Based on a well-received course designed for philosophy students, this book is an informal introduction to mathematical thinking. The work will be rewarding not only for philosophers concerned with mathematical questions but also for serious amateur mathematicians with an interest in the "frontiers" as well as the foundations of mathematics. In what might be termed a sampler of the discipline, Konrad Jacobs discusses an unusually wide range of topics, including such items of contemporary interest as knot theory, optimization theory, and dynamical systems. Using Euclidean geometry and algebra to introduce the mathematical mode of thought, the author then turns to recent developments. In the process he offers what he calls a "Smithsonian of mathematical showpieces": the five Platonic Solids, the Mbius Strip, the Cantor Discontinuum, the Peano Curve, Reidemeister's Knot Table, the plane ornaments, Alexander's Horned Sphere, and Antoine's Necklace. The treatments of geometry and algebra are followed by a chapter on induction and one on optimization, game theory, and mathematical economics. The chapter on topology includes a discussion of topological spaces and continuous mappings, curves and knots, Euler's polyhedral formula for surfaces, and the fundamental group. The last chapter deals with dynamics and contains material on the Game of Life, circle rotation, Smale's "horseshoe," and stability and instability, among other topics.
Probability and Mathematical Statistics: Measure and Integral provides information pertinent to the general mathematical notions and notations. This book discusses how the machinery of ?-extension works and how ?-content is derived from ?-measure. Organized into 16 chapters, this book begins with an overview of the classical Hahn–Banach theorem and introduces the Banach limits in the form of a major exercise. This text then presents the Daniell extension theory for positive ?-measures. Other chapters consider the transform of ?-contents and ?-measures by measurable mappings and kernels. This text is also devoted to a thorough study of the vector lattice of signed contents. This book discusses as well an abstract regularity theory and applied to the standard cases of compact, locally compact, and Polish spaces. The final chapter deals with the rudiments of the Krein–Milman theorem, along with some of their applications. This book is a valuable resource for graduate students.
Discrete stochastics is the theory of discrete probability spaces. This undergraduate textbook gives a concise introduction into discrete stochastics in general, and into a variety of typical special topics in this field, such as information theory, fluctuation theory, and semigroups of stochastic matrices. The emphasis lies on probability theory rather than on statistical methodology. Motivations, interpretations, and numerous examples and exercises relate the mathematical theory to stochastic experience.
Probability and Mathematical Statistics: Measure and Integral provides information pertinent to the general mathematical notions and notations. This book discusses how the machinery of ?-extension works and how ?-content is derived from ?-measure. Organized into 16 chapters, this book begins with an overview of the classical Hahn–Banach theorem and introduces the Banach limits in the form of a major exercise. This text then presents the Daniell extension theory for positive ?-measures. Other chapters consider the transform of ?-contents and ?-measures by measurable mappings and kernels. This text is also devoted to a thorough study of the vector lattice of signed contents. This book discusses as well an abstract regularity theory and applied to the standard cases of compact, locally compact, and Polish spaces. The final chapter deals with the rudiments of the Krein–Milman theorem, along with some of their applications. This book is a valuable resource for graduate students.
