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The Computer as Crucible

The Computer as Crucible Author Jonathan Borwein
ISBN-10 9781439876916
Release 2008-10-28
Pages 170
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Keith Devlin and Jonathan Borwein, two well-known mathematicians with expertise in different mathematical specialties but with a common interest in experimentation in mathematics, have joined forces to create this introduction to experimental mathematics. They cover a variety of topics and examples to give the reader a good sense of the current state of play in the rapidly growing new field of experimental mathematics. The writing is clear and the explanations are enhanced by relevant historical facts and stories of mathematicians and their encounters with the field over time.

Introduction to Experimental Mathematics

Introduction to Experimental Mathematics Author Søren Eilers
ISBN-10 9781108132794
Release 2017-06-01
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Mathematics is not, and never will be, an empirical science, but mathematicians are finding that the use of computers and specialized software allows the generation of mathematical insight in the form of conjectures and examples, which pave the way for theorems and their proofs. In this way, the experimental approach to pure mathematics is revolutionizing the way research mathematicians work. As the first of its kind, this book provides material for a one-semester course in experimental mathematics that will give students the tools and training needed to systematically investigate and develop mathematical theory using computer programs written in Maple. Accessible to readers without prior programming experience, and using examples of concrete mathematical problems to illustrate a wide range of techniques, the book gives a thorough introduction to the field of experimental mathematics, which will prepare students for the challenge posed by open mathematical problems.

Pi The Next Generation

Pi  The Next Generation Author David H. Bailey
ISBN-10 9783319323770
Release 2016-08-20
Pages 507
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This book contains a compendium of 25 papers published since the 1970s dealing with pi and associated topics of mathematics and computer science. The collection begins with a Foreword by Bruce Berndt. Each contribution is preceded by a brief summary of its content as well as a short key word list indicating how the content relates to others in the collection. The volume includes articles on actual computations of pi, articles on mathematical questions related to pi (e.g., “Is pi normal?”), articles presenting new and often amazing techniques for computing digits of pi (e.g., the “BBP” algorithm for pi, which permits one to compute an arbitrary binary digit of pi without needing to compute any of the digits that came before), papers presenting important fundamental mathematical results relating to pi, and papers presenting new, high-tech techniques for analyzing pi (i.e., new graphical techniques that permit one to visually see if pi and other numbers are “normal”). This volume is a companion to Pi: A Source Book whose third edition released in 2004. The present collection begins with 2 papers from 1976, published by Eugene Salamin and Richard Brent, which describe “quadratically convergent” algorithms for pi and other basic mathematical functions, derived from some mathematical work of Gauss. Bailey and Borwein hold that these two papers constitute the beginning of the modern era of computational mathematics. This time period (1970s) also corresponds with the introduction of high-performance computer systems (supercomputers), which since that time have increased relentlessly in power, by approximately a factor of 100,000,000, advancing roughly at the same rate as Moore’s Law of semiconductor technology. This book may be of interest to a wide range of mathematical readers; some articles cover more advanced research questions suitable for active researchers in the field, but several are highly accessible to undergraduate mathematics students.

Mathematics by Experiment 2nd Edition

Mathematics by Experiment  2nd Edition Author Jonathan Borwein
ISBN-10 9781568814421
Release 2008-10-27
Pages 377
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This revised and updated second edition maintains the content and spirit of the first edition and includes a new chapter, "Recent Experiences", that provides examples of experimental mathematics that have come to light since the publication of the first edition in 2003. For more examples and insights, Experimentation in Mathematics: Computational Paths to Discovery is a highly recommended companion.

Convex Analysis and Nonlinear Optimization

Convex Analysis and Nonlinear Optimization Author Jonathan Borwein
ISBN-10 9780387312569
Release 2010-05-05
Pages 310
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Optimization is a rich and thriving mathematical discipline, and the underlying theory of current computational optimization techniques grows ever more sophisticated. This book aims to provide a concise, accessible account of convex analysis and its applications and extensions, for a broad audience. Each section concludes with an often extensive set of optional exercises. This new edition adds material on semismooth optimization, as well as several new proofs.

Experimentation in Mathematics

Experimentation in Mathematics Author Jonathan M. Borwein
ISBN-10 9781439864197
Release 2004-04-12
Pages 368
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New mathematical insights and rigorous results are often gained through extensive experimentation using numerical examples or graphical images and analyzing them. Today computer experiments are an integral part of doing mathematics. This allows for a more systematic approach to conducting and replicating experiments. The authors address the role of experimental research in the statement of new hypotheses and the discovery of new results that chart the road to future developments. Following the lead of Mathematics by Experiment: Plausible Reasoning in the 21st Century this book gives numerous additional case studies of experimental mathematics in action, ranging from sequences, series, products, integrals, Fourier series, zeta functions, partitions, primes and polynomials. Some advanced numerical techniques are also presented. To get a taste of the material presented in both books view the condensed version.

The Mathematical Mechanic

The Mathematical Mechanic Author Mark Levi
ISBN-10 9780691154565
Release 2012
Pages 186
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In this delightful book, Levi turns math and physics upside down, revealing how physics can simplify proofs and lead to quicker solutions and new theorems, and how physical solutions can illustrate why results are true in ways lengthy mathematical calculations never can.

