Curious Curves is self-contained and unified in presentation. This book is suitable for a topics course, capstone course, or senior seminar; it is also intended for independent study by students and others interested in mathematics.Curves can often provide a better representation of natural phenomena than do the figures of classical geometry. Thus the content — presented with an emphasis on the geometric intuition characteristic of the study of curves — is highly relevant not only for people working in mathematics, but also those in other sciences. The explanations are detailed and illustrative to capture the interest of the reader, as well as complete to provide the necessary background information needed to go further into the subject.
This book analyzes stochastic processes on networks and regular structures such as lattices by employing the Markovian random walk approach. Part 1 is devoted to the study of local and non-local random walks. It shows how non-local random walk strategies can be defined by functions of the Laplacian matrix that maintain the stochasticity of the transition probabilities. A major result is that only two types of functions are admissible: type (i) functions generate asymptotically local walks with the emergence of Brownian motion, whereas type (ii) functions generate asymptotically scale-free non-local “fractional” walks with the emergence of Lévy flights. In Part 2, fractional dynamics and Lévy flight behavior are analyzed thoroughly, and a generalization of Pólya's classical recurrence theorem is developed for fractional walks. The authors analyze primary fractional walk characteristics such as the mean occupation time, the mean first passage time, the fractal scaling of the set of distinct nodes visited, etc. The results show the improved search capacities of fractional dynamics on networks.
This legendary work presents a comprehensive survey that covers every issue of significance to today's performers, with numerous musical examples, authoritative citations, and scholarly interpretations and syntheses.
What exactly is analysis? What are infinitely small or infinitely large quantities? What are indivisibles and infinitesimals? What are real numbers, continuity, the continuum, differentials, and integrals? You’ll find the answers to these and other questions in this unique book! It explains in detail the origins and evolution of this important branch of mathematics, which Euler dubbed the “analysis of the infinite.” A wealth of diagrams, tables, color images and figures serve to illustrate the fascinating history of analysis from Antiquity to the present. Further, the content is presented in connection with the historical and cultural events of the respective epochs, the lives of the scholars seeking knowledge, and insights into the subfields of analysis they created and shaped, as well as the applications in virtually every aspect of modern life that were made possible by analysis.
This book is a comprehensive, unifying introduction to the field of mathematical analysis and the mathematics of computing. It develops the relevant theory at a modern level and it directly relates modern mathematical ideas to their diverse applications. The authors develop the whole theory. Starting with a simple axiom system for the real numbers, they then lay the foundations, developing the theory, exemplifying where it's applicable, in turn motivating further development of the theory. They progress from sets, structures, and numbers to metric spaces, continuous functions in metric spaces, linear normed spaces and linear mappings; and then differential calculus and its applications, the integral calculus, the gamma function, and linear integral operators. They then present important aspects of approximation theory, including numerical integration. The remaining parts of the book are devoted to ordinary differential equations, the discretization of operator equations, and numerical solutions of ordinary differential equations. This textbook contains many exercises of varying degrees of difficulty, suitable for self-study, and at the end of each chapter the authors present more advanced problems that shed light on interesting features, suitable for classroom seminars or study groups. It will be valuable for undergraduate and graduate students in mathematics, computer science, and related fields such as engineering. This is a rich field that has experienced enormous development in recent decades, and the book will also act as a reference for graduate students and practitioners who require a deeper understanding of the methodologies, techniques, and foundations.
This monograph covers the recent major advances in various areas of set theory. From the reviews: "One of the classical textbooks and reference books in set theory....The present ‘Third Millennium’ edition...is a whole new book. In three parts the author offers us what in his view every young set theorist should learn and master....This well-written book promises to influence the next generation of set theorists, much as its predecessor has done." --MATHEMATICAL REVIEWS
Voices Found: Leader's Guide presents the music from Voices Found in a spiral bound format, easy for an accompanist to use. There are alternate harmonizations, guitar chords, descants, and expanded arrangements of the basic hymns and songs. The Scriptural and Topical Indices along with the Three-Year Lectionary Index (including the Revised Common Lectionary) provide excellent guidance for service planning. The Leader's Guide is not designed just for musicians and clergy. The Guide presents a great deal of background information about the composers, text writers, and arrangers who contributed to the volume. Many parishioners, as well as church professionals, will want to read about the fascinating women who contributed to the Church's Song for over 13 centuries, from the 8th Century to the present.
