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A Mathematical Journey to Quantum Mechanics (UNITEXT for Physics)
by Wladimir-Georges Boskoff Salvatore CapozzielloThis book provides an itinerary to quantum mechanics taking into account the basic mathematics to formulate it. Specifically, it features the main experiments and postulates of quantum mechanics pointing out their mathematical prominent aspects showing how physical concepts and mathematical tools are deeply intertwined. The material covers topics such as analytic mechanics in Newtonian, Lagrangian, and Hamiltonian formulations, theory of light as formulated in special relativity, and then why quantum mechanics is necessary to explain experiments like the double-split, atomic spectra, and photoelectric effect. The Schrödinger equation and its solutions are developed in detail. It is pointed out that, starting from the concept of the harmonic oscillator, it is possible to develop advanced quantum mechanics. Furthermore, the mathematics behind the Heisenberg uncertainty principle is constructed towards advanced quantum mechanical principles. Relativistic quantum mechanics is finally considered.The book is devoted to undergraduate students from University courses of Physics, Mathematics, Chemistry, and Engineering. It consists of 50 self-contained lectures, and any statement and theorem are demonstrated in detail. It is the companion book of "A Mathematical Journey to Relativity", by the same Authors, published by Springer in 2020.
A Mathematical Journey to Relativity: Deriving Special and General Relativity with Basic Mathematics (UNITEXT for Physics)
by Wladimir-Georges Boskoff Salvatore CapozzielloThis book opens with an axiomatic description of Euclidean and non-Euclidean geometries. Euclidean geometry is the starting point to understand all other geometries and it is the cornerstone for our basic intuition of vector spaces. The generalization to non-Euclidean geometry is the following step to develop the language of Special and General Relativity. These theories are discussed starting from a full geometric point of view. Differential geometry is presented in the simplest way and it is applied to describe the physical world. The final result of this construction is deriving the Einstein field equations for gravitation and spacetime dynamics. Possible solutions, and their physical implications are also discussed: the Schwarzschild metric, the relativistic trajectory of planets, the deflection of light, the black holes, the cosmological solutions like de Sitter, Friedmann-Lemaître-Robertson-Walker, and Gödel ones. Some current problems like dark energy are also scketched. The book is self-contained and includes details of all proofs. It provides solutions or tips to solve problems and exercises. It is designed for undergraduate students and for all readers who want a first geometric approach to Special and General Relativity.
A Mathematical Journey to Relativity: Deriving Special and General Relativity with Basic Mathematics (UNITEXT for Physics)
by Wladimir-Georges Boskoff Salvatore CapozzielloThe 2nd edition of this textbook features more than 100 pages of new material, including four new chapters, as well as an improved discussion of differential geometry concepts and their applications. The textbook aims to provide a comprehensive geometric description of Special and General Relativity, starting from basic Euclidean geometry to more advanced non-Euclidean geometry and differential geometry. Readers will learn about the Schwarzschild metric, the relativistic trajectory of planets, the deflection of light, the black holes, and the cosmological solutions like de Sitter, Friedman-Lemaître-Robertson-Walker, and Gödel ones, as well as the implications of each of them for the observed physical world. In addition, the book provides step-by-step solutions to problems and exercises, making it an ideal introduction for undergraduate students and readers looking to gain a better understanding of Special and General Relativity. In this new edition, a wide discussion on metric-affine theories of gravity and equivalent formulations of General Relativity is reported. The aim is presenting also topics which could be useful for PhD students and researchers studying General Relativity from an advanced point of view.
A Mathematical Look at Politics
by E. Arthur Robinson Jr. Daniel H. UllmanWhat Ralph Nader's spoiler role in the 2000 presidential election tells us about the American political system. Why Montana went to court to switch the 1990 apportionment to Dean's method. How the US tried to use game theory to win the Cold War, and why it didn't work. When students realize that mathematical thinking can address these sorts of pres
A Mathematical Modeling Approach from Nonlinear Dynamics to Complex Systems (Nonlinear Systems and Complexity #22)
by Elbert E. MacauThis book collects recent developments in nonlinear and complex systems. It provides up-to-date theoretic developments and new techniques based on a nonlinear dynamical systems approach that can be used to model and understand complex behavior in nonlinear dynamical systems. It covers symmetry groups, conservation laws, risk reduction management, barriers in Hamiltonian systems, and synchronization and chaotic transient. Illustrating mathematical modeling applications to nonlinear physics and nonlinear engineering, the book is ideal for academic and industrial researchers concerned with machinery and controls, manufacturing, and controls.· Introduces new concepts for understanding and modeling complex systems;· Explains risk reduction management in complex systems;· Examines the symmetry group approach to understanding complex systems;· Illustrates the relation between transient chaos and crises.
