Zusammenfassung: Felix Hausdorff is a singular phenomenon in the history of science. As a mathematician, he played a major role in shaping the development of modern mathematics in the 20th century. He founded general topology as an independent mathematical discipline, while enriching set theory with a number of fundamental concepts and results. His general approach to measure and dimension led to profound developments in numerous mathematical disciplines, and today Hausdorff dimension plays a central role in fractal theory with its many fascinating applications by means of computer graphics. Hausdorff 's remarkable mathematical versatility is reflected in his published work: today, no fewer than thirteen concepts, theorems and procedures carry his name. Yet he was not only a creative mathematician - Hausdorff was also an original philosophical thinker, a poet, essayist and man of letters. Under the pseudonym Paul Mongré, he published a volume of aphorisms, an epistemological study, a book of poetry, an oft-performed play, and a number of notable essays in leading literary journals. As a Jew, Felix Hausdorff was increasingly persecuted and humiliated under the National Socialist dictatorship. When deportation to a concentration camp was imminent, he, along with his wife and sister-in law, decided to take their own lives. This book will be of interest to historians and mathematicians already fascinated by the rich life of Felix Hausdorff, as well as to those readers who wish to immerse themselves in the intricate web of intellectual and political transformations during this pivotal period in European history
This classic work offers scores of stimulating, mind-expanding games and puzzles: arithmetical and geometrical problems, chessboard recreations, magic squares, map-coloring problems, cryptography and cryptanalysis, much more. "A must to add to your mathematics library" ? The Mathematics Teacher. Index. References for Further Study. Includes 150 black-and-white line illustrations.
The rich history of Egypt has provided famous examples of board games played in antiquity. Each of these games provides evidence of contact between Egypt and its neighbours. From pre-dynastic rule to Arab and Ottoman invasions, Egypt's past is visible on game boards. This volume starts by introducing the reader to board games as well as instruments of chance and goes on to trace the history and distribution of ancient Egyptian games, looking particularly at how they show contact with other cultures and civilizations. Game practices, which were also part of Egyptian rituals and divination, travelled throughout the eastern Mediterranean. This book explores the role of Egypt in accepting and disseminating games during its long history. Over the last few years, the extent and the modes of contact have become better understood through museum and archival research projects as well as surveys of archaeological sites in Egypt and its surrounding regions. The results allow new insight into ancient Egypt's international relations and the role of board games research in understanding its extent. Written by three authors known internationally for their expertise on this topic, this will be the first volume on Ancient Egyptian games of its kind and a much-needed contribution to the field of both Egyptology and board games studies.
What Is Combinatorics Anyway? Broadly speaking, combinatorics is the branch of mathematics dealing with different ways of selecting objects from a set or arranging objects. It tries to answer two major kinds of questions, namely, counting questions: how many ways can a selection or arrangement be chosen with a particular set of properties; and structural questions: does there exist a selection or arrangement of objects with a particular set of properties? The authors have presented a text for students at all levels of preparation. For some, this will be the first course where the students see several real proofs. Others will have a good background in linear algebra, will have completed the calculus stream, and will have started abstract algebra. The text starts by briefly discussing several examples of typical combinatorial problems to give the reader a better idea of what the subject covers. The next chapters explore enumerative ideas and also probability. It then moves on to enumerative functions and the relations between them, and generating functions and recurrences., Important families of functions, or numbers and then theorems are presented. Brief introductions to computer algebra and group theory come next. Structures of particular interest in combinatorics: posets, graphs, codes, Latin squares, and experimental designs follow. The authors conclude with further discussion of the interaction between linear algebra and combinatorics. Features Two new chapters on probability and posets. Numerous new illustrations, exercises, and problems. More examples on current technology use A thorough focus on accuracy Three appendices: sets, induction and proof techniques, vectors and matrices, and biographies with historical notes, Flexible use of MapleTM and MathematicaTM
Following his blockbuster biography of Steve Jobs, Walter Isaacson’s New York Times bestselling and critically acclaimed The Innovators is a “riveting, propulsive, and at times deeply moving” (The Atlantic) story of the people who created the computer and the internet. What were the talents that allowed certain inventors and entrepreneurs to turn their visionary ideas into disruptive realities? What led to their creative leaps? Why did some succeed and others fail? The Innovators is a masterly saga of collaborative genius destined to be the standard history of the digital revolution—and an indispensable guide to how innovation really happens. Isaacson begins the adventure with Ada Lovelace, Lord Byron’s daughter, who pioneered computer programming in the 1840s. He explores the fascinating personalities that created our current digital revolution, such as Vannevar Bush, Alan Turing, John von Neumann, J.C.R. Licklider, Doug Engelbart, Robert Noyce, Bill Gates, Steve Wozniak, Steve Jobs, Tim Berners-Lee, and Larry Page. This is the story of how their minds worked and what made them so inventive. It’s also a narrative of how their ability to collaborate and master the art of teamwork made them even more creative. For an era that seeks to foster innovation, creativity, and teamwork, The Innovators is “a sweeping and surprisingly tenderhearted history of the digital age” (The New York Times).