Discovering Dynamical Systems Through Experiment and Inquiry differs from most texts on dynamical systems by blending the use of computer simulations with inquiry-based learning (IBL). IBL is an excellent tool to move students from merely remembering the material to deeper understanding and analysis. This method relies on asking students questions first, rather than presenting the material in a lecture. Another unique feature of this book is the use of computer simulations. Students can discover examples and counterexamples through manipulations built into the software. These tools have long been used in the study of dynamical systems to visualize chaotic behavior. We refer to this unique approach to teaching mathematics as ECAP—Explore, Conjecture, Apply, and Prove. ECAP was developed to mimic the actual practice of mathematics in an effort to provide students with a more holistic mathematical experience. In general, each section begins with exercises guiding students through explorations of the featured concept and concludes with exercises that help the students formally prove the results. While symbolic dynamics is a standard topic in an undergraduate dynamics text, we have tried to emphasize it in a way that is more detailed and inclusive than is typically the case. Finally, we have chosen to include multiple sections on important ideas from analysis and topology independent from their application to dynamics.
This book presents a rigorous treatment of the mathematical instruments available for dealing with income distributions, in particular Lorenz curves and related methods. The methods examined allow us to analyze, compare and modify such distributions from an economic and social perspective. Though balanced income distributions are key to peaceful coexistence within and between nations, it is often difficult to identify the right kind of balance needed, because there is an interesting interaction with innovation and economic growth. The issue of justice, as discussed in Thomas Piketty’s bestseller “Capital in the Twenty-First Century” or in the important book “The Price of Inequality” by Nobel laureate Joseph Stiglitz, is also touched on. Further, there is a close connection to the issue of democracy in the context of globalization. One highlight of the book is its rigorous treatment of the so-called Atkinson theorem and some extensions, which help to explain under which type of societal utility functions nations tend to operate either in the direction of more balance or less balance. Finally, there are some completely new insights into changing the balance pattern of societies and the kind of coalitions between richer and poorer parts of society to organize political support in democracies in either case. Oxford University's Sir Tony Atkinson, well known for his so-called Atkinson theorem, writes in his foreword to the book: “[The authors] contribute directly to t he recent debates that are going on in politics. [...] with this book the foundation of arguments concerning a proper balance in income distribution in the sense of identifying an ‘efficient inequality range’ has got an additional push from mathematics, which I appreciate very much.”
Controversies in Exercise Science introduces a series of selected unresolved issues in the field of human exercise science. The common thread to all of these topics is that, in their ultimate resolution, they offer promise of insights into the essential principles of physiological systems and how these respond to the stresses of exercise. Each case study includes an examination of research surrounding each issue; the innovative aspect, however, will be that each of these controversies will be presented in the context of an historical and/or philosophical perspective. These chapter include topics related to basic exercise physiology, sports, physical activity, and exercise health. Underlying each of these debates lie clues which may offer insights into the basic nature of living beings. Aimed at both academics and practitioners in the fields of exercise science, biology, and related sports science disciplines, Controversies in Exercise Science provides arguments for both sides of several selected contemporary controversies in the field of exercise science and, while no ultimate resolution will be provided, the goal is, rather, to offer the reader sufficient "raw material" on which he or she might make their own judgement on the matters presented.
This volume contains a collection of articles from the special program on algebraic and topological dynamics and a workshop on dynamical systems held at the Max-Planck Institute (Bonn, Germany). It reflects the extraordinary vitality of dynamical systems in its interaction with a broad range of mathematical subjects. Topics covered in the book include asymptotic geometric analysis, transformation groups, arithmetic dynamics, complex dynamics, symbolic dynamics, statisticalproperties of dynamical systems, and the theory of entropy and chaos. The book is suitable for graduate students and researchers interested in dynamical systems.
