Classical Recursion Theory

The past few years have witnessed significant developments in algebraic coding theory. This book provides an advanced treatment of the subject from an engineering perspective, covering the basic principles and their application in communications and signal processing. Emphasis is on codes defined on the line, on the plane, and on curves, with the core ideas presented using commutative algebra and computational algebraic geometry made accessible using the Fourier transform. Starting with codes defined on a line, a background framework is established upon which the later chapters concerning codes on planes, and on curves, are developed. The decoding algorithms are developed using the standard engineering approach applied to those of Reed-Solomon codes, enabling them to be evaluated against practical applications. Integrating recent developments in the field into the classical treatment of algebraic coding, this is an invaluable resource for graduate students and researchers in telecommun

This textbook on the calculus of variations leads the reader from the basics to modern aspects of the theory. One-dimensional problems and the classical issues like Euler-Lagrange equations are treated, as are Noether's theorem, Hamilton-Jacobi theory, and in particular geodesic lines, thereby developing some important geometric and topological aspects. The basic ideas of optimal control theory are also given. The second part of the book deals with multiple integrals. After a review of Lebesgue integration, Banach and Hilbert space theory and Sobolev spaces (with complete and detailed proofs), there is a treatment of the direct methods and the fundamental lower semicontinuity theorems. Subsequent chapters introduce the basic concepts of the modern calculus of variations, namely relaxation, Gamma convergence, bifurcation theory and minimax methods based on the Palais–Smale condition. The only prerequisites are basic results from calculus of one and several variables. After having studie

Descriptive set theory and definable proper forcing are two areas of set theory that developed quite independently of each other. This monograph unites them and explores the connections between them. Forcing is presented in terms of quotient algebras of various natural sigma-ideals on Polish spaces, and forcing properties in terms of Fubini-style properties or in terms of determined infinite games on Boolean algebras. Many examples of forcing notions appear, some newly isolated from measure theory, dynamical systems, and other fields. The descriptive set theoretic analysis of operations on forcings opens the door to applications of the theory: absoluteness theorems for certain classical forcing extensions, duality theorems, and preservation theorems for the countable support iteration. Containing original research, this text highlights the connections that forcing makes with other areas of mathematics, and is essential reading for academic researchers and graduate students in set theor

This monograph is concerned with the qualitative theory of best L1-approximation from finite-dimensional subspaces. It presents a survey of recent research that extends 'classical' results concerned with best uniform approximation to the L1 case. The work is organized in such a way as to be useful for self-study or as a text for advanced courses. It begins with a basic introduction to the concepts of approximation theory before addressing one- or two-sided best approximation from finite-dimensional subspaces and approaches to the computation of these. At the end of each chapter is a series of exercises; these give the reader an opportunity to test understanding and also contain some theoretical digressions and extensions of the text.

Acoustics of Fluid-Structure Interactions addresses an increasingly important branch of fluid mechanics - the absorption of noise and vibration by fluid flow. This subject, which offers numerous challenges to conventional areas of acoustics, is of growing concern in places where the environment is adversely affected by sound. Howe presents useful background material on fluid mechanics and the elementary concepts of classical acoustics and structural vibrations. Using examples, many of which include complete worked solutions, he vividly illustrates the theoretical concepts involved. He provides the basis for all calculations necessary for the determination of sound generation by aircraft, ships, general ventilation and combustion systems, as well as musical instruments. Both a graduate textbook and a reference for researchers, Acoustics of Fluid-Structure Interactions is an important synthesis of information in this field. It will also aid engineers in the theory and practice of noise

Orthonormal Systems and Banach Space Geometry describes the interplay between orthonormal expansions and Banach space geometry. Using harmonic analysis as a starting platform, classical inequalities and special functions are used to study orthonormal systems leading to an understanding of the advantages of systems consisting of characters on compact Abelian groups. Probabilistic concepts such as random variables and martingales are employed and Ramsey's theorem is used to study the theory of super-reflexivity. The text yields a detailed insight into concepts including type and co-type of Banach spaces, B-convexity, super-reflexivity, the vector-valued Fourier transform, the vector-valued Hilbert transform and the unconditionality property for martingale differences (UMD). A long list of unsolved problems is included as a starting point for research. This book should be accessible to graduate students and researchers with some basic knowledge of Banach space theory, real analysis, proba