Walter Bagehot was one of the most famous 19th-century British journalists and essayists, whose major works refer to government, economics, and literature. This is the first out of nine volumes with his most important writings, this one containing: Memoir To The Roman Catholic Church Second Memoir Letters On The French Coup D’état Of 1851 Oxford Hartley Coleridge Shakespeare - The Man Bishop Butler
A collection of fascinating stories, entertainingly told, revealing the human face of science. Eurekas and Euphorias encompasses some 200 anecdotes brilliantly illustrating scientists in all their shapes: the obsessive and the dilettantish, the genial, the envious, the preternaturally brilliant and the slow-witted who sometimes see further in the end, the open-minded and the intolerant, recluses and arrivistes. Told with wit and relish by Walter Gratzer, here are stories to delight, astonish, instruct, and most especially, entertain the general reader, scientist and non-scientist alike.
In the last two decades modal logic has undergone an explosive growth, to thepointthatacompletebibliographyofthisbranchoflogic,supposingthat someone were capable to compile it, would ?ll itself a ponderous volume. What is impressive in the growth of modal logic has not been so much the quick accumulation of results but the richness of its thematic dev- opments. In the 1960s, when Kripke semantics gave new credibility to the logic of modalities? which was already known and appreciated in the Ancient and Medieval times? no one could have foreseen that in a short time modal logic would become a lively source of ideas and methods for analytical philosophers,historians of philosophy,linguists, epistemologists and computer scientists. The aim which oriented the composition of this book was not to write a new manual of modal logic (there are a lot of excellent textbooks on the market, and the expert reader will realize how much we bene?ted from manyofthem)buttoo?ertoeveryreader,evenwithnospeci?cbackground in logic, a conceptually linear path in the labyrinth of the current panorama of modal logic. The notion which in our opinion looked suitable to work as a compass in this enterprise was the notion of multimodality, or, more speci?cally, the basic idea of grounding systems on languages admitting more than one primitive modal operator.
This book is the first in the field of paraconsistency to offer a comprehensive overview of the subject, including connections to other logics and applications in information processing, linguistics, reasoning and argumentation, and philosophy of science. It is recommended reading for anyone interested in the question of reasoning and argumentation in the presence of contradictions, in semantics, in the paradoxes of set theory and in the puzzling properties of negation in logic programming. Paraconsistent logic comprises a major logical theory and offers the broadest possible perspective on the debate of negation in logic and philosophy. It is a powerful tool for reasoning under contradictoriness as it investigates logic systems in which contradictory information does not lead to arbitrary conclusions. Reasoning under contradictions constitutes one of most important and creative achievements in contemporary logic, with deep roots in philosophical questions involving negation and consistency This book offers an invaluable introduction to a topic of central importance in logic and philosophy. It discusses (i) the history of paraconsistent logic; (ii) language, negation, contradiction, consistency and inconsistency; (iii) logics of formal inconsistency (LFIs) and the main paraconsistent propositional systems; (iv) many-valued companions, possible-translations semantics and non-deterministic semantics; (v) paraconsistent modal logics; (vi) first-order paraconsistent logics; (vii) applications to information processing, databases and quantum computation; and (viii) applications to deontic paradoxes, connections to Eastern thought and to dialogical reasoning.
This volume provides a comprehensive introduction to the history of ancient Israel—from the creation account to setting the stage for the New Testament era. This edition has been thoroughly revised, but maintains its focus on Old Testament texts as well as ancient Near Eastern literary and archeological sources to highlight the important modern controversies surrounding this part of Scripture. The work provides an up-to-date, conservative, evangelical position on matters relating to ancient Israel’s history and is illustrated with over 600 figures, charts, and maps.
This book presents a study on the foundations of a large class of paraconsistent logics from the point of view of the logics of formal inconsistency. It also presents several systems of non-standard logics with paraconsistent features.
Starting with simple examples showing the relevance of cutting and pasting logics, the monograph develops a mathematical theory of combining and decomposing logics, ranging from propositional and first-order based logics to higher-order based logics as well as to non-truth functional logics. The theory covers mechanisms for combining semantic structures and deductive systems either of the same or different nature. The issue of preservation of properties is addressed.
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