I. Introduction.- 1. Encountering Random.- 2. Specimens of Stochastic Reasoning.- II. Markovian Dynamics.- 1. Finite-state Markovian dynamical systems.- 2. The convex set of stochastic matrices.- 3. The asymptotic behavior of Pn: some special cases.- 4. Asymptotic behavior of P, P2, ...: the method of invariant sets.- III. Discrete Probability Spaces.- 1. The Notion of a Discrete Probability Space (DPS).- 2. Obtaining New Probability Spaces from Given Ones.- 3. Independence.- IV. Independent Identically Distributed (IID) Random Variables.- 1. Addition of independent RVs.- 2. Expectation and Variance.- 3. The Weak Law of Large Numbers (WLLN).- 4. The Central Limit Theorem (CLT) I.- 5. The Central Limit Theorem (CLT) II.- 6. Outlook.- V. Statistics.- 1. Specimens of Statistical Reasoning.- 2. The Game-Theoretical Framework of Statistical Theory.- 3. Tests.- 4. Outlook.- VI. Markov Processes.- 1. Conditional Probabilities.- 2. Markov Processes.- VII. Elements of Information Theory.- 1. Combinatorial and Algebraic Coding Theory.- 2. Source Coding.- 3. Noisy Channels.- VIII. Fluctuation Theory.- 1. The Combinatorial Arcsin Law of Erik Sparre Andersen.- 2. Arcsin.- 3. Symmetrically Distributed Random Variables.- 4. Fluctuations of Random Walks.- 5. The Andersen-Spitzer Formula.- 6. Outlook.- IX. Optimal Strategies in Casinoes: Red and Black.- 1. Strategies and Their Probability of Success.- 2. Some Properties of BOLD.- 3. The Optimality of BOLD for p ? 1/2 ? r.- 4. Non-Optimality of BOLD if p ? 1/2 ? r Fails.- X. Foundational Problems.- 1. The Theory of Randomness.- 2. Subjective Probabilities.- 3. Belief ("bel") Functions.- Appendix A: The Marriage Theorem.- Appendix B: Markovian Semigroups.- Appendix C: One-parameter semigroups of stochastic matrices.
Based on a well-received course designed for philosophy students, this book is an informal introduction to mathematical thinking. The work will be rewarding not only for philosophers concerned with mathematical questions but also for serious amateur mathematicians with an interest in the "frontiers" as well as the foundations of mathematics. In what might be termed a sampler of the discipline, Konrad Jacobs discusses an unusually wide range of topics, including such items of contemporary interest as knot theory, optimization theory, and dynamical systems. Using Euclidean geometry and algebra to introduce the mathematical mode of thought, the author then turns to recent developments. In the process he offers what he calls a "Smithsonian of mathematical showpieces": the five Platonic Solids, the Mbius Strip, the Cantor Discontinuum, the Peano Curve, Reidemeister's Knot Table, the plane ornaments, Alexander's Horned Sphere, and Antoine's Necklace. The treatments of geometry and algebra are followed by a chapter on induction and one on optimization, game theory, and mathematical economics. The chapter on topology includes a discussion of topological spaces and continuous mappings, curves and knots, Euler's polyhedral formula for surfaces, and the fundamental group. The last chapter deals with dynamics and contains material on the Game of Life, circle rotation, Smale's "horseshoe," and stability and instability, among other topics.
Plant nutrition; The soil as a plant nutrient medium; Nutrient uptake and assimilation; Plant water relationships; Plant growth and crop production; Fertilizer application; Nitrogen; Sulphur; Phosphorus; Potassium; Calcium; Magnesium; Iron; Manganese; Zinc; Copper; Molybdenum; Boron; Further elements of importance; Elements with more toxic effects.
This guide provides an overview of the thematic areas, analytical aspects, and avenues of research which, together, form a broader conversation around doing spatial history. Spatial history is not a field with clearly delineated boundaries. For the most part, it lacks a distinct, unambiguous scholarly identity. It can only be thought of in relation to other, typically more established fields. Indeed, one of the most valuable utilities of spatial history is its capacity to facilitate conversations across those fields. Consequently, it must be discussed in relation to a variety of historiographical contexts. Each of these have their own intellectual genealogies, institutional settings, and conceptual path dependencies. With this in mind, this guide surveys the following areas: territoriality, infrastructure, and borders; nature, environment, and landscape; city and home; social space and political protest; spaces of knowledge; spatial imaginaries; cartographic representations; and historical GIS research.
