John A. Adam - Böcker

From rainbows, river meanders, and shadows to spider webs, honeycombs, and the markings on animal coats, the visible world is full of patterns that can be described mathematically. Examining such readily observable phenomena, this book introduces readers to the beauty of nature as revealed by mathematics and the beauty of mathematics as revealed in nature. Generously illustrated, written in an informal style, and replete with examples from everyday life, Mathematics in Nature is an excellent and undaunting introduction to the ideas and methods of mathematical modeling. It illustrates how mathematics can be used to formulate and solve puzzles observed in nature and to interpret the solutions. In the process, it teaches such topics as the art of estimation and the effects of scale, particularly what happens as things get bigger. Readers will develop an understanding of the symbiosis that exists between basic scientific principles and their mathematical expressions as well as a deeper appreciation for such natural phenomena as cloud formations, halos and glories, tree heights and leaf patterns, butterfly and moth wings, and even puddles and mud cracks.Developed out of a university course, this book makes an ideal supplemental text for courses in applied mathematics and mathematical modeling. It will also appeal to mathematics educators and enthusiasts at all levels, and is designed so that it can be dipped into at leisure.

Guesstimation is a book that unlocks the power of approximation--it's popular mathematics rounded to the nearest power of ten! The ability to estimate is an important skill in daily life. More and more leading businesses today use estimation questions in interviews to test applicants' abilities to think on their feet. Guesstimation enables anyone with basic math and science skills to estimate virtually anything--quickly--using plausible assumptions and elementary arithmetic. Lawrence Weinstein and John Adam present an eclectic array of estimation problems that range from devilishly simple to quite sophisticated and from serious real-world concerns to downright silly ones. How long would it take a running faucet to fill the inverted dome of the Capitol? What is the total length of all the pickles consumed in the US in one year? What are the relative merits of internal-combustion and electric cars, of coal and nuclear energy? The problems are marvelously diverse, yet the skills to solve them are the same.The authors show how easy it is to derive useful ballpark estimates by breaking complex problems into simpler, more manageable ones--and how there can be many paths to the right answer. The book is written in a question-and-answer format with lots of hints along the way. It includes a handy appendix summarizing the few formulas and basic science concepts needed, and its small size and French-fold design make it conveniently portable. Illustrated with humorous pen-and-ink sketches, Guesstimation will delight popular-math enthusiasts and is ideal for the classroom.

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

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 mathematics unveils the beauty of the natural worldMathematics in Nature reveals how mathematics provides a unifying language for understanding the hidden order of nature. In this richly illustrated book, John Adam guides readers from basic models using everyday arithmetic to the modeling of intricate, ever-evolving patterns, showing how even simple equations can illuminate the structure and behavior of complex systems.Adam introduces arithmetic and algebraic models that capture essential ideas of population growth, resource consumption, and environmental feedbacks. Through discussions of shape, size, and scale, he explains why proportions and dimensions matter across biology and physics. He delves into the physics of light and air to reveal the mathematical patterns behind atmospheric beauty—from rainbows, halos, and glories to mirages and cloud formations—and demonstrates how equations can be used to describe ripples on water, sound in air, and the dramatic surges of tidal bores. Adam progresses from Fibonacci sequences, metallic ratios, and natural spirals to pattern formation and self-organization in living and nonliving systems.With new chapters on the dynamics of climate change and pandemics, this fully revised edition reveals how mathematical modeling brings coherence and clarity to our understanding of nature’s complexity and the forces that shape our environment.

How mathematics unveils the beauty of the natural worldMathematics in Nature reveals how mathematics provides a unifying language for understanding the hidden order of nature. In this richly illustrated book, John Adam guides readers from basic models using everyday arithmetic to the modeling of intricate, ever-evolving patterns, showing how even simple equations can illuminate the structure and behavior of complex systems.Adam introduces arithmetic and algebraic models that capture essential ideas of population growth, resource consumption, and environmental feedbacks. Through discussions of shape, size, and scale, he explains why proportions and dimensions matter across biology and physics. He delves into the physics of light and air to reveal the mathematical patterns behind atmospheric beauty—from rainbows, halos, and glories to mirages and cloud formations—and demonstrates how equations can be used to describe ripples on water, sound in air, and the dramatic surges of tidal bores. Adam progresses from Fibonacci sequences, metallic ratios, and natural spirals to pattern formation and self-organization in living and nonliving systems.With new chapters on the dynamics of climate change and pandemics, this fully revised edition reveals how mathematical modeling brings coherence and clarity to our understanding of nature’s complexity and the forces that shape our environment.

A collection of seven interdisciplinary surveys on modelling tumour dynamics and interactions between tumours and immune systems. Modelling and simulation of general behaviours of immune systems is also discussed. Each survey covers a specialized field and provides a detailed description of the current state of research. the reader should be able to obtain essential information on the methodological approach used and on the models that are categorized and used. Topics covered include: general tumour biology modelling; growth kinetics; kinetic cellular theory; tumour-immune system interactions; and heterogeneity and growth control. There is also a glossary of scientific terms in immunology and biology to ensure a clear understanding of biological terms.

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.

This is a textbook on basic to intermediate mathematics for undergraduate students majoring in the physical sciences and engineering. Many chapters, covering topics like Green's functions, calculus of variations, and functions of a complex variable, are well-suited for graduate classes. Additionally, researchers can benefit from the book as a mathematical refresher for their professional work.The book provides readers with a fundamental understanding of underlying principles, using derivations based more on mathematical intuition rather than exposing them to multiple theorems, proofs, and lemmas. Each chapter includes highly relevant examples with detailed solutions and explanations, promoting a practical application of knowledge to real problems in the physical sciences. For the convenience of both students and instructors, there are end-of-chapter exercises with answers that can be easily utilized for assignments.The book is not a replacement for calculus textbooks, but rather a guide to the mathematics most relevant to the physical sciences and engineering.In conclusion, this book can be readily adapted for upper-level undergraduate and graduate classes, particularly those focusing on mathematical methods for students in physical sciences, applied mathematics, and engineering majors.