For students and scholars of classical studies, philosophy, and political theory, Recco (St. John's College, Annapolis) attempts to show that despite the typical thought that Plato's Republic recommen

This book provides a self-contained and systematic introduction to classical electron theory and its quantization, non-relativistic quantum electrodynamics. The first half of the book covers the classical theory. It discusses the well-defined Abraham model of extended charges in interaction with the electromagnetic field, and gives a study of the effective dynamics of charges under the condition that, on the scale given by the size of the charge distribution, they are far apart and the applied potentials vary slowly. The second half covers the quantum theory, leading to a coherent presentation of non-relativistic quantum electrodynamics. Topics discussed include non-perturbative properties of the basic Hamiltonian, the structure of resonances, the relaxation to the ground state through emission of photons, the non-perturbative derivation of the g-factor of the electron and the stability of matter.

Professor Merrie Bergmann presents an accessible introduction to the subject of many-valued and fuzzy logic designed for use on undergraduate and graduate courses in non-classical logic. Bergmann discusses the philosophical issues that give rise to fuzzy logic - problems arising from vague language - and returns to those issues as logical systems are presented. For historical and pedagogical reasons, three-valued logical systems are presented as useful intermediate systems for studying the principles and theory behind fuzzy logic. The major fuzzy logical systems - Lukasiewicz, Gödel, and product logics - are then presented as generalisations of three-valued systems that successfully address the problems of vagueness. A clear presentation of technical concepts, this book includes exercises throughout the text that pose straightforward problems, that ask students to continue proofs begun in the text, and that engage students in the comparison of logical systems.

Professor Merrie Bergmann presents an accessible introduction to the subject of many-valued and fuzzy logic designed for use on undergraduate and graduate courses in non-classical logic. Bergmann discusses the philosophical issues that give rise to fuzzy logic - problems arising from vague language - and returns to those issues as logical systems are presented. For historical and pedagogical reasons, three-valued logical systems are presented as useful intermediate systems for studying the principles and theory behind fuzzy logic. The major fuzzy logical systems - Lukasiewicz, Gödel, and product logics - are then presented as generalisations of three-valued systems that successfully address the problems of vagueness. A clear presentation of technical concepts, this book includes exercises throughout the text that pose straightforward problems, that ask students to continue proofs begun in the text, and that engage students in the comparison of logical systems.

Physical phenomena in astrophysics and cosmology involve gravitational collapse in a fundamental way. The final fate of a massive star when it collapses under its own gravity at the end of its life cycle is one of the most important questions in gravitation theory and relativistic astrophysics, and is the foundation of black hole physics. General relativity predicts that continual gravitational collapse gives rise to a space-time singularity. Quantum gravity may take over in such regimes to resolve the classical space-time singularity. This book investigates these issues, and shows how the visible ultra-dense regions arise naturally and generically as an outcome of dynamical gravitational collapse. It will be of interest to graduate students and academic researchers in gravitation physics, fundamental physics, astrophysics, and cosmology. It includes a detailed review of research into gravitational collapse, and several examples of collapse models are investigated in detail.

Stoic work on ambiguity represents one of the most innovative, sophisticated and rigorous contributions to philosophy and the study of language in western antiquity. This book is both a comprehensive survey of the often difficult and scattered sources, and an attempt to locate Stoic material in the rich array of contexts, ancient and modern, which alone can guarantee full appreciation of its subtlety, scope and complexity. The comparisons and contrasts which this book constructs will intrigue not just classical scholars, and philosophers, but also logicians, theoretical linguists, communication theorists and historians of grammar and of literary theory. The Stoics on Ambiguity is designed to be intelligible to readers with no Greek or Latin.

Power grids, flexible manufacturing, cellular communications: interconnectedness has consequences. This remarkable book gives the tools and philosophy you need to build network models detailed enough to capture essential dynamics but simple enough to expose the structure of effective control solutions. Core chapters assume only exposure to stochastic processes and linear algebra at undergraduate level; later chapters are for advanced graduate students and researchers/practitioners. This gradual development bridges classical theory with the state-of-the-art. The workload model at the heart of traditional analysis of the single queue becomes a foundation for workload relaxations used in the treatment of complex networks. Lyapunov functions and dynamic programming equations lead to the celebrated MaxWeight policy along with many generalizations. Other topics include methods for synthesizing hedging and safety stocks, stability theory for networks, and techniques for accelerated simulation