America's worsening nightmare of gridlock is given full attention in this illuminating study of the transportation crisis in Atlanta. Inconveniences and hardships created by too many automobiles and too few alternatives for movement have reached untenable levels. Miriam Konrad investigates three major transportation projects involving public transit and use of space issues in the Atlanta area: the Metropolitan Atlanta Rapid Transit Authority (MARTA), the bus and rail system that has been the backbone of metropolitan Atlanta's public transportation system for the past thirty years; the Georgia Regional Transportation Authority (GRTA), a superagency created in 1999 to address air quality issues in the region; and the Belt Line, a popular proposal to build a twenty-two-mile loop of greenspace, transit, and other amenities around an inner loop of the city on existing rail beds. She reveals how gridlock, over regional transportation policy and procedures, has emerged out of the competition between growth promoters, environmentalists, and social justice actors.
This is the 5th edition of a well-established book Principles of Plant Nutrition which was first published in 1978. The same format is maintained as in previous editions with the primary aim of the authors to consider major processes in soils and plants that are of relevance to plant nutrition.This new edition gives an up-to-date account of the scientific advances of the subject by making reference to about 2000 publications. An outstanding feature of the book, which distinguishes it from others, is its wide approach encompassing not only basic nutrition and physiology, but also practical aspects of plant nutrition involving fertilizer usage and crop production of direct importance to human nutrition. Recognizing the international readership of the book, the authors, as in previous editions, have attempted to write in a clear concise style of English for the benefit of the many readers for whom English is not their mother tongue. The book will be of use to undergraduates and postgraduates in Agriculture, Horticulture, Forestry and Ecology as well as those researching in Plant Nutrition.
Child and Cross from the beginning puts children in the center, listening to how they perceive the man on the cross. Three initial chapters trace the life of this Jesus bar Abbas according to highly respected sources, in a very human, down-to-earth way from mother's womb to rebels' cross. How the picture of the rabbi's deadly torture became the obsessive icon of the West and in an "automatic and preconscious" way (Melvin Lerner) continues working as the learning tool for Jew-hate is explained thanks to the sensitivity of psychologists like Søren Kierkegaard, Jean Piaget and Helena Antipoff, exposed in 73 pictures. The return of Passion details in Christian views of Jews, the reenactment of those scaring details in thousand years of "just punishment", racism as product of inquisition, the still solid cross taboo in Germany, the complex of cross and Zionism and the kafkaesque cross judgement of the European Court for Human Rights in Strasbourg are examined while the human obsession with sacrifice itself gets analyzed in "The Lamb on Cross" whose pegged legs shaped western use of animals more than this Nazarene who in his last action fought precisely animal sacrifice. The final exam "Why Johanna fed him vanilla cake and other child's play questions" intends to sensitize the reader once again concerning the child & cross issue, well in accordance with the Galilean who "called a child and set him in their midst ..." Thus Child and Cross is mainly a) an exemplary study about the power of visual images and for respecting children's empathic ways of viewing this world; b) a consistent, comprising and explaining analysis of anti-Judaism by taking serious those human beings that academic research of "anti-Semitism" deems too small and childish to deal with; c) a contribution to Christian-Muslim-Jewish dialogue by detailed elaboration of not only the Christian symbol's role in the anti-Judaism that led to Zionism and thus to Gaza, but also of the connecting potential of this man from Galilee whom Matthew (27:16-17 in original Greek wording) calls Jesus bar Abbas; and d) a human rehabilitation of this Bar Abbas ("Son of Father") and his relatives, especially his brother Judas.
In this meticulously researched study, Konrad Schmid offers a historical clarification of the concept of “theology.” He then examines the theologies of the three constituent parts of the Hebrew Bible—the Torah, the Prophets, and the Writings— before tracing how these theological concepts developed throughout the history of ancient Israel and early Judaism. Schmid not only explores the theology of the biblical books in isolation, but he also offers unifying principles and links between the distinct units that make up the Hebrew Bible. By focusing on both the theology of the whole Hebrew Bible as well as its individual pieces, A Historical Theology of the Hebrew Bible provides a comprehensive discussion of theological work within the Hebrew Bible.
