and insights with perfect pitch and clarity. With 24 chapters covering topics from the electoral college to human genetics to the reasons not to trust statistics, Math with Bad Drawings is a life-changing book for the math-estranged and math-enamored alike.

Concrete Mathematics
Concrete Mathematics

Author: Ronald L. Graham

Publisher: Addison-Wesley Professional

Published: 1994-02-28

Total Pages: 811

ISBN-13: 0134389980

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This book introduces the mathematics that supports advanced computer programming and the analysis of algorithms. The primary aim of its well-known authors is to provide a solid and relevant base of mathematical skills - the skills needed to solve complex problems, to evaluate horrendous sums, and to discover subtle patterns in data. It is an indispensable text and reference not only for computer scientists - the authors themselves rely heavily on it! - but for serious users of mathematics in virtually every discipline. Concrete Mathematics is a blending of CONtinuous and disCRETE mathematics. "More concretely," the authors explain, "it is the controlled manipulation of mathematical formulas, using a collection of techniques for solving problems." The subject matter is primarily an expansion of the Mathematical Preliminaries section in Knuth's classic Art of Computer Programming, but the style of presentation is more leisurely, and individual topics are covered more deeply. Several new topics have been added, and the most significant ideas have been traced to their historical roots. The book includes more than 500 exercises, divided into six categories. Complete answers are provided for all exercises, except research problems, making the book particularly valuable for self-study. Major topics include: Sums Recurrences Integer functions Elementary number theory Binomial coefficients Generating functions Discrete probability Asymptotic methods This second edition includes important new material about mechanical summation. In response to the widespread use of the first edition as a reference book, the bibliography and index have also been expanded, and additional nontrivial improvements can be found on almost every page. Readers will appreciate the informal style of Concrete Mathematics. Particularly enjoyable are the marginal graffiti contributed by students who have taken courses based on this material. The authors want to convey not only the importance of the techniques presented, but some of the fun in learning and using them.

Light after Dark III
Light after Dark III

Author: Charles Francis

Publisher: Troubador Publishing Ltd

Published: 2016-09-19

Total Pages: 320

ISBN-13: 1785898558

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Light after Dark III: The Mathematics of Gravity and Quanta proves the most important results described in Light after Dark II, from fundamental principles, as elegantly as possible and with the minimum of verbiage. This is a first principles account of the mathematical structure of modern theoretical physics, showing that it is not just a disparate bunch of algorithms and procedures, but is a unified structure based on observation, sound principles and solid logic, and allowing a unique physical interpretation in terms of fundamental constituents, or particles. Light after Dark III: The Mathematics of Gravity and Quanta explains essential mathematics at undergraduate level. Part I covers many core topics in a mathematics degree. Part II is a concise account of results in relativity, including the Lorentz transform from first principles, Riemann curvature, Einstein’s equation, derivations of the Schwarzschild and Friedmann solutions, and proofs of key results. Part III contains the mathematical foundations of relativistic quantum mechanics and constructs quantum electrodynamics. Divergence problems are treated with greater rigour than usual in theoretical physics, but without excessive formality. Classical electromagnetism is derived from fundamental principles. Part IV shows how quantum electrodynamics and general relativity can be described in a single structure. Light after Dark III: The Mathematics of Gravity and Quanta will interest students of mathematics and students of physics and philosophy with a mathematical leaning who are seeking a rigorous treatment and deeper mathematical insight into physical theory.