A Mathematical Mystery Tour: Higher-Thinking Math Tasks (Grades 5-12)
by Mark WahlA Mathematical Mystery Tour has been used by thousands of students and has inspired adults to greater appreciation of the secret number language of nature. It is multidisciplinary, visual, and hands-on, practicing skills while also requiring deep math thinking. The activities are reproducible and each is accompanied with informational teacher pages giving answers, historical notes, teacher suggestions, and activity extensions.Let this geographically alive Mystery Tour integrate math with art, science, philosophy, history, social studies, and language arts. The use of the calculator, geometric construction, metric measurement, problem solving, formulating results, building models and making inferences is woven throughout the book.Each book purchase includes a link to a downloadable student newspaper, the Mathematical Mystery Tour Guide, coordinated with the book content. It is capable of being broken up into various assignments and handed out as print or sent whole electronically to each student. It is filled with games, riddles, dramatic historical information, crosswords, provocative questions, and additional math thought activities.
A Mathematical Nature Walk
by John A. AdamHow 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.
A Mathematical Odyssey: Journey from the Real to the Complex
by Harold R. Parks Steven G. KrantzMathematics is a poem. It is a lucid, sensual, precise exposition of beautiful ideas directed to specific goals. It is worthwhile to have as broad a cross-section of mankind as possible be conversant with what goes on in mathematics. Just as everyone knows that the Internet is a powerful and important tool for communication, so everyone should know that the Poincaré conjecture gives us important information about the shape of our universe. Just as every responsible citizen realizes that the mass-production automobile was pioneered by Henry Ford, so everyone should know that the P/NP problem has implications for security and data manipulation that will affect everyone. This book endeavors to tell the story of the modern impact of mathematics, of its trials and triumphs and insights, in language that can be appreciated by a broad audience. It endeavors to show what mathematics means for our lives, how it impacts all of us, and what new thoughts it should cause us to entertain. It introduces new vistas of mathematical ideas and shares the excitement of new ideas freshly minted. It discusses the significance and impact of these ideas, and gives them meaning that will travel well and cause people to reconsider their place in the universe. Mathematics is one of mankind's oldest disciplines. Along with philosophy, it has shaped the very modus of human thought. And it continues to do so. To be unaware of modern mathematics is to miss out on a large slice of life. It is to be left out of essential modern developments. We want to address this point, and do something about it. This is a book to make mathematics exciting for people of all interests and all walks of life. Mathematics is exhilarating, it is ennobling, it is uplifting, and it is fascinating. We want to show people this part of our world, and to get them to travel new paths.
A Mathematical Prelude to the Philosophy of Mathematics
by Stephen PollardThis book is based on two premises: one cannot understand philosophy of mathematics without understanding mathematics and one cannot understand mathematics without doing mathematics. It draws readers into philosophy of mathematics by having them do mathematics. It offers 298 exercises, covering philosophically important material, presented in a philosophically informed way. The exercises give readers opportunities to recreate some mathematics that will illuminate important readings in philosophy of mathematics. Topics include primitive recursive arithmetic, Peano arithmetic, Gödel's theorems, interpretability, the hierarchy of sets, Frege arithmetic and intuitionist sentential logic. The book is intended for readers who understand basic properties of the natural and real numbers and have some background in formal logic.
A Mathematical Primer for Social Statistics
by Dr John FoxJohn Fox's A Mathematical Primer for Social Statistics covers many often ignored yet important topics in mathematics and mathematical statistics. This text provides readers with the foundation on which an understanding of applied statistics rests. Intended Audience This book is ideal for advanced undergraduates, graduate students, and researchers in the social sciences who need to understand and use relatively advanced statistical methods but whose mathematical preparation for this work is insufficient. Learn more about "The Little Green Book" QASS Series! Click Here.