Illustrated Guide to Home Chemistry Experiments

Illustrated Guide to Home Chemistry Experiments Author Robert Bruce Thompson
ISBN-10 9781449331429
Release 2012-02-17
Pages 432
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For students, DIY hobbyists, and science buffs, who can no longer get real chemistry sets, this one-of-a-kind guide explains how to set up and use a home chemistry lab, with step-by-step instructions for conducting experiments in basic chemistry -- not just to make pretty colors and stinky smells, but to learn how to do real lab work: Purify alcohol by distillation Produce hydrogen and oxygen gas by electrolysis Smelt metallic copper from copper ore you make yourself Analyze the makeup of seawater, bone, and other common substances Synthesize oil of wintergreen from aspirin and rayon fiber from paper Perform forensics tests for fingerprints, blood, drugs, and poisons and much more From the 1930s through the 1970s, chemistry sets were among the most popular Christmas gifts, selling in the millions. But two decades ago, real chemistry sets began to disappear as manufacturers and retailers became concerned about liability. ,em>The Illustrated Guide to Home Chemistry Experiments steps up to the plate with lessons on how to equip your home chemistry lab, master laboratory skills, and work safely in your lab. The bulk of this book consists of 17 hands-on chapters that include multiple laboratory sessions on the following topics: Separating Mixtures Solubility and Solutions Colligative Properties of Solutions Introduction to Chemical Reactions & Stoichiometry Reduction-Oxidation (Redox) Reactions Acid-Base Chemistry Chemical Kinetics Chemical Equilibrium and Le Chatelier's Principle Gas Chemistry Thermochemistry and Calorimetry Electrochemistry Photochemistry Colloids and Suspensions Qualitative Analysis Quantitative Analysis Synthesis of Useful Compounds Forensic Chemistry With plenty of full-color illustrations and photos, Illustrated Guide to Home Chemistry Experiments offers introductory level sessions suitable for a middle school or first-year high school chemistry laboratory course, and more advanced sessions suitable for students who intend to take the College Board Advanced Placement (AP) Chemistry exam. A student who completes all of the laboratories in this book will have done the equivalent of two full years of high school chemistry lab work or a first-year college general chemistry laboratory course. This hands-on introduction to real chemistry -- using real equipment, real chemicals, and real quantitative experiments -- is ideal for the many thousands of young people and adults who want to experience the magic of chemistry.

Illustrated Guide to Home Biology Experiments

Illustrated Guide to Home Biology Experiments Author Robert Thompson
ISBN-10 9781449396596
Release 2012-04-19
Pages 359
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Perfect for middle- and high-school students and DIY enthusiasts, this full-color guide teaches you the basics of biology lab work and shows you how to set up a safe lab at home. Features more than 30 educational (and fun) experiments.

An Introduction to Modern Mathematical Computing

An Introduction to Modern Mathematical Computing Author Jonathan M. Borwein
ISBN-10 1461401224
Release 2011-07-15
Pages 216
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Thirty years ago mathematical, as opposed to applied numerical, computation was difficult to perform and so relatively little used. Three threads changed that: the emergence of the personal computer; the discovery of fiber-optics and the consequent development of the modern internet; and the building of the Three “M’s” Maple, Mathematica and Matlab. We intend to persuade that Maple and other like tools are worth knowing assuming only that one wishes to be a mathematician, a mathematics educator, a computer scientist, an engineer or scientist, or anyone else who wishes/needs to use mathematics better. We also hope to explain how to become an `experimental mathematician' while learning to be better at proving things. To accomplish this our material is divided into three main chapters followed by a postscript. These cover elementary number theory, calculus of one and several variables, introductory linear algebra, and visualization and interactive geometric computation.

Tools and Mathematics

Tools and Mathematics Author John Monaghan
ISBN-10 9783319023960
Release 2016-04-18
Pages 483
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This book is an exploration of tools and mathematics and issues in mathematics education related to tool use. The book has five parts. The first part reflects on doing a mathematical task with different tools, followed by a mathematician's account of tool use in his work. The second considers prehistory and history: tools in the development from ape to human; tools and mathematics in the ancient world; tools for calculating; and tools in mathematics instruction. The third part opens with a broad review of technology and intellectual trends, circa 1970, and continues with three case studies of approaches in mathematics education and the place of tools in these approaches. The fourth part considers issues related to mathematics instructions: curriculum, assessment and policy; the calculator debate; mathematics in the real world; and teachers' use of technology. The final part looks to the future: task and tool design and new forms of activity via connectivity and computer games.