This superb exposition of a complex subject examines new developments in the theory and practice of computation from a mathematical perspective, with topics ranging from classical computability to com

This book addresses a gap in the model-theoretic understanding of valued fields that had limited the interactions of model theory with geometry. It contains significant developments in both pure and applied model theory. Part I of the book is a study of stably dominated types. These form a subset of the type space of a theory that behaves in many ways like the space of types in a stable theory. This part begins with an introduction to the key ideas of stability theory for stably dominated types. Part II continues with an outline of some classical results in the model theory of valued fields and explores the application of stable domination to algebraically closed valued fields. The research presented here is made accessible to the general model theorist by the inclusion of the introductory sections of each part.

This book is an introduction to the Schwinger action principle in quantum mechanics and quantum field theory, with applications to a variety of different models including Bose–Einstein condensation, the Casimir effect and trapped Fermi gases. The book begins with a brief review of the action principle in classical mechanics and classical field theory. It then moves on to quantum field theory, focusing on the effective action method. This is introduced as simply as possible by using the zero-point energy of the simple harmonic oscillator as the starting point. The book concludes with a more complete definition of the effective action, and demonstrates how the provisional definition used earlier is the first term in the systematic loop expansion. The renormalization of interacting scalar field theory is presented to two-loop order. This book will interest graduate students and researchers in theoretical physics who are familiar with quantum mechanics.

Topological solitons occur in many nonlinear classical field theories. They are stable, particle-like objects, with finite mass and a smooth structure. Examples are monopoles and Skyrmions, Ginzburg-Landau vortices and sigma-model lumps, and Yang-Mills instantons. This book is a comprehensive survey of static topological solitons and their dynamical interactions. Particular emphasis is placed on the solitons which satisfy first-order Bogomolny equations. For these, the soliton dynamics can be investigated by finding the geodesics on the moduli space of static multi-soliton solutions. Remarkable scattering processes can be understood this way. The book starts with an introduction to classical field theory, and a survey of several mathematical techniques useful for understanding many types of topological soliton. Subsequent chapters explore key examples of solitons in one, two, three and four dimensions. The final chapter discusses the unstable sphaleron solutions which exist in several

Traces the central role played by aristocratic patronage in the transformation of the city of Rome at the end of antiquity. It moves away from privileging the administrative and institutional developments related to the rise of papal authority as the paramount theme in the city's post-classical history. Instead the focus shifts to the networks of reciprocity between patrons and their dependents. Using material culture and social theory to challenge traditional readings of the textual sources, the volume undermines the teleological picture of ecclesiastical sources such as the Liber Pontificalis, and presents the lay, clerical, and ascetic populations of the city of Rome at the end of antiquity as interacting in a fluid environment of alliance-building and status negotiation. By focusing on the city whose aristocracy is the best documented of any ancient population, the volume makes an important contribution to understanding the role played by elites across the end of antiquity.

Diophantine geometry has been studied by number theorists for thousands of years, since the time of Pythagoras, and has continued to be a rich area of ideas such as Fermat's Last Theorem, and most recently the ABC conjecture. This monograph is a bridge between the classical theory and modern approach via arithmetic geometry. The authors provide a clear path through the subject for graduate students and researchers. They have re-examined many results and much of the literature, and give a thorough account of several topics at a level not seen before in book form. The treatment is largely self-contained, with proofs given in full detail. Many results appear here for the first time. The book concludes with a comprehensive bibliography. It is destined to be a definitive reference on modern diophantine geometry, bringing a new standard of rigor and elegance to the field.

This philosophical treatise on the foundations of semantics is a systematic effort to clarify, deepen and defend the classical doctrine that words are conventional signs of mental states, principally thoughts and ideas, and that meaning consists in their expression. This expression theory of meaning is developed by carrying out the Gricean programme, explaining what it is for words to have meaning in terms of speaker meaning, and what it is for a speaker to mean something in terms of intention. But Grice's own formulations are rejected and alternatives developed. The foundations of the expression theory are explored at length, and the author develops the theory of thought as a fundamental cognitive phenomenon distinct from belief and desire, argues for the thesis that thoughts have parts, and identifies ideas or concepts with parts of thoughts. This book will appeal to students and professionals interested in the philosophy of language.