A Mathematical Primer for Social Statistics (Quantitative Applications in the Social Sciences)
by John FoxA Mathematical Primer for Social Statistics, Second Edition presents mathematics central to learning and understanding statistical methods beyond the introductory level: the basic "language" of matrices and linear algebra and its visual representation, vector geometry; differential and integral calculus; probability theory; common probability distributions; statistical estimation and inference, including likelihood-based and Bayesian methods. The volume concludes by applying mathematical concepts and operations to a familiar case, linear least-squares regression. The Second Edition pays more attention to visualization, including the elliptical geometry of quadratic forms and its application to statistics. It also covers some new topics, such as an introduction to Markov-Chain Monte Carlo methods, which are important in modern Bayesian statistics. A companion website includes materials that enable readers to use the R statistical computing environment to reproduce and explore computations and visualizations presented in the text. The book is an excellent companion to a "math camp" or a course designed to provide foundational mathematics needed to understand relatively advanced statistical methods.
A Mathematical Primer for Social Statistics (Quantitative Applications in the Social Sciences)
by John FoxA Mathematical Primer for Social Statistics, Second Edition presents mathematics central to learning and understanding statistical methods beyond the introductory level: the basic "language" of matrices and linear algebra and its visual representation, vector geometry; differential and integral calculus; probability theory; common probability distributions; statistical estimation and inference, including likelihood-based and Bayesian methods. The volume concludes by applying mathematical concepts and operations to a familiar case, linear least-squares regression. The Second Edition pays more attention to visualization, including the elliptical geometry of quadratic forms and its application to statistics. It also covers some new topics, such as an introduction to Markov-Chain Monte Carlo methods, which are important in modern Bayesian statistics. A companion website includes materials that enable readers to use the R statistical computing environment to reproduce and explore computations and visualizations presented in the text. The book is an excellent companion to a "math camp" or a course designed to provide foundational mathematics needed to understand relatively advanced statistical methods.
A Mathematical Primer on Quantum Mechanics (UNITEXT for Physics)
by Alessandro TetaThis book offers a rigorous yet elementary approach to quantum mechanics that will meet the needs of Master’s-level Mathematics students and is equally suitable for Physics students who are interested in gaining a deeper understanding of the mathematical structure of the theory. Throughout the coverage, which is limited to single-particle quantum mechanics, the focus is on formulating theory and developing applications in a mathematically precise manner. Following a review of selected key concepts in classical physics and the historical background, the basic elements of the theory of operators in Hilbert spaces are presented and used to formulate the rules of quantum mechanics. The discussion then turns to free particles, harmonic oscillators, delta potential, and hydrogen atoms, providing rigorous proofs of the corresponding dynamical properties. Starting from an analysis of these applications, readers are subsequently introduced to more advanced topics such as the classical limit, scattering theory, and spectral analysis of Schrödinger operators. The main content is complemented by numerous exercises that stimulate interactive learning and help readers check their progress.
A Mathematical Tapestry
by Peter Hilton Jean Pedersen Sylvie DonmoyerThis easy-to-read 2010 book demonstrates how a simple geometric idea reveals fascinating connections and results in number theory, the mathematics of polyhedra, combinatorial geometry, and group theory. Using a systematic paper-folding procedure it is possible to construct a regular polygon with any number of sides. This remarkable algorithm has led to interesting proofs of certain results in number theory, has been used to answer combinatorial questions involving partitions of space, and has enabled the authors to obtain the formula for the volume of a regular tetrahedron in around three steps, using nothing more complicated than basic arithmetic and the most elementary plane geometry. All of these ideas, and more, reveal the beauty of mathematics and the interconnectedness of its various branches. Detailed instructions, including clear illustrations, enable the reader to gain hands-on experience constructing these models and to discover for themselves the patterns and relationships they unearth.
