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Felix Hausdorff
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Download or read book Set Theory written by Felix Hausdorff and published by American Mathematical Soc.. This book was released on 2021-08-24 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is a translation into English of the Third Edition of the classic German language work Mengenlehre by Felix Hausdorff published in 1937. From the Preface (1937): “The present book has as its purpose an exposition of the most important theorems of the theory of sets, along with complete proofs, so that the reader should not find it necessary to go outside this book for supplementary details while, on the other hand, the book should enable him to undertake a more detailed study of the voluminous literature on the subject. The book does not presuppose any mathematical knowledge beyond the differential and integral calculus, but it does require a certain maturity in abstract reasoning; qualified college seniors and first year graduate students should have no difficulty in making the material their own … The mathematician will … find in this book some things that will be new to him, at least as regards formal presentation and, in particular, as regards the strengthening of theorems, the simplification of proofs, and the removal of unnecessary hypotheses.”
Book Synopsis Hausdorff on Ordered Sets by : Felix Hausdorff
Download or read book Hausdorff on Ordered Sets written by Felix Hausdorff and published by American Mathematical Soc.. This book was released on 2005 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: Georg Cantor, the founder of set theory, published his last paper on sets in 1897. In 1900, David Hilbert made Cantor's Continuum Problem and the challenge of well-ordering the real numbers the first problem in his famous Paris lecture. It was time for the appearance of the second generation of Cantorians. They emerged in the decade 1900-1909, and foremost among them were Ernst Zermelo and Felix Hausdorff. Zermelo isolated the Choice Principle, proved that every set could be well-ordered, and axiomatized the concept of set. He became the father of abstract set theory. Hausdorff eschewed foundations and pursued set theory as part of the mathematical arsenal. He was recognized as the era's leading Cantorian. From 1901-1909, Hausdorff published seven articles in which he created a representation theory for ordered sets and investigated sets of real sequences partially ordered by eventual dominance, together with their maximally ordered subsets. These papers are translated and appear in this volume. Each is accompanied by an introductory essay. These highly accessible works are of historical significance, not only for set theory, but also for model theory, analysis and algebra.
Book Synopsis Felix Hausdorff by : Egbert Brieskorn
Download or read book Felix Hausdorff written by Egbert Brieskorn and published by Springer Nature. This book was released on 2024 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Paradoxes of Measures and Dimensions Originating in Felix Hausdorff's Ideas by : Janusz Czy?
Download or read book Paradoxes of Measures and Dimensions Originating in Felix Hausdorff's Ideas written by Janusz Czy? and published by World Scientific. This book was released on 1994 with total page 768 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, many ideas by Felix Hausdorff are described and contemporary mathematical theories stemming from them are sketched.
Book Synopsis Paradoxes Of Measures And Dimensions Originating In Felix Hausdorff's Ideas by : Janusz Czyz
Download or read book Paradoxes Of Measures And Dimensions Originating In Felix Hausdorff's Ideas written by Janusz Czyz and published by World Scientific. This book was released on 1994-01-14 with total page 767 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, many ideas by Felix Hausdorff are described and contemporary mathematical theories stemming from them are sketched.
Book Synopsis Fractals in Probability and Analysis by : Christopher J. Bishop
Download or read book Fractals in Probability and Analysis written by Christopher J. Bishop and published by Cambridge University Press. This book was released on 2017 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: A mathematically rigorous introduction to fractals, emphasizing examples and fundamental ideas while minimizing technicalities.
Download or read book Galileo Unbound written by David D. Nolte and published by Oxford University Press. This book was released on 2018-07-12 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Galileo Unbound traces the journey that brought us from Galileo's law of free fall to today's geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying the foundation upon which Newton built the first theory of dynamics. Early in the twentieth century, geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, forcing light rays to bend past the Sun. Possibly more radical was Feynman's dilemma of quantum particles taking all paths at once — setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant, the need to track ever more complex changes and to capture their essence, to find patterns in the chaos as we try to predict and control our world.
Book Synopsis Consequences of the Axiom of Choice by : Paul Howard
Download or read book Consequences of the Axiom of Choice written by Paul Howard and published by American Mathematical Soc.. This book was released on 1998 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, Consequences of the Axiom of Choice, is a comprehensive listing of statements that have been proved in the last 100 years using the axiom of choice. Each consequence, also referred to as a form of the axiom of choice, is assigned a number. Part I is a listing of the forms by number. In this part each form is given together with a listing of all statements known to be equivalent to it (equivalent in set theory without the axiom of choice). In Part II the forms are arranged by topic. In Part III we describe the models of set theory which are used to show non-implications between forms. Part IV, the notes section, contains definitions, summaries of important sub-areas and proofs that are not readily available elsewhere. Part V gives references for the relationships between forms and Part VI is the bibliography. Part VII is contained on the floppy disk which is enclosed in the book. It contains a table with form numbers as row and column headings. The entry in the table in row $n$, column $k$ gives the status of the implication ``form $n$ implies form $k$''. Software for easily extracting information from the table is also provided. Features: complete summary of all the work done in the last 100 years on statements that are weaker than the axiom of choice software provided gives complete, convenient access to information about relationships between the various consequences of the axiom of choice and about the models of set theory descriptions of more than 100 models used in the study of the axiom of choice an extensive bibliography About the software: Tables 1 and 2 are accessible on the PC-compatible software included with the book. In addition, the program maketex.c in the software package will create TeX files containing copies of Table 1 and Table 2 which may then be printed. (Tables 1 and 2 are also available at the authors' Web sites: http://www.math.purdue.edu/$\sim$jer/ or http://www.emunix.emich.edu/$\sim$phoward/.) Detailed instructions for setting up and using the software are included in the book's Introduction, and technical support is available directly from the authors.