This 2007 book presents a developed general conceptual and basic quantitative analysis as well as the theory of mechanical efficiency of heat engines that a level of ideality and generality compatible with the treatment given to thermal efficiency in classical thermodynamics. This yields broad bearing results concerning the overall cyclic conversion of heat into usable mechanical energy. The work reveals intrinsic limits on the overall performance of reciprocating heat engines. The theory describes the general effects of parameters such as compression ratio and external or buffer pressure on engine output. It also provides rational explanations of certain operational characteristics such as how engines generally behave when supercharged or pressurized. The results also identify optimum geometric configurations for engines operating in various regimes from isothermal to adiabatic and are extended to cover multi-workspace engines and heat pumps. Limited heat transfer due to finite-time e

What is the nature of law? Does our obligation to obey the law extend to unjust laws? From what source do lawmakers derive legitimate authority? What principles should guide us in the design of political institutions? The essays in this collection, written by prominent contemporary philosophers, explore how these questions were addressed by ancient political thinkers, including the Pre-Socratics, Plato, Aristotle, and the Stoics and Epicureans. Classical theories of human nature and their implications for political theory are examined, as is the meaning of freedom and coercion in Plato's thought. Plato's idea that philosophers should be political rulers receives scrutiny, too. Other essays ask what we can learn from ancient thinkers like Aristotle about the principles of constitutional design or the limits of political obligation.

Provides an understanding of the relationship between classical military theory and modern asymmetric conflict, current asymmetric threats facing the U.S., and a clear set of lessons learned from rec

This book, first published in 2007, is an introductory textbook on quantum field theory in gravitational backgrounds intended for undergraduate and beginning graduate students in the fields of theoretical astrophysics, cosmology, particle physics, and string theory. The book covers the basic (but essential) material of quantization of fields in an expanding universe and quantum fluctuations in inflationary spacetime. It also contains a detailed explanation of the Casimir, Unruh, and Hawking effects, and introduces the method of effective action used for calculating the back-reaction of quantum systems on a classical external gravitational field. The broad scope of the material covered will provide the reader with a thorough perspective of the subject. Every major result is derived from first principles and thoroughly explained. The book is self-contained and assumes only a basic knowledge of general relativity. Exercises with detailed solutions are provided throughout the book.

An introduction to the theory of orbifolds from a modern perspective, combining techniques from geometry, algebraic topology and algebraic geometry. One of the main motivations, and a major source of examples, is string theory, where orbifolds play an important role. The subject is first developed following the classical description analogous to manifold theory, after which the book branches out to include the useful description of orbifolds provided by groupoids, as well as many examples in the context of algebraic geometry. Classical invariants such as de Rham cohomology and bundle theory are developed, a careful study of orbifold morphisms is provided, and the topic of orbifold K-theory is covered. The heart of this book, however, is a detailed description of the Chen-Ruan cohomology, which introduces a product for orbifolds and has had significant impact. The final chapter includes explicit computations for a number of interesting examples.

Under what conditions is a group of scientists rational? How would rational scientists collectively agree to make their group more effective? What sorts of negotiations would occur among them and under what conditions? What effect would their final agreement have on science and society? These questions have been central to the philosophy of science for the last two decades. In this 2007 book, Husain Sarkar proposes answers to them by building on classical solutions - the skeptical view, two versions of the subjectivist view, the objectivist view, and the view of Hilary Putnam. Although he finds these solutions not completely adequate, Sarkar retrieves what is of value from them and also expropriates the arguments of John Rawls and Amartya Sen, in order to weave a richer, deeper, and more developed theory of group rationality.

Since ancient Athens, democrats have taken pride in their power and inclination to change their laws, yet they have also sought to counter this capacity by creating immutable laws. In Democracy and Legal Change, Melissa Schwartzberg argues that modifying law is a fundamental and attractive democratic activity. Against those who would defend the use of 'entrenchment clauses' to protect key constitutional provisions from revision, Schwartzberg seeks to demonstrate historically the strategic and even unjust purposes unamendable laws have typically served, and to highlight the regrettable consequences that entrenchment may have for democracies today. Drawing on historical evidence, classical political theory, and contemporary constitutional and democratic theory, Democracy and Legal Change reexamines the relationship between democracy and the rule of law from a new, and often surprising, set of vantage points.