An accessible introduction to constructing and interpreting Bayesian models of perceptual decision-making and action. Many forms of perception and action can be mathematically modeled as probabilistic—or Bayesian—inference, a method used to draw conclusions from uncertain evidence. According to these models, the human mind behaves like a capable data scientist or crime scene investigator when dealing with noisy and ambiguous data. This textbook provides an approachable introduction to constructing and reasoning with probabilistic models of perceptual decision-making and action. Featuring extensive examples and illustrations, Bayesian Models of Perception and Action is the first textbook to teach this widely used computational framework to beginners. Introduces Bayesian models of perception and action, which are central to cognitive science and neuroscience Beginner-friendly pedagogy includes intuitive examples, daily life illustrations, and gradual progression of complex concepts Broad appeal for students across psychology, neuroscience, cognitive science, linguistics, and mathematics Written by leaders in the field of computational approaches to mind and brain
No public action of the Roman state, the populus Romanus, at home or at war, was to be carried out without prior permission from Iuppiter Optimus Maximus. Permission was obtained, in a procedure known as auspices, by the magistrate in charge of the intended action-usually a Consul, Praetor, or Dictator. Auspices thus occupy a fundamental place in the-unwritten-constitution of the Roman State. Yet especially in the 3rd century BCE, acceptance of the principle was not always universal. The Challenge to the Auspices presents an investigation into the interaction of Roman magistrates during the Middle Republic with the practice of auspices, with a focus on attempts to avoid, ignore, or resist this requirement. Proceeding from an examination of the Roman concepts of imperium and auspices (auspicia), especially as they relate to the realm of war, and of the constitutional position and powers of the Dictator and the Master-of-Horse (magister equitum) relative to each other and to the Consuls and lower magistrates, the work offers six case studies in which Roman commanders questioned, violated, or openly rejected the need for auspices. It is argued that these instances reflect a not insignificant minority view within the Roman ruling class regarding the efficacy of auspices and the necessity of observing them. The catastrophic outcome in several of these events, particularly during the early years of the Second Punic War, rendered further resistance to the practice politically unsustainable, and by the second century resulted in its universal acceptance, regardless of personal belief.
This book provides a theoretical background in computation to scientists who use computational methods. It explains how computing is used in the natural sciences, and provides a high-level overview of those aspects of computer science and software engineering that are most relevant for computational science. The focus is on concepts, results, and applications, rather than on proofs and derivations. The unique feature of this book is that it “connects the dots between computational science, the theory of computation and information, and software engineering. The book should help scientists to better understand how they use computers in their work, and to better understand how computers work. It is meant to compensate a bit for the general lack of any formal training in computer science and information theory. Readers will learn something they can use throughout their careers.
A sweeping history of twentieth-century Europe that examines its unprecedented destruction—and abiding promise A sweeping history of twentieth-century Europe, Out of Ashes tells the story of an era of unparalleled violence and barbarity yet also of humanity, prosperity, and promise. Konrad Jarausch describes how the European nations emerged from the nineteenth century with high hopes for continued material progress and proud of their imperial command over the globe, only to become embroiled in the bloodshed of World War I, which brought an end to their optimism and gave rise to competing democratic, communist, and fascist ideologies. He shows how the 1920s witnessed renewed hope and a flourishing of modernist art and literature, but how the decade ended in economic collapse and gave rise to a second, more devastating world war and genocide on an unprecedented scale. Jarausch further explores how Western Europe surprisingly recovered due to American help and political integration. Finally, he examines how the Cold War pushed the divided continent to the brink of nuclear annihilation, and how the unforeseen triumph of liberal capitalism came to be threatened by Islamic fundamentalism, global economic crisis, and an uncertain future. A gripping narrative, Out of Ashes explores the paradox of the European encounter with modernity in the twentieth century, shedding new light on why it led to cataclysm, inhumanity, and self-destruction, but also social justice, democracy, and peace.
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