A Mathematical View of Our World
by Harold Parks Gary Musser Lynn Trimpe Roger Maurer Vikki MaurerHighlighting the connections and patterns of mathematics in everyday life, this textbook explains the mathematics of choice, management applications, basic statistics and probability, and how growth and decay relate to finance. Topics include voting systems, project scheduling, picturing data, survey sampling methods, and Malthusian population growth.
A Mathematician Like Me
by Dr Shini SomaraStriking illustrations and an empowering story combine to introduce young readers to the world of maths, creative thinking and problem-solving.Setting off on a camping adventure with her cousin, Aliyah soon discovers that numbers are everywhere, whether it's counting out money at the shops, planning trips on the train or even stargazing in a forest. As Aliyah solves some sums of her own, she learns about the brilliant mathematicians who have helped us understand our world. Soon she can't wait to become a maths whizz too!With pages encouraging kids to play maths games with their friends, this brilliant picture book written by engineer and TV presenter Dr Shini Somara unlocks a love of numbers and creative thinking, and celebrates women in STEM.Also available in the series:- A Scientist Like Me- A Coder Like Me- An Engineer Like Me
A Mathematician Reads the Newspaper
by John Allen PaulosIn this lively volume, mathematician John Allen Paulos employs his singular wit to guide us through an unlikely mathematical jungle--the pages of the daily newspaper. From the Senate and sex to celebrities and cults, Paulos takes stories that may not seem to involve math at all and demonstrates how mathematical naïveté can put readers at a distinct disadvantage. Whether he’s using chaos theory to puncture economic and environmental predictions, applying logic to clarify the hazards of spin doctoring and news compression, or employing arithmetic and common sense to give us a novel perspective on greed and relationships, Paulos never fails to entertain and enlighten.
A Mathematician at the Ballpark: Odds and Probabilities for Baseball Fans
by Ken RossIn A Mathematician at the Ballpark, professor Ken Ross reveals the math behind the stats. This lively and accessible book shows baseball fans how to harness the power of made predictions and better understand the game. <P><P> Using real-world examples from historical and modern-day teams, Ross shows: * Why on-base and slugging percentages are more important than batting averages <P>* How professional odds makers predict the length of a seven-game series <P>* How to use mathematics to make smarter bets . <P>A Mathematician at the Ballpark is the perfect guide to the science of probability for the stats-obsessed baseball fans--and, with a detailed new appendix on fantasy baseball, an essential tool for anyone involved in a fantasy league.
A Mathematician's Journeys: Otto Neugebauer and Modern Transformations of Ancient Science (Archimedes #45)
by Alexander Jones John M. Steele Christine ProustThis book explores facets of Otto Neugebauer's career, his impact on the history and practice of mathematics, and the ways in which his legacy has been preserved or transformed in recent decades, looking ahead to the directions in which the study of the history of science will head in the twenty-first century. Neugebauer, more than any other scholar of recent times, shaped the way we perceive premodern science. Through his scholarship and influence on students and collaborators, he inculcated both an approach to historical research on ancient and medieval mathematics and astronomy through precise mathematical and philological study of texts, and a vision of these sciences as systems of knowledge and method that spread outward from the ancient Near Eastern civilizations, crossing cultural boundaries and circulating over a tremendous geographical expanse of the Old World from the Atlantic to India.
A Mathematician's Lament
by Paul Lockhart Keith Devlin"One of the best critiques of current mathematics education I have ever seen."--Keith Devlin, math columnist on NPR's Morning EditionA brilliant research mathematician who has devoted his career to teaching kids reveals math to be creative and beautiful and rejects standard anxiety-producing teaching methods. Witty and accessible, Paul Lockhart's controversial approach will provoke spirited debate among educators and parents alike and it will alter the way we think about math forever.Paul Lockhart, has taught mathematics at Brown University and UC Santa Cruz. Since 2000, he has dedicated himself to K-12 level students at St. Ann's School in Brooklyn, New York.
