Mathematical Modeling and Immunology An enormous amount of human effort and economic resources has been directed in this century to the fight against cancer. The purpose, of course, has been to find strategies to overcome this hard, challenging and seemingly endless struggle. We can readily imagine that even greater efforts will be required in the next century. The hope is that ultimately humanity will be successful; success will have been achieved when it is possible to activate and control the immune system in its competition against neoplastic cells. Dealing with the above-mentioned problem requires the fullest pos sible cooperation among scientists working in different fields: biology, im munology, medicine, physics and, we believe, mathematics. Certainly, bi ologists and immunologists will make the greatest contribution to the re search. However, it is now increasingly recognized that mathematics and computer science may well able to make major contributions to such prob lems. We cannot expect mathematicians alone to solve fundamental prob lems in immunology and (in particular) cancer research, but valuable sup port, however modest, can be provided by mathematicians to the research aspirations of biologists and immunologists working in this field."

Mathematical Modeling and Immunology An enormous amount of human effort and economic resources has been directed in this century to the fight against cancer. The purpose, of course, has been to find strategies to overcome this hard, challenging and seemingly endless struggle. We can readily imagine that even greater efforts will be required in the next century. The hope is that ultimately humanity will be successful; success will have been achieved when it is possible to activate and control the immune system in its competition against neoplastic cells. Dealing with the above-mentioned problem requires the fullest pos sible cooperation among scientists working in different fields: biology, im munology, medicine, physics and, we believe, mathematics. Certainly, bi ologists and immunologists will make the greatest contribution to the re search. However, it is now increasingly recognized that mathematics and computer science may well able to make major contributions to such prob lems. We cannot expect mathematicians alone to solve fundamental prob lems in immunology and (in particular) cancer research, but valuable sup port, however modest, can be provided by mathematicians to the research aspirations of biologists and immunologists working in this field."

"Have you wondered how rainbows or sand dunes form? Does it puzzle you why drying mud forms polygonally shaped cracks? Can you explain the patterns on a butterfly's wings or how birds fly? In this delightful book, John Adam invites us to question and to share his enthusiasm for developing mathematical models to explore a wide range of everyday natural phenomena. "Mathematics in Nature" can be used as a text on mathematical modeling or as a book to dip into and encourage us to observe and wonder at the beauty of nature. It has the potential of becoming a classic."--Brian Sleeman, University of Leeds

"This is a book that I will want to keep close to hand so that I will not be stumped by all those seemingly simple yet subtle questions about nature: Why can fleas jump so high? Why is visibility better in rain than in fog? Why does a river meander? How high can trees grow? But it is much more than a compendium of useful facts and explanations. It is the clearest guide I have seen to the art of conceptualizing, simplifying, and modeling natural phenomena--no less than an exegesis on how good quantitative science is done."--Phillip Ball, Consultant Editor, "Nature"

""Mathematics in Nature" leads the calculus-literate reader on a vigorous tour of nature's visible patterns--from the radiator-sailed dinosaur Dimetrodon to fracturing of dried mud and ceramic glazes, from the dispersion of rainbows and iridescence of beetles to the pearling of spider silk. Eschewing phenomena that are too small to see or too large to grasp, Adam shows how elementary college mathematics, rigorously applied, can give precise expression to everyday natural phenomena. His extraordinary range of examples andmeticulous explanations document mathematics' wonderful capacity to describe and explain nature's patterns."--Lynn Arthur Steen, St. Olaf College

"This work is outstanding! The color photographs are beautiful. The writing style is splendid."--Robert B. Banks, author of "Towing Icebergs, Falling Dominoes, and Other Adventures in Applied Mathematics"

"This is a unique, even great book. It is in the spirit of a number of books on topics like symmetry and chaos that look at mathematics in the context of visually striking natural and other phenomena but is more broadly based. The author leads with the phenomena and follows with the math, making the book accessible to a wider audience while still appealing to math students and faculty."--Frank Wattenberg

"This is one of the best contemporary texts on the subject, appealing to a very broad audience that will definitely love this excellent book."--Yuri V. Rogovchenko, "Zentralblatt Math" (European Mathematical Society)

"X and the City," a book of diverse and accessible math-based topics, uses basic modeling to explore a wide range of entertaining questions about urban life. How do you estimate the number of dental or doctor's offices, gas stations, restaurants, or movie theaters in a city of a given size? How can mathematics be used to maximize traffic flow through tunnels? Can you predict whether a traffic light will stay green long enough for you to cross the intersection? And what is the likelihood that your city will be hit by an asteroid?

Every math problem and equation in this book tells a story and examples are explained throughout in an informal and witty style. The level of mathematics ranges from precalculus through calculus to some differential equations, and any reader with knowledge of elementary calculus will be able to follow the materials with ease. There are also some more challenging problems sprinkled in for the more advanced reader.

Filled with interesting and unusual observations about how cities work, "X and the City" shows how mathematics undergirds and plays an important part in the metropolitan landscape.

"X and the City," a book of diverse and accessible math-based topics, uses basic modeling to explore a wide range of entertaining questions about urban life. How do you estimate the number of dental or doctor's offices, gas stations, restaurants, or movie theaters in a city of a given size? How can mathematics be used to maximize traffic flow through tunnels? Can you predict whether a traffic light will stay green long enough for you to cross the intersection? And what is the likelihood that your city will be hit by an asteroid?