Illustrated Guide to Home Forensic Science Experiments

Illustrated Guide to Home Forensic Science Experiments Author Robert Bruce Thompson
ISBN-10 9781449334475
Release 2012-08-07
Pages 448
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Have you ever wondered whether the forensic science you’ve seen on TV is anything like the real thing? There’s no better way to find out than to roll up your sleeves and do it yourself. This full-color book offers advice for setting up an inexpensive home lab, and includes more than 50 hands-on lab sessions that deal with forensic science experiments in biology, chemistry, and physics. You’ll learn the practical skills and fundamental knowledge needed to pursue forensics as a lifelong hobby—or even a career. The forensic science procedures in this book are not merely educational, they’re the real deal. Each chapter includes one or more lab sessions devoted to a particular topic. You’ll find a complete list of equipment and chemicals you need for each session. Analyze soil, hair, and fibers Match glass and plastic specimens Develop latent fingerprints and reveal blood traces Conduct drug and toxicology tests Analyze gunshot and explosives residues Detect forgeries and fakes Analyze impressions, such as tool marks and footprints Match pollen and diatom samples Extract, isolate, and visualize DNA samples Through their company, The Home Scientist, LLC (, the authors also offer inexpensive custom kits that provide specialized equipment and supplies you’ll need to complete the experiments. Add a microscope and some common household items and you’re good to go.

Experimental Mathematics in Action

Experimental Mathematics in Action Author David H. Bailey
ISBN-10 9781439864333
Release 2007-05-31
Pages 337
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With the continued advance of computing power and accessibility, the view that "real mathematicians don't compute" no longer has any traction for a newer generation of mathematicians. The goal in this book is to present a coherent variety of accessible examples of modern mathematics where intelligent computing plays a significant role and in so doing to highlight some of the key algorithms and to teach some of the key experimental approaches.

Python Scripting for Computational Science

Python Scripting for Computational Science Author Hans Petter Langtangen
ISBN-10 9783662054505
Release 2013-03-14
Pages 732
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Scripting with Python makes you productive and increases the reliability of your scientific work. Here, the author teaches you how to develop tailored, flexible, and efficient working environments built from small programs (scripts) written in Python. The focus is on examples and applications of relevance to computational science: gluing existing applications and tools, e.g. for automating simulation, data analysis, and visualization; steering simulations and computational experiments; equipping programs with graphical user interfaces; making computational Web services; creating interactive interfaces with a Maple/Matlab-like syntax to numerical applications in C/C++ or Fortran; and building flexible object-oriented programming interfaces to existing C/C++ or Fortran libraries.

Caveman Chemistry

Caveman Chemistry Author Kevin M. Dunn
ISBN-10 1581125666
Release 2003
Pages 409
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Half a million years ago our ancestors learned to make fire from scratch. They crafted intricate tools from stone and brewed mind-altering elixirs from honey. Their descendants transformed clay into pottery, wool into clothing, and ashes into cleansers. In ceramic crucibles they won metal from rock, the metals lead to colored glazes and glass. Buildings of brick and mortar enshrined books of parchment and paper. Kings and queens demanded ever more colorful clothing and accessories in order to out-class clod-hoppers and call-girls. Kingdoms rose and fell by the power of saltpeter, sulfur, and charcoal. And the demands of everyday folk for glass and paper and soap stimulated the first round of chemical industrialization. From sulfuric acid to sodium carbonate. From aniline dyes to analgesic drugs. From blasting powder to fertilizers and plastics. In a phrase, From Caveman to Chemist. Your guides on this journey are the four alchemical elements; Fire, Earth, Air and Water. These archetypical characters deliver first-hand accounts of the births of their respective technologies. The spirit of Fire, for example, was born in the first creature to cultivate the flame. This spirit passed from one person to another, from one generation to another, from one millennium to another, arriving at last in the pages of this book. The spirit of Earth taught folks to make tools of stone, the spirit of Air imparted knowledge of units and the spirit of Water began with the invention of spirits. Having traveled the world from age to age, who can say where they will find their next home? Perhaps they will find one in you.

Standard and Microscale Experiments in General Chemistry

Standard and Microscale Experiments in General Chemistry Author Carl B. Bishop
ISBN-10 0534424570
Release 2003
Pages 556
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This comprehensive lab manual contains a wide array of experiments without sacrificing organizational clarity and includes categories on Energy, Kinetics, and Equilibrium. All experiments have undergone significant testing before being finalized, and many microscale experiments have been added to allow for more efficient and cost-effective means of conducting experiments.

Crucible Zero

Crucible Zero Author Devon Monk
ISBN-10 9780698140240
Release 2015-09-01
Pages 368
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The national bestselling author of Infinity Bell returns to her “fresh and unique”* world where the truce between the ruling Houses has shattered and chaos now reigns. Only one woman has the power to save the world—but she could also destroy it. . . . Matilda Case never thought of herself as a hero. But because she is galvanized—and nearly immortal in her stitched, endlessly healing body—she doesn’t have much of a choice. Even if she doesn’t want to save the world, she’s the only one capable of traveling in time to do so. But her rescue attempt hasn’t gone as planned. She’s stuck in an alternate universe, and her world is in danger of disappearing. Worst of all, an unfathomably powerful man who can also travel through history doesn’t want her to put things to rights. He’s willing to wage bloody war to stop Matilda, unless she surrenders control of time to him. Now, with the minutes ticking, Matilda must make impossible decisions, knowing that one wrong choice will destroy her—and any chance of saving everything she loves. . . . *A Book Obsession