This is a pedagogical introduction to the harmonic superspace method in extended supersymmetry. Inspired by exciting developments in superstring theory, it provides a systematic treatment of the quantum field theories with N=2 and N=3 supersymmetry in harmonic superspace. The authors present the harmonic superspace approach as a means of providing an off-shell description of the N=2 supersymmetric theories, both at the classical and quantum levels. Furthermore, they show how it offers a unique way to construct an off-shell formulation of a theory with higher supersymmetry, namely the N=3 supersymmetric Yang-Mills theory. Harmonic Superspace makes manifest many remarkable geometric properties of the N=2 theories, for example, the one-to-one correspondence between N=2 supersymmetric matter, and hyper-Kähler and quaternionic manifolds. This book will be of interest to researchers and graduate students working in the areas of supersymmetric quantum field theory, string theory and complex g

Rousseau and Geneva reconstructs the main aspects of Genevan socio-economic, political and religious thought in the first half of the eighteenth century. In this way Dr Rosenblatt effectively contextualizes the development of Rousseau's thought from the First Discourse through to the Social Contract. Over time Rousseau has been adopted as a French thinker, but this adoption obscures his Genevan origin. Dr Rosenblatt points out that he is, in fact, a Genevan thinker and illustrates that Rousseau's classical republicanism, his version of natural law theory, his civil religion and his hostility to the arguments of doux commerce theorists are all responses to the political use of such arguments in Geneva. The author also points out that it was this relationship with Geneva that played an integral part in his development into an original political thinker.

The predominant view of moral virtue can be traced back to Aristotle. He believed that moral virtue must involve intellectual excellence. To have moral virtue one must have practical wisdom - the ability to deliberate well and to see what is morally relevant in a given context. Julia Driver challenges this classical theory of virtue, arguing that it fails to take into account virtues which do seem to involve ignorance or epistemic defect. Some 'virtues of ignorance' are counterexamples to accounts of virtue which hold that moral virtue must involve practical wisdom. Modesty, for example, is generally considered to be a virtue even though the modest person may be making an inaccurate assessment of his or her accomplishments. Driver argues that we should abandon the highly intellectualist view of virtue and instead adopt a consequentialist perspective which holds that virtue is simply a character trait which systematically produces good consequences.

Beginning with a sustained analysis of Seneca's theory of monarchy in the treatise De clementia, in this text Peter Stacey traces the formative impact of ancient Roman political philosophy upon medieval and Renaissance thinking about princely government on the Italian peninsula from the time of Frederick II to the early modern period. Roman Monarchy and the Renaissance Prince offers a systematic reconstruction of the pre-humanist and humanist history of the genre of political reflection known as the mirror-for-princes tradition - a tradition which, as Stacey shows, is indebted to Seneca's speculum above all other classical accounts of the virtuous prince - and culminates with a comprehensive and controversial reading of the greatest work of renaissance political theory, Machiavelli's The Prince. Peter Stacey brings to light a story which has been lost from view in recent accounts of the Renaissance debt to classical antiquity, providing a radically revisionist account of the history of

In Virginia Woolf and the Visible World, Emily Dalgarno examines Woolf's engagement with notions of the subject and codes of the visible. Dalgarno examines how Woolf's writing engages with visible and non-visible realms of experience, and draws on ideas from the diverse fields of psychoanalytic theory, classical Greek tragedy, astronomy, photography and photojournalism. The solar eclipse of 1927 marks a dividing line in Woolf's career, after which she portrayed the visible world in terms of light, and shifted her interest from painting to photography. Dalgarno offers textual analyses of Woolf's individual works, including To the Lighthouse, The Waves and Three Guineas, arguing for the importance of her ongoing interest in Greek translation. In later chapters, she explores the theory of the subject that emerges from Woolf's representation of the visible in her autobiography.