A Mathematics Boot Camp for Science and Engineering Students
by Ying MaMany students have difficulty applying mathematical techniques to solve problems in science and engineering, even after completing Calculus I and II. Students who are beginning the core coursework in their field of study often need additional guidance on practicing, learning, and improving their problem-solving skills for application. The objectives of A Mathematics Boot Camp for Science and Engineering Students are to offer a solution to this issue and are specifically designed to address common errors in mathematical problem-solving for undergraduate science and engineering students. Teaches readers how to apply math skills as they transition to coursework in their chosen field of study Includes strategies and recommendations for quick improvement in problem-solving skills Emphasizes the physical meanings of the problem, which helps students develop a deep understanding of their field of study Features a broad range of example problems with detailed and easy-to-follow solutions for students to learn problem-solving techniques and additional exercise problems for further practice and improvement Bridges the gap between the knowledge of mathematical techniques and the ability to apply those techniques to solve real-world problems This concise and practical text offers "basic training" in mathematical problem-solving skills for undergraduate students in science and engineering disciplines. A Solutions Manual is available to qualifying adopting professors.
A Mathematics Sampler: Topics for the Liberal Arts
by William P. Berlinghoff Kerry E. Grant Dale SkrienNow in its fifth edition, A Mathematics Sampler presents mathematics as both science and art, focusing on the historical role of mathematics in our culture. It uses selected topics from modern mathematics—including computers, perfect numbers, and four-dimensional geometry—to exemplify the distinctive features of mathematics as an intellectual endeavor, a problem-solving tool, and a way of thinking about the rapidly changing world in which we live. <p><p> A Mathematics Sampler also includes unique LINK sections throughout the book, each of which connects mathematical concepts with areas of interest throughout the humanities. The original course on which this text is based was cited as an innovative approach to liberal arts mathematics in Lynne Cheney's report, "50 HOURS: A Core Curriculum for College Students", published by the National Endowment for the Humanities.
A Matrix Algebra Approach to Artificial Intelligence
by Xian-Da ZhangMatrix algebra plays an important role in many core artificial intelligence (AI) areas, including machine learning, neural networks, support vector machines (SVMs) and evolutionary computation. This book offers a comprehensive and in-depth discussion of matrix algebra theory and methods for these four core areas of AI, while also approaching AI from a theoretical matrix algebra perspective.The book consists of two parts: the first discusses the fundamentals of matrix algebra in detail, while the second focuses on the applications of matrix algebra approaches in AI. Highlighting matrix algebra in graph-based learning and embedding, network embedding, convolutional neural networks and Pareto optimization theory, and discussing recent topics and advances, the book offers a valuable resource for scientists, engineers, and graduate students in various disciplines, including, but not limited to, computer science, mathematics and engineering.
A Matter of Life and Death: Hunting in Contemporary Vermont
by Marc BoglioliIn A Matter of Life and Death, anthropologist Marc Boglioli puts a human face on a group widely regarded as morally suspect, one that currently stands in the crossfire of America's so-called culture wars. Drawing on extensive ethnographic fieldwork in Addison County, Vermont, which took him from hunting camps and sporting goods stores to local bars and kitchen tables, Boglioli focuses on how contemporary hunters, women as well as men, understand their relationship to their prey. He shows how hunters' attitudes toward animals flow directly from the rural lifeways they have continued to maintain in the face of encroaching urban sensibilities. The result is a rare glimpse into a culture that experiences wild animals in a way that is at once violent, consumptive, and respectful, and that regards hunting as an enduring link to a vanishing past. It is a book that will challenge readers―hunters, non-hunters, and anti-hunters alike―to reconsider what constitutes a morally appropriate relationship with the non-human residents of this planet.
A Measure Theoretical Approach to Quantum Stochastic Processes (Lecture Notes in Physics #878)
by Wilhelm WaldenfelsThis monograph takes as starting point that abstract quantum stochastic processes can be understood as a quantum field theory in one space and in one time coordinate. As a result it is appropriate to represent operators as power series of creation and annihilation operators in normal-ordered form, which can be achieved using classical measure theory. Considering in detail four basic examples (e. g. a two-level atom coupled to a heat bath of oscillators), in each case the Hamiltonian of the associated one-parameter strongly continuous group is determined and the spectral decomposition is explicitly calculated in the form of generalized eigen-vectors. Advanced topics include the theory of the Hudson-Parthasarathy equation and the amplified oscillator problem. To that end, a chapter on white noise calculus has also been included.