The present book is an introduction to the philosophy of mathematics. It asks philosophical questions concerning fundamental concepts, constructions and methods - this is done from the standpoint of mathematical research and teaching. It looks for answers both in mathematics and in the philosophy of mathematics from their beginnings till today. The reference point of the considerations is the introducing of the reals in the 19th century that marked an epochal turn in the foundations of mathematics. In the book problems connected with the concept of a number, with the infinity, the continuum and the infinitely small, with the applicability of mathematics as well as with sets, logic, provability and truth and with the axiomatic approach to mathematics are considered. In Chapter 6 the meaning of infinitesimals to mathematics and to the elements of analysis is presented. The authors of the present book are mathematicians. Their aim is to introduce mathematicians and teachers of mathematics as well as students into the philosophy of mathematics. The book is suitable also for professional philosophers as well as for students of philosophy, just because it approaches philosophy from the side of mathematics. The knowledge of mathematics needed to understand the text is elementary. Reports on historical conceptions. Thinking about today‘s mathematical doing and thinking. Recent developments. Based on the third, revised German edition. For mathematicians - students, teachers, researchers and lecturers - and readersinterested in mathematics and philosophy. Contents On the way to the reals On the history of the philosophy of mathematics On fundamental questions of the philosophy of mathematics Sets and set theories Axiomatic approach and logic Thinking and calculating infinitesimally – First nonstandard steps Retrospection
Why are we here? How should we live? What happens after we die? Why does evil exist? Religion For Dummies explains how the world’s great religions answer questions that persist through generations. Authors Rabbi Marc Gellman and Monsignor Thomas Hartman are trusted religious advisors known as the God Squad. With wonderful wit and incredible wisdom, they host a daily talk show which reaches nearly 4 million homes in the New York area, and have appeared on numerous TV and radio shows. This book is not a scholarly theological treatise; it’s a lively, practical, hands-on resource that will help you better understand your own religion and others. You’ll explore: Religion's role in the family and in the workplace The beliefs and practices of Christianity, Judaism, Islam, and other religions Religion's impact during major passages in life such as birth, death, and marriage How to join a religion and how to pray How religion can help you deal with issues in every day life such as conflict, adversity, marriage, divorce, and more Religious rituals and ethics Religion for Dummies touches on lesser-known religions (such as, Zoroastrianism, Jainism, Sikhism). It explores how people of various faiths pray, celebrate life and death, and view moral issues. The book does not tell you what to believe, but rather encourages you to live as you believe and let your religion infuse every aspect of your life. It doesn’t give simple answers to haunting, complex questions; it helps you find your own answers and pursue your own spiritual path!
This approachable text studies discrete objects and the relationsips that bind them. It helps students understand and apply the power of discrete math to digital computer systems and other modern applications. It provides excellent preparation for courses in linear algebra, number theory, and modern/abstract algebra and for computer science courses in data structures, algorithms, programming languages, compilers, databases, and computation.* Covers all recommended topics in a self-contained, comprehensive, and understandable format for students and new professionals * Emphasizes problem-solving techniques, pattern recognition, conjecturing, induction, applications of varying nature, proof techniques, algorithm development and correctness, and numeric computations* Weaves numerous applications into the text* Helps students learn by doing with a wealth of examples and exercises: - 560 examples worked out in detail - More than 3,700 exercises - More than 150 computer assignments - More than 600 writing projects* Includes chapter summaries of important vocabulary, formulas, and properties, plus the chapter review exercises* Features interesting anecdotes and biographies of 60 mathematicians and computer scientists* Instructor's Manual available for adopters* Student Solutions Manual available separately for purchase (ISBN: 0124211828)
