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A Short Course on Operator Semigroups by Klaus-Jochen Engel
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The Book of Mormon: A Very Short Introduction
Terryl L. Givens - 2009
Written by Terryl Givens, a leading authority on Mormonism, this compact volume offers the only concise, accessible introduction to this extraordinary work.Givens examines the Book of Mormon first and foremost in terms of the claims that its narrators make for its historical genesis, its purpose as a sacred text, and its meaning for an audience which shifts over the course of the history it unfolds. The author traces five governing themes in particular--revelation, Christ, Zion, scripture, and covenant--and analyzes the Book's central doctrines and teachings. Some of these resonate with familiar nineteenth-century religious preoccupations; others consist of radical and unexpected takes on topics from the fall of Man to Christ's mortal ministries and the meaning of atonement. Givens also provides samples of a cast of characters that number in the hundreds, and analyzes representative passages from a work that encompasses tragedy, poetry, sermons, visions, family histories and military chronicles. Finally, this introduction surveys the contested origins and production of a work held by millions to be scripture, and reviews the scholarly debates that address questions of the record's historicity.Here then is an accessible guide to what is, by any measure, an indispensable key to understanding Mormonism. But it is also an introduction to a compelling and complex text that is too often overshadowed by the controversies that surround it.About the Series: Combining authority with wit, accessibility, and style, Very Short Introductions offer an introduction to some of life's most interesting topics. Written by experts for the newcomer, they demonstrate the finest contemporary thinking about the central problems and issues in hundreds of key topics, from philosophy to Freud, quantum theory to Islam.
The Infinity Puzzle: Quantum Field Theory and the Hunt for an Orderly Universe
Frank Close - 2011
If found, the Higgs boson would help explain why everything has mass. But there’s more at stake—what we’re really testing is our capacity to make the universe reasonable. Our best understanding of physics is predicated on something known as quantum field theory. Unfortunately, in its raw form, it doesn’t make sense—its outputs are physically impossible infinite percentages when they should be something simpler, like the number 1. The kind of physics that the Higgs boson represents seeks to “renormalize” field theory, forcing equations to provide answers that match what we see in the real world.The Infinity Puzzle is the story of a wild idea on the road to acceptance. Only Close can tell it.
Proofs and Refutations: The Logic of Mathematical Discovery
Imre Lakatos - 1976
Much of the book takes the form of a discussion between a teacher and his students. They propose various solutions to some mathematical problems and investigate the strengths and weaknesses of these solutions. Their discussion (which mirrors certain real developments in the history of mathematics) raises some philosophical problems and some problems about the nature of mathematical discovery or creativity. Imre Lakatos is concerned throughout to combat the classical picture of mathematical development as a steady accumulation of established truths. He shows that mathematics grows instead through a richer, more dramatic process of the successive improvement of creative hypotheses by attempts to 'prove' them and by criticism of these attempts: the logic of proofs and refutations.
Basic Category Theory for Computer Scientists
Benjamin C. Pierce - 1991
Assuming a minimum of mathematical preparation, Basic Category Theory for Computer Scientists provides a straightforward presentation of the basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, and cartesian closed categories. Four case studies illustrate applications of category theory to programming language design, semantics, and the solution of recursive domain equations. A brief literature survey offers suggestions for further study in more advanced texts.
Introduction to Real Analysis
Robert G. Bartle - 1982
Therefore, this book provides the fundamental concepts and techniques of real analysis for readers in all of these areas. It helps one develop the ability to think deductively, analyze mathematical situations and extend ideas to a new context. Like the first two editions, this edition maintains the same spirit and user-friendly approach with some streamlined arguments, a few new examples, rearranged topics, and a new chapter on the Generalized Riemann Integral.
Differential Equations with Boundary-Value Problems
Dennis G. Zill - 1986
This proven and accessible text speaks to beginning engineering and math students through a wealth of pedagogical aids, including an abundance of examples, explanations, "Remarks" boxes, definitions, and group projects. Using a straightforward, readable, and helpful style, this book provides a thorough treatment of boundary-value problems and partial differential equations.
The Logical Leap: Induction in Physics
David Harriman - 2010
Inspired by and expanding on a series of lectures presented by Leonard Peikoff, David Harriman presents a fascinating answer to the problem of induction-the epistemological question of how we can know the truth of inductive generalizations.Ayn Rand presented her revolutionary theory of concepts in her book Introduction to Objectivist Epistemology. As Dr. Peikoff subsequently explored the concept of induction, he sought out David Harriman, a physicist who had taught philosophy, for his expert knowledge of the scientific discovery process.Here, Harriman presents the result of a collaboration between scientist and philosopher. Beginning with a detailed discussion of the role of mathematics and experimentation in validating generalizations in physics-looking closely at the reasoning of scientists such as Galileo, Kepler, Newton, Lavoisier, and Maxwell-Harriman skillfully argues that the inductive method used in philosophy is in principle indistinguishable from the method used in physics.
The Meaning of Relativity
Albert Einstein - 1922
These four lectures constituted an overview of his then-controversial theory of relativity. Princeton University Press made the lectures available under the title The Meaning of Relativity, the first book by Einstein to be produced by an American publisher. As subsequent editions were brought out by the Press, Einstein included new material amplifying the theory. A revised version of the appendix Relativistic Theory of the Non-Symmetric Field, added to the posthumous edition of 1956, was Einstein's last scientific paper.-- "Physics Today"
Mathematical Proofs: A Transition to Advanced Mathematics
Gary Chartrand - 2002
This text introduces students to proof techniques and writing proofs of their own. As such, it is an introduction to the mathematics enterprise, providing solid introductions to relations, functions, and cardinalities of sets.