The study of vibration in physical systems is central to almost all fields in physics and engineering. This work, originally published in two volumes, examines the classical aspects in Part I and the quantum oscillator in Part II. The classical linear vibrator is treated first and the underlying unity of all linear oscillations in electrical, mechanical and acoustic systems is emphasized. The treatment of nonlinear vibrations, a field with which engineers and physicists are generally less familiar, is then examined. Part II then concentrates on quantum systems, looking at the vibrations in atoms and molecules and their interaction with electromagnetic radiation. The similarities of classical and quantum methods are stressed and the limits of the classical treatment are examined. Throughout the book, each phenomenon discussed is well illustrated with many examples; and theory and experiment are compared. This is a useful introduction to the more advanced mathematical treatment of vibrat

The classical theory of stochastic processes has important applications arising from the need to describe irreversible evolutions in classical mechanics; analogously quantum stochastic processes can be used to model the dynamics of irreversible quantum systems. Noncommutative, i.e. quantum, geometry provides a framework in which quantum stochastic structures can be explored. This book is the first to describe how these two mathematical constructions are related. In particular, key ideas of semigroups and complete positivity are combined to yield quantum dynamical semigroups (QDS). Sinha and Goswami also develop a general theory of Evans-Hudson dilation for both bounded and unbounded coefficients. The unique features of the book, including the interaction of QDS and quantum stochastic calculus with noncommutative geometry and a thorough discussion of this calculus with unbounded coefficients, will make it of interest to graduate students and researchers in functional analysis, probabili

This book presents the development of modern molecular models for fluids from the interdisciplinary fundamentals of classical and statistical mechanics, of electrodynamics and of quantum mechanics. The concepts and working equations of the various fields are briefly derived and illustrated in the context of understanding the properties of molecular systems. Special emphasis is devoted to the quantum mechanical basis, since this is used throughout in the calculation of the molecular energy of a system. The book is application oriented. It stresses those elements that are essential for practical model development. The fundamentals are then used to derive models for various types of applications. Finally, equation of state models are presented based on quantum chemically based models for the intermolecular potential energy and perturbation theory. The book is suited for graduate courses in chemical and mechanical engineering, physics and chemistry, but may also, by proper selection, be fo

This 2007 book provides a systematic and self-contained account of the fast-developing theory of complex social networks. Social networks are central to the understanding of most socio-economic phenomena in the modern world. The classical approach to studying them relies on a methodology that abstracts from their size and complexity. In contrast, the approach taken in this book keeps complexity at the core, whilst integrating it with the incentive considerations that are preeminent in traditional economic analysis. The treatment starts with a detailed discussion of the basic models that act as 'benchmarks' for the complex-network literature: random networks, small worlds, and scale-free networks, before studying three different forces that underlie almost all network phenomena in social contexts: diffusion, search, and play. Finally, these forces are combined into a unified framework that is brought to bear on the issue of network formation and the coevolution of agents' behaviour and

This first volume takes the story from its beginnings in Ionian philosophy as far as the formation of the Atomic Theory and the first criticisms of it by Plato and Aristotle. The second volume will describe the cosmology of Plato and Aristotle, the attempt by Epicurean opponents to revive Atomism and later developments of the debate in classical philosophy and science up to the sixth century of our era. Both are accessible to anyone interested in the history of science and philosophy, even if they have no specialized knowledge of Greek philosophy and no Greek; but professional scholars too will find much of importance to them.

Can an abstract theory of Empfindsamkeit aesthetics have any value to a musician wishing to study composition in the classical style? The eighteenth-century German theorist and pedagogue Heinrich Koch showed how this question could be answered with a resounding yes. Starting with the systematic aesthetic theory of the Swiss encyclopedist Johann Sulzer, Koch was creatively able to adapt Sulzer's conservative ideas on ethical mimesis and rhetoric to concrete problems of music analysis and composition. In this collaborative study, Thomas Christensen and Nancy Baker have translated and analysed selected writings of Sulzer and Koch respectively, bringing to life a little-known confluence of philosophical and musical thought from the German Enlightenment. Koch's appropriation of Sulzer's ideas to the service of music represents an important development in the evolution of Western musical thought.

Scholars of literature explore how classical rhetorical theory was accommodated to the needs of a post-classical Christian culture, and the context in which this development took place. The obvious ve

This book gives a detailed study of the development and the interpretation given to Niels Bohr's Principle of Correspondence. It also describes the role that this principle played in guiding Bohr's research over the critical period from 1920 to 1927. Quantum mechanics, developed in the 1920s and 1930s by Bohr, Heisenberg, Born, Schrödinger and Dirac, represents one of the most profound turning points in science. This theory required a wholly new kind of physics in which many of the principles, concepts and models representing reality, that had formed the basis of classical physics since Galileo and Newton, had to be abandoned. This book re-examines the birth of quantum mechanics, in particular examining the development of crucial and original insights of Niels Bohr.