Members of the United States Congress where having long and passionate debates over how to deal with radical Islamist doctrine that permitted and practiced brazen extortion on non-Muslims merchants ships. Some Americans wanted to talk with the pirates to convince them that their actions were wrong. Some of our citizens and politicians wanted to continue paying ransom, thinking the problem would eventually go away. The Muslim terrorists in Northern Africa, with the approval of the Dey of Algiers, were sworn to carry out jihad against all Western powers. Captain William Bainbridge suggested that a continuous policy of burying ones head in the sand was going to shut trade off. Bainbridge takes tributes to the Dey of Algiers.Bainbridge lost his ship and was captured in 1803 and imprisoned until 1805. Hostilities against Americans was plenteous. Americans at sea were thought to be weak and easily intimidated. The book details Bainbridge's victorious sea battle in 1812 of Old Ironsides defeating the British war-ship, HMS Java. President Jefferson addressed Congress: Gentlemen we must change our non-defense attitude. The lack of a United States navy has placed us into accepting the domination of England over the European seas. The Congress would rather lose the war without defending the United States rights. "May our country never be reluctant to spend money for those who spend their lives for us. Bainbridge was standing near the wheel when the ball hit and drove a small copper bolt into his thigh. This was a dangerous wound that laid him out on the deck. The cries of the wounded was an eerie and constant reminder of the carnage that was taking place on the ship. Cries of help were going unnoticed, many were not heard because the roar of the cannons had deafen most of the ship's crew.
Ontology and Providence in Creation critically examines a particular Leibnizean inspired understanding of God's creation of the world and proposes that a different understanding should be adopted. The Leibnizean argument proposes that God's understanding encompassed a host of possible worlds, only one of which he actualized. This proposition is the current orthodoxy when philosopher and theologians talk about the philosophical understanding of creation. Mark Robson argues that this commits the Leibnizean to the notion that possibility is determinate. He proposes that this understanding of creation does not do justice to the doctrine that God created the world out of nothing. Instead of possible worlds, Robson argues that we should understand possibility as indeterminate. There are no things in possibility, hence God created out of nothing. He examines how this conception of possibility is held by C.S. Peirce and how it was developed by Charles Hartshorne. Robson contends that not only does the indeterminate understanding of possibility take seriously the nothing of ex nihilo, but that it also offers a new solution to the problem of evil.
Not every presidential visit to the theatre is as famous as Lincoln's last night at Ford's, but American presidents attended the theatre long before and long after that ill-fated night. In 1751, George Washington saw his first play, The London Merchant, during a visit to Barbados. John Quincy Adams published dramatic critiques. William McKinley avoided the theatre while in office, on professional as well as moral grounds. Richard Nixon met his wife at a community theatre audition. Surveying 255 years, this volume examines presidential theatre-going as it has reflected shifting popular tastes in America.
The Hussite movement is essential for understanding medieval Europe and the development of Western civilization. Matthew Spinka and Howard Kaminsky stand at the forefront of scholarship introducing this subject to the Anglophone world. Thomas A. Fudge argues their role in the religious historiography of late medieval Europe is a precursor to global medievalism. Combining commitment to the Christian faith with firm opposition to the Soviet-mandated Marxist-Communist ideology that dominated twentieth-century Czechoslovakia, Spinka strove to present Jan Hus as a medieval figure driven by religious devotion. Motivated by Jewish atheism and a modified form of Marxist analysis, Kaminsky rescued the medieval Hussites from oblivion and political agendas. Fudge explores biography, history, and historiography as an essential intellectual segue between medieval Hussites and modern scholarship. Matthew Spinka, Howard Kaminsky, and the Medieval Hussites considers biography, evaluates the work of both historians, elaborates their methods, assesses their interpretations, and analyzes their historiographical significance for the study of Hussite history.
Founded in the Mahoning Valley during 1837, a tiny settlement of secular German immigrants grew into one of the most influential centers of Jewish life in the Midwest. Home to nationally renowned rabbis and Zionist firebrands alike, the community produced an astonishing array of leaders in an impressive range of fields throughout the twentieth century. This notable legacy ranges from the entertainment juggernaut of Warner Brothers to the Arby's fast-food empire and the prominent Youngstown Sheet & Tube, among many others. Authors Thomas Welsh, Joshua Foster and Gordon F. Morgan trace the unique history of one of Ohio's oldest Jewish communities from its humble beginnings into the challenging climate of the new millennium.