Dark Nights, Bright Lights
Dark Nights, Bright Lights

Author: Susanne Bach

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2015-10-16

Total Pages: 213

ISBN-13: 3110415623

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Light and darkness shape our perception of the world. This is true in a literal sense, but also metaphorically: in theology, philosophy, literature and the arts the light of day signifies life, safety, knowledge and all that is good, while the darkness of the night suggests death, danger, ignorance and evil. A closer inspection, however, reveals that things are not quite so clear cut and that light and darkness cannot be understood as simple binary opposites. On a biological level, for example, daylight and darkness are inseparable factors in the calibration of our circadian rhythms, and a lack of periodical darkness appears to be as contrary to health as a lack of exposure to sunlight. On a cultural level, too, night and darkness are far from being universally condemnable: in fiction, drama and poetry the darkness of the night allows not only nightmares but also dreams, it allows criminals to ply their trade and allows lovers to meet, it allows the pursuit of pleasure as well as deep thought, it allows metamorphoses, transformations and transgressions unthinkable in the light of day. But night is not merely darkness. The night gains significance as an alternative space, as an ‘other of the day’, only when it is at least partially illuminated. The volume examines the interconnection of night, darkness and nocturnal illumination across a broad range of literary texts. The individual essays examine historically specific light conditions in literature, tracing the symbolic and metaphoric content of darkness and illumination and the attitudes towards them.

Why It Works Light and Dark
Why It Works Light and Dark

Author: Anna Claybourne

Publisher: QED Publishing

Published: 2009-08

Total Pages: 24

ISBN-13: 9781848350441

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"Describes properties of light and dark, color, shadows, and more. Includes experiments"--Provided by publisher.

The Legacy of the Inverse Scattering Transform in Applied Mathematics
The Legacy of the Inverse Scattering Transform in Applied Mathematics

Author: J. L. Bona

Publisher: American Mathematical Soc.

Published: 2002

Total Pages: 346

ISBN-13: 0821831615

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Swift progress and new applications characterize the area of solitons and the inverse scattering transform. There are rapid developments in current nonlinear optical technology: Larger intensities are more available; pulse widths are smaller; relaxation times and damping rates are less significant. In keeping with these advancements, exactly integrable soliton equations, such as $3$-wave resonant interactions and second harmonic generation, are becoming more and more relevant inexperimental applications. Techniques are now being developed for using these interactions to frequency convert high intensity sources into frequency regimes where there are no lasers. Other experiments involve using these interactions to develop intense variable frequency sources, opening up even morepossibilities. This volume contains new developments and state-of-the-art research arising from the conference on the ``Legacy of the Inverse Scattering Transform'' held at Mount Holyoke College (South Hadley, MA). Unique to this volume is the opening section, ``Reviews''. This part of the book provides reviews of major research results in the inverse scattering transform (IST), on the application of IST to classical problems in differential geometry, on algebraic and analytic aspects ofsoliton-type equations, on a new method for studying boundary value problems for integrable partial differential equations (PDEs) in two dimensions, on chaos in PDEs, on advances in multi-soliton complexes, and on a unified approach to integrable systems via Painleve analysis. This conference provided aforum for general exposition and discussion of recent developments in nonlinear waves and related areas with potential applications to other fields. The book will be of interest to graduate students and researchers interested in mathematics, physics, and engineering.

MCAT Physics and Math Review 2019-2020
MCAT Physics and Math Review 2019-2020

Author: Kaplan Test Prep

Publisher: Simon and Schuster

Published: 2018-07-03

Total Pages: 855

ISBN-13: 1506235476

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Kaplan's MCAT Physics and Math Review 2019-2020 offers an expert study plan, detailed subject review, and hundreds of online and in-book practice questions – all authored by the experts behind the MCAT prep course that has helped more people get into medical school than all other major courses combined. Prepping for the MCAT is a true challenge. Kaplan can be your partner along the way – offering guidance on where to focus your efforts and how to organize your review. This book has been updated to match the AAMC's guidelines precisely—no more worrying if your MCAT review is comprehensive! The Most Practice More than 350 questions in the book and access to even more online – more practice than any other MCAT physics and math book on the market. The Best Practice Comprehensive physics and math subject review is written by top-rated, award-winning Kaplan instructors. Full-color, 3-D illustrations from Scientific American, charts, graphs and diagrams help turn even the most complex science into easy-to-visualize concepts. All material is vetted by editors with advanced science degrees and by a medical doctor. Online resources, including a full-length practice test, help you practice in the same computer-based format you'll see on Test Day. Expert Guidance High-yield badges throughout the book identify the top 100 topics most-tested by the AAMC. We know the test: The Kaplan MCAT team has spent years studying every MCAT-related document available. Kaplan's expert psychometricians ensure our practice questions and study materials are true to the test.