A quantity can be made smaller and smaller without it ever vanishing. This fact has profound consequences for science, technology, and even the way we think about numbers. In this book, we will explore this idea by moving at an easy pace through an account of elementary real analysis and, in particular, will focus on numbers, sequences, and series. Almost all textbooks on introductory analysis assume some background in calculus. This book doesn't and, instead, the emphasis is on the application of analysis to number theory. The book is split into two parts. Part 1 follows a standard university course on analysis and each chapter closes with a set of exercises. Here, numbers, inequalities, convergence of sequences, and infinite series are all covered. Part 2 contains a selection of more unusual topics that aren't usually found in books ofthis type. It includes proofs of the irrationality of e and *p, continued fractions, an introduction to the Riemann zeta function, Cantor's theory of the infinite, and Dedekind cuts. There is also a survey of what analysis can do for the calculus and a brief history of the subject. A lot of material found in a standard university course on
A Metaphysics for Freedom argues that agency itself-and not merely the special, distinctively human variety of it-is incompatible with determinism. For determinism is threatened just as surely by the existence of powers which can be unproblematically accorded to many sorts of animals, as by the distinctively human powers on which the free will debate has tended to focus. She suggests that a tendency to approach the question of free will solely through theissue of moral responsibility has obscured the fact that there is a quite different route to incompatibilism, based on the idea that animal agents above a certain level of complexity possess a range of distinctive 'two-way' powers, not found in simpler substances. Determinism is not a doctrine of physics, butof metaphysics; and the idea that it is physics which will tell us whether our world is deterministic or not presupposes what must not be taken for granted-that is, that physics settles everything else, and that we are already in a position to say that there could be no irreducibly top-down forms of causal influence. Steward considers questions concerning supervenience, laws, and levels of explanation, and explores an outline of a variety of top-down causation which might sustain the idea thatan animal itself, rather than merely events and states going on in its parts, might be able to bring something about. The resulting position permits certain important concessions to compatibilism to be made; and a convincing response is also offered to the charge that even if it is agreed thatdeterminism is incompatible with agency, indeterminism can be of no possible help. The whole is an argument for a distinctive and resolutely non-dualistic, naturalistically respectable version of libertarianism, rooted in a conception of what biological forms of organisation might make possible in the way of freedom.
According to the doctrine of the Trinity, the Father, Son, and Spirit are supposed to be distinct from each other, and yet be one and the same God. As if that were not perplexing enough, there is also supposed to be an internal process of production that gives rise to the Son and Spirit: the Son is said to be 'begotten' by the Father, while the Spirit is said to 'proceed' either from the Father and the Son together, or from the Father, but through the Son. One might wonder, though, just how this sort of divine production is supposed to work. Does the Father, for instance, fashion the Son out of materials, or does he conjure up the Son out of nothing? Is there a middle ground one could take here, or is the whole idea of divine production simply unintelligible? In the late 13th and early 14th centuries, scholastic theologians subjected these questions to detailed philosophical analysis, and those discussions make up one of the most important, and one of the most neglected, aspects of late medieval trinitarian theology. This book examines the central ideas and arguments that defined this debate, namely those of Henry of Ghent, John Duns Scotus, and William Ockham. Their discussions are significant not only for the history of trinitarian theology, butalso for the history of philosophy, especially regarding the notions of production and causal powers.
The search for a quantum theory of the gravitational field is one of the great open problems in theoretical physics. This book presents a self-contained discussion of the concepts, methods and applications that can be expected in such a theory. The two main approaches to its construction -- the direct quantisation of Einstein's general theory of relativity and string theory -- are covered. Whereas the first attempts to construct a viable theory for the gravitationalfield alone, string theory assumes that a quantum theory of gravity will be achieved only through a unification of all the interactions. However, both employ the general method of quantization of constrained systems, which is described together with illustrative examples relevant for quantum gravity. There is a detailed presentation of the main approaches employed in quantum general relativity: path-integral quantization, the background-field method and canonical quantum gravity in the metric, connection and loop formulations. The discussion of string theory centres around its quantum-gravitational aspects and the comparison with quantum general relativity. Physical applications discussed at length include the quantization of black holes, quantum cosmology, the indications of a discretestructure of spacetime, and the origin of irreversibility. This third edition contains new chapters or sections on quantum gravity phenomenology, Horava-Lifshitz quantum gravity, analogue gravity, the holographic principle, and affine quantum gravity. It will present updates on loop quantum cosmology, the LTB model, asymptotic safety, and various discrete approaches. The third edition also contains pedagogical extensions throughout the text. This book will be of interest to researchers and students working in relativity and gravitation, cosmology, quantum field theory and related topics. It will also be of interest to mathematicians and philosophers of science.
Climate change is a major topic of concern today, scientifically, socially, and politically. It will undoubtedly continue to be so for the foreseeable future, as predicted changes in global temperatures, rainfall, and sea level take place, and as human society adapts to these changes. In this remarkable new work, Jan Zalasiewicz and Mark Williams demonstrate how the Earth's climate has continuously altered over its 4.5 billion-year history. The story can be read from clues preserved in the Earth's strata - the evidence is abundant, though always incomplete, and also often baffling, puzzling, infuriating, tantalizing, seemingly contradictory. Geologists, though, are becoming ever more ingenious at interrogating this evidence, and the story of the Earth's climate is now beingreconstructed in ever-greater detail - maybe even providing us with clues to the future of contemporary climate change. The history is dramatic and often abrupt. Changes in global and regional climate range from bitterly cold to sweltering hot, from arid to humid, and they have impacted hugely upon the planet's evolving animal and plant communities, and upon its physical landscapes of the Earth. And yet, through all of this, the Earth has remained consistently habitable for life for over three billion years - in stark contrast to its planetary neighbours. Not too hot, not too cold; not too dry, not too wet, itis aptly known as 'the Goldilocks planet'.