Games Indians Play: Why We Are the Way We Are
V. Raghunathan - 2006
Raghunathan uses the props of game theory and behavioural economics to provide an insight into the difficult conundrum of why we are the way we are. He puts under the scanner our attitudes towards rationality and irrationality, selflessness and selfishness, competition and cooperation, and collaboration and deception. Drawing examples from the way we behave in day-to-day situations, Games Indians Play tries to show how in the long run each one of us—whether businessmen, politicians, bureaucrats, or just plain us—stand to profit more if we were to assume a little self-regulation, give fairness a chance and strive to cooperate and collaborate a little more even if self-interests were to be our main driving force.
Game Theory. Analysis of conflict
Roger B. Myerson - 1991
Myerson introduces, clarifies, and synthesizes the extraordinary advances made in the subject over the past fifteen years, presents an overview of decision theory, and comprehensively reviews the development of the fundamental models: games in extensive form and strategic form, and Bayesian games with incomplete information.Game Theory will be useful for students at the graduate level in economics, political science, operations research, and applied mathematics. Everyone who uses game theory in research will find this book essential.
The Puzzler's Dilemma: From the Lighthouse of Alexandria to Monty Hall, a Fresh Look at Classic Conundrums of Logic, Mathematics, and Life
Derrick Niederman - 2012
Among the old chestnuts he cracks wide open are the following classics: Knights and knaves The monk and the mountain The dominoes and the chessboard The unexpected hanging The Tower of HanoiUsing real-world analogies, infectious humor, and a fresh approach, this deceptively simple volume will challenge, amuse, enlighten, and surprise even the most experienced puzzle solver.
Neoliberalism: A Very Short Introduction
Manfred B. Steger - 2010
In its heyday during the late 1990s, neoliberalism emerged as the world's dominant economic paradigm, stretching from the Anglo-American heartlands of capitalism to the former communist bloc all the way to the developing regions of the global South. Today, however, neoliberalism has been discredited as the global economy, built on its principles, has been shaken to its core by the worst financial calamity since the 1930s. Is neoliberalism doomed or will it regain its former status? Will the new U.S. President Barack Obama embrace or reject the neoliberal agenda of his predecessors in the White House? And how will his decision impact the current global economic order? Is there a viable alternative to neoliberalism? Exploring the origins, core claims, and various forms of neoliberalism, this Very Short Introduction offers a concise and accessible introduction to one of the most debated "isms" of our time.
Mathematics: Its Content, Methods and Meaning
A.D. Aleksandrov - 1963
. . Nothing less than a major contribution to the scientific culture of this world." — The New York Times Book ReviewThis major survey of mathematics, featuring the work of 18 outstanding Russian mathematicians and including material on both elementary and advanced levels, encompasses 20 prime subject areas in mathematics in terms of their simple origins and their subsequent sophisticated developement. As Professor Morris Kline of New York University noted, "This unique work presents the amazing panorama of mathematics proper. It is the best answer in print to what mathematics contains both on the elementary and advanced levels."Beginning with an overview and analysis of mathematics, the first of three major divisions of the book progresses to an exploration of analytic geometry, algebra, and ordinary differential equations. The second part introduces partial differential equations, along with theories of curves and surfaces, the calculus of variations, and functions of a complex variable. It furthur examines prime numbers, the theory of probability, approximations, and the role of computers in mathematics. The theory of functions of a real variable opens the final section, followed by discussions of linear algebra and nonEuclidian geometry, topology, functional analysis, and groups and other algebraic systems.Thorough, coherent explanations of each topic are further augumented by numerous illustrative figures, and every chapter concludes with a suggested reading list. Formerly issued as a three-volume set, this mathematical masterpiece is now available in a convenient and modestly priced one-volume edition, perfect for study or reference."This is a masterful English translation of a stupendous and formidable mathematical masterpiece . . ." — Social Science
Indiscrete Thoughts
Gian-Carlo Rota - 1996
The era covered by this book, 1950 to 1990, was surely one of the golden ages of science as well as the American university.Cherished myths are debunked along the way as Gian-Carlo Rota takes pleasure in portraying, warts and all, some of the great scientific personalities of the period Stanislav Ulam (who, together with Edward Teller, signed the patent application for the hydrogen bomb), Solomon Lefschetz (Chairman in the 50s of the Princeton mathematics department), William Feller (one of the founders of modern probability theory), Jack Schwartz (one of the founders of computer science), and many others.Rota is not afraid of controversy. Some readers may even consider these essays indiscreet. After the publication of the essay "The Pernicious Influence of Mathematics upon Philosophy" (reprinted six times in five languages) the author was blacklisted in analytical philosophy circles. Indiscrete Thoughts should become an instant classic and the subject of debate for decades to come."Read Indiscrete Thoughts for its account of the way we were and what we have become; for its sensible advice and its exuberant rhetoric."--The Mathematical Intelligencer"Learned, thought-provoking, politically incorrect, delighting in paradox, and likely to offend but everywhere readable and entertaining."--The American Mathematical Monthly"It is about mathematicians, the way they think, and the world in which the live. It is 260 pages of Rota calling it like he sees it... Readers are bound to find his observations amusing if not insightful. Gian-Carlo Rota has written the sort of book that few mathematicians could write. What will appeal immediately to anyone with an interest in research mathematics are the stories he tells about the practice of modern mathematics."--MAA Reviews"