Every math problem and equation in this book tells a story and examples are explained throughout in an informal and witty style. The level of mathematics ranges from precalculus through calculus to some differential equations, and any reader with knowledge of elementary calculus will be able to follow the materials with ease. There are also some more challenging problems sprinkled in for the more advanced reader.

Filled with interesting and unusual observations about how cities work, "X and the City" shows how mathematics undergirds and plays an important part in the metropolitan landscape.

How heavy is that cloud? Why can you see farther in rain than in fog? Why are the droplets on that spider web spaced apart so evenly? If you have ever asked questions like these while outdoors, and wondered how you might figure out the answers, this is a book for you. An entertaining and informative collection of fascinating puzzles from the natural world around us, "A Mathematical Nature Walk" will delight anyone who loves nature or math or both.

John Adam presents ninety-six questions about many common natural phenomena--and a few uncommon ones--and then shows how to answer them using mostly basic mathematics. Can you weigh a pumpkin just by carefully looking at it? Why can you see farther in rain than in fog? What causes the variations in the colors of butterfly wings, bird feathers, and oil slicks? And why are large haystacks prone to spontaneous combustion? These are just a few of the questions you'll find inside. Many of the problems are illustrated with photos and drawings, and the book also has answers, a glossary of terms, and a list of some of the patterns found in nature. About a quarter of the questions can be answered with arithmetic, and many of the rest require only precalculus. But regardless of math background, readers will learn from the informal descriptions of the problems and gain a new appreciation of the beauty of nature and the mathematics that lies behind it.

""Guesstimation" is a delightful book that, page after page, gleams with insight into the measure of all things--from house pets to lottery tickets and from the kitchen to the cosmos. Meanwhile, the authors cleverly teach you some fundamental chemistry, physics, and biology, leaving you enlightened and curiously comfortable with all that once seemed intractable in the world."--Neil deGrasse Tyson, astrophysicist at the American Museum of Natural History, author of "Death by Black Hole: And Other Cosmic Quandaries"

"Wow, I suddenly grasped concepts that have eluded me for a lifetime. If you work anywhere in the professional world and are aiming for the corner office, this little book could have significant impact on both your analytical abilities and the way you are perceived by others. An absolute eye-opener!"--Martin Yate, New York Times best-selling author of the "Knock 'Em Dead" job-search and career-management books

"In a world where we are constantly bombarded with quantitative information (and disinformation) and where implausible factoids become established truths by repetition, acquiring a sound grounding in 'numeric literacy' has almost become a civic duty. Weinstein and Adam show to us that it can also be fun! An extremely useful book--not just for the intelligent layperson, but for virtually everyone: politicians, students, policymakers and, yes, sometimes even physicists."--Riccardo Rebonato, Royal Bank of Scotland, author of "Plight of the Fortune Tellers"

"As well as giving insight into how scientists think, this book packs in more amazing facts than you could shake a stick at. Learn the technique of 'guesstimation' and you will be able to astound your friends atparties, as well as avoid getting ripped off by misleading advertising claims. You may even be able to work out how many facts you can shake a stick at."--John Gribbin, author of "Deep Simplicity: Bringing Order to Chaos and Complexity"

"A very interesting and informative work, showing both how important and how easy it can be to estimate magnitudes. This book will amuse you while it instructs."--Gino Segre, author of "A Matter of Degrees"

"This is definitely my kind of book. The authors show, using numerous examples, how readers can make numerical estimates of quantities--some absurd and some fascinating--in a wide variety of areas. This is a very useful talent--be it in everyday life, in one's career, or in job interviews."--Robert Ehrlich, author of "Eight Preposterous Propositions"

"This book will benefit teachers and students in science and engineering, from grade school to college. The problems are well chosen to illustrate increasingly complex themes, culminating in energy conservation, risk assessment, and environmental problems. The solutions are careful, complete, and illuminating. General readers with a taste for mathematical puzzles will enjoy it."--Hans Christian von Baeyer, author of "The Fermi Solution"

This one-of-a-kind book presents many of the mathematical concepts, structures, and techniques used in the study of rays, waves, and scattering. Panoramic in scope, it includes discussions of how ocean waves are refracted around islands and underwater ridges, how seismic waves are refracted in the earth's interior, how atmospheric waves are scattered by mountains and ridges, how the scattering of light waves produces the blue sky, and meteorological phenomena such as rainbows and coronas. Rays, Waves, and Scattering is a valuable resource for practitioners, graduate students, and advanced undergraduates in applied mathematics, theoretical physics, and engineering. Bridging the gap between advanced treatments of the subject written for specialists and less mathematical books aimed at beginners, this unique mathematical compendium features problems and exercises throughout that are geared to various levels of sophistication, covering everything from Ptolemy's theorem to Airy integrals (as well as more technical material), and several informative appendixes. * Provides a panoramic look at wave motion in many different contexts* Features problems and exercises throughout* Includes numerous appendixes, some on topics not often covered* An ideal reference book for practitioners* Can also serve as a supplemental text in classical applied mathematics, particularly wave theory and mathematical methods in physics and engineering* Accessible to anyone with a strong background in ordinary differential equations, partial differential equations, and functions of a complex variable

"Adams has skillfully analyzed hundreds of primary source docu-ments and integrated contemporary political, social and cultural elements in bringing to light the values, customs, and controver-sies which have shaped the Corps' 125-year history."--"Texas"" Aggie"