What was it like to be Charles Dickens? His letters are the nearest we can get to a Dickens autobiography: vivid close-up snapshots of a life lived at maximum intensity. This is the first selection to be made from the magisterial twelve-volume British Academy Pilgrim Edition of his letters. From over fourteen thousand, four hundred and fifty have been cherry-picked to give readers the best essence of 'the Sparkler of Albion'. Dickens was a man with ten times the energy of ordinary mortals. There seem to have been twice the number of hours in his day, and he threw himself into letter-writing as he did into everything else. This eagerly awaited selection takes us straight to the heart of his life, to show us Dickens at first hand. Here he is writing out of the heat of the moment: as a novelist, journalist, and magazine editor; as a social campaigner and traveller in Europe and America, and as friend, lover, husband,and father. Reading and writing letters punctuated the rhythms of Dickens's day. 'I walk about brimful of letters', he told a friend. He claimed to write 'at the least, a dozen a day'. Sometimes it was a chore but more often a pleasure: an outlet for high spirits, sparkling wit, and caustic commentary - always as seen through his highly individual and acutely observing eye. Whether you dip in or read straight through, this selection of his letters creates afresh the brilliance of being Dickens, and the sheer pleasure of being in his company.
Niels Bohr and the Quantum Atom is the first book that focuses in detail on the birth and development of Bohr's atomic theory and gives a comprehensive picture of it. At the same time it offers new insight into Bohr's peculiar way of thinking, what Einstein once called his 'unique instinct and tact'. Contrary to most other accounts of the Bohr atom, the book presents it in a broader perspective which includes the reception among other scientists and the criticismlaunched against it by scientists of a more conservative inclination. Moreover, it discusses the theory as Bohr originally conceived it, namely, as an ambitious theory covering the structure of atoms as well as molecules. By discussing the theory in its entirety it becomes possible to understand why itdeveloped as it did and thereby to use it as an example of the dynamics of scientific theories.
Heavily influenced by Dreiser's own life and experiences, this roman a clef was regarded as shockingly frank in its treatment of sexuality, particularly the sensual nature and intimate conquests of female protagonist Eugene Witla, an up-and-coming artist. As a result of the novel's titillating subject matter, Dreiser encountered a great deal of difficulty when it came to finding a willing publisher, and the book has been banned often in the ensuing decades since its completion.
In this sequel to Dreiser's novel The Financier, the author continues his exploration of the social and economic forces at play in the rise of the new class of super-rich capitalists in early twentieth-century America. Protagonist Frank Cowperwood attempts to leave his shameful past behind and settles in Chicago with his new wife. Will this quintessentially American act of self-reinvention succeed?
Groundbreaking author Kate Chopin was known for her innovative portraits of nineteenth-century heroines facing the challenges of life under strictly constrained gender roles. At Fault is a richly detailed historical romance set on a Louisiana plantation that delves deftly into the tangled web woven by a trio of star-crossed lovers whose lives have been rent asunder by misbegotten passion.
This hilarious collection of interconnected tall tales, anecdotes, and amusing incidents is a must-read for fans of the Hopalong Cassidy stories or the Western humor genre in general. A perfect introduction to the Hopalong Cassidy tales for young or first-time readers, Hopalong Cassidy's Rustler Round-Up is a rootin'-tootin' good time.
Part of the much-loved Hopalong Cassidy series, Bar-20 Days continues the saga of the cantankerous cowboy and his crew of rowdy ranch hands. The Bar-20 ranch features prominently in this hilarious and action-packed collection of stories and episodes dealing with different aspects of life on the range.
Ready for an engrossing read that encapsulates the magic and madness of the Wild West? This classic of the Western genre features everything you're looking for -- heroic cowboys, rowdy ranch hands, rollicking adventure, and the vast Western landscape.
Pining for a stiff dose of classic Western humor? Dive into Wolfville Nights from author Alfred Henry Lewis. This loosely intertwined connection of yarns, legends, episodes and escapades is packed with local color and will leave you howling with laughter.
The ever-popular Ronicky Doone series from renowned Western author Max Brand features one of the most indelibly memorable protagonists in the genre. Although Ronicky is a stand-up guy with a deep-seated sense of honor and loyalty, he often finds himself stuck in scrapes that require some creative thinking to get out of. If you love unforgettable characters mixed up in action-packed adventures, you'll love Ronicky Doone.
The thrill, allure and fatal attraction of gambling are brought to life in Max Brand's classic Western, The Garden of Eden. Boxing matches, card games, horse races, and more -- there's nothing that the thrill-seeking hero won't place a bet on. Is his luck about to run out?
Grab your hat and horse and hit the dusty trail with prolific Western writer Max Brand. In Trailin', Brand unfurls the tale of Anthony Bard, a well-born fellow who longs for adventure and ultimately finds it in the aftermath of a family tragedy. Bard sets out to capture the outlaw who wronged his kin -- and finds love along the way. A must-read for fans of classic Westerns.
This Western from prolific author Max Brand is a classic revenge story that is sure to please readers who are hankering for a solid dose of action-packed adventure. Riders of the Silences recounts the tale of hardened gunslinger Red Pierre, who will stop at nothing to exact vengeance on the ne'er-do-well who killed his father.