Numericon tells the stories of the numbers, mathematical discoveries, oddities and personalities that have shaped the way we understand the world around us. Each chapter is its own story about a number: why 12 is a sublime number, why 13 is unlucky and 7 lucky, and how imaginary numbers hold up buildings. The book tells the stories of ancient mathematicians, ground-breaking discoveries and mathematical applications that affect our world and our lives in so many ways.
For four hundred years, Virginia's politicians have preached a "Virginia Way" of honor, gentility and democracy. In reality, this ideology bred a corrupt political class, a runaway electricity company, a university that reflected the values of donors and a school system that suffered from cronyism. This Virginia Way prevented rather than promoted the success of its stated democratic ideals. Readers from the right, left and middle will learn much about how their government operates and understand Virginia in a whole new way. Author Jeff Thomas explodes the myth of the Virginia Way with an insightful portrait of the people, politics and power that run the Commonwealth.
The modern political landscape of Virginia bears little resemblance to the past. The commonwealth is a nationally influential swing state alongside stalwarts like Florida or Ohio. But with increased power comes greater scrutiny--and corruption. Governor Bob McDonnell received a jail sentence on federal corruption charges, later vacated by the U.S. Supreme Court. Corporate influence on the state legislature and other leaders resulted in numerous ethics violations. Scandal erupted at the prestigious University of Virginia when the school ousted its president amid political drama and intrigue. Author Jeff Thomas reveals the intersection of money, power and politics and the corrosive effect on government in a new era.
Thoroughly revised, updated, expanded, and reorganized to serve as a primary text for mathematics courses, Introduction to Set Theory, Third Edition covers the basics: relations, functions, orderings, finite, countable, and uncountable sets, and cardinal and ordinal numbers. It also provides five additional self-contained chapters, consolidates the material on real numbers into a single updated chapter affording flexibility in course design, supplies end-of-section problems, with hints, of varying degrees of difficulty, includes new material on normal forms and Goodstein sequences, and adds important recent ideas including filters, ultrafilters, closed unbounded and stationary sets, and partitions.
The book is a brief journey through centuries and jurisdictions and expands on examples of enactment practices of states that support, challenge or even reject communication during pending litigations. England, as the main representative of a jurisdiction, suggests communication solutions potentially different than the practice in the United States where litigation communication first time occurred. Accordingly, the author offers a comprehensive analysis and detailed historical narrative of the positions of various jurisdictions in relation to communication in the legal process. As a kind of applied legal history, the book provides an exploration of historical events that were significant in a legal communication context and addresses their implications for modern enactments. The account looks at the history of regulations to allow a better understanding of the strict rules that have often been cited over the years support or restrict communication in the legal process. The author provides the reader with proper contexts on different judicial and communication considerations, as well as the collaboration of legal and public relations experts, in a particular form of crisis and reputation management, in the litigation process. As such, this book is an attempt to present an accurate and thoughtful account of the theory and history of litigation communication, which is directly relevant in various debates such as the work on the meaning and context of the Contempt of Court Act in England or the American First and Sixth Amendments in different centuries.
An overview of recent experimental and theoretical developments in the field of the physics of membranes, including new insights from the past decade. The author uses classical thermal physics and physical chemistry to explain our current understanding of the membrane. He looks at domain and 'raft' formation, and discusses it in the context of thermal fluctuations that express themselves in heat capacity and elastic constants. Further topics are lipid-protein interactions, protein binding, and the effect of sterols and anesthetics. Many seemingly unrelated properties of membranes are shown to be intimately intertwined, leading for instance to a coupling between membrane state, domain formation and vesicular shape. This also applies to non-equilibrium phenomena like the propagation of density pulses during nerve activity. Also included is a discussion of the application of computer simulations on membranes. For both students and researchers of biophysics, biochemistry, physical chemistry, and soft matter physics.
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