Book Synopsis Transcending Tradition: Jewish Mathematicians in German Speaking Academic Culture by : Birgit Bergmann
Download or read book Transcending Tradition: Jewish Mathematicians in German Speaking Academic Culture written by Birgit Bergmann and published by Springer Science & Business Media. This book was released on 2012-10-22 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: A companion publication to the international exhibition "Transcending Tradition: Jewish Mathematicians in German-Speaking Academic Culture", the catalogue explores the working lives and activities of Jewish mathematicians in German-speaking countries during the period between the legal and political emancipation of the Jews in the 19th century and their persecution in Nazi Germany. It highlights the important role Jewish mathematicians played in all areas of mathematical culture during the Wilhelmine Empire and the Weimar Republic, and recalls their emigration, flight or death after 1933.
Book Synopsis Geometric Integration Theory by : Steven G. Krantz
Download or read book Geometric Integration Theory written by Steven G. Krantz and published by Springer Science & Business Media. This book was released on 2008-12-15 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook introduces geometric measure theory through the notion of currents. Currents, continuous linear functionals on spaces of differential forms, are a natural language in which to formulate types of extremal problems arising in geometry, and can be used to study generalized versions of the Plateau problem and related questions in geometric analysis. Motivating key ideas with examples and figures, this book is a comprehensive introduction ideal for both self-study and for use in the classroom. The exposition demands minimal background, is self-contained and accessible, and thus is ideal for both graduate students and researchers.
Book Synopsis Fundamentals of Functions and Measure Theory by : Valeriy K. Zakharov
Download or read book Fundamentals of Functions and Measure Theory written by Valeriy K. Zakharov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-02-05 with total page 597 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive two-volume work is devoted to the most general beginnings of mathematics. It goes back to Hausdorff’s classic Set Theory (2nd ed., 1927), where set theory and the theory of functions were expounded as the fundamental parts of mathematics in such a way that there was no need for references to other sources. Along the lines of Hausdorff’s initial work (1st ed., 1914), measure and integration theory is also included here as the third fundamental part of contemporary mathematics. The material about sets and numbers is placed in Volume 1 and the material about functions and measures is placed in Volume 2. Contents Historical foreword on the centenary after Felix Hausdorff’s classic Set Theory Fundamentals of the theory of functions Fundamentals of the measure theory Historical notes on the Riesz – Radon – Frechet problem of characterization of Radon integrals as linear functionals
Book Synopsis Mathematics without Apologies by : Michael Harris
Download or read book Mathematics without Apologies written by Michael Harris and published by Princeton University Press. This book was released on 2017-05-30 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: An insightful reflection on the mathematical soul What do pure mathematicians do, and why do they do it? Looking beyond the conventional answers—for the sake of truth, beauty, and practical applications—this book offers an eclectic panorama of the lives and values and hopes and fears of mathematicians in the twenty-first century, assembling material from a startlingly diverse assortment of scholarly, journalistic, and pop culture sources. Drawing on his personal experiences and obsessions as well as the thoughts and opinions of mathematicians from Archimedes and Omar Khayyám to such contemporary giants as Alexander Grothendieck and Robert Langlands, Michael Harris reveals the charisma and romance of mathematics as well as its darker side. In this portrait of mathematics as a community united around a set of common intellectual, ethical, and existential challenges, he touches on a wide variety of questions, such as: Are mathematicians to blame for the 2008 financial crisis? How can we talk about the ideas we were born too soon to understand? And how should you react if you are asked to explain number theory at a dinner party? Disarmingly candid, relentlessly intelligent, and richly entertaining, Mathematics without Apologies takes readers on an unapologetic guided tour of the mathematical life, from the philosophy and sociology of mathematics to its reflections in film and popular music, with detours through the mathematical and mystical traditions of Russia, India, medieval Islam, the Bronx, and beyond.
Book Synopsis Model and Mathematics: From the 19th to the 21st Century by : Michael Friedman
Download or read book Model and Mathematics: From the 19th to the 21st Century written by Michael Friedman and published by Springer Nature. This book was released on 2022-08-08 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book collects the historical and medial perspectives of a systematic and epistemological analysis of the complicated, multifaceted relationship between model and mathematics, ranging from, for example, the physical mathematical models of the 19th century to the simulation and digital modelling of the 21st century. The aim of this anthology is to showcase the status of the mathematical model between abstraction and realization, presentation and representation, what is modeled and what models. This book is open access under a CC BY 4.0 license.
Book Synopsis Driven to Innovate by : Ioan Mackenzie James
Download or read book Driven to Innovate written by Ioan Mackenzie James and published by Peter Lang. This book was released on 2009 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ioan James celebrates the extraordinary contribution made by Jewish people in mathematics and physics, from the mathematician Norbert Wiener, the founder of cybernetics, to distinguished nuclear physicist and Nobel Prize-winner Niels Bohr. He tells the life-stories of thirty-five men and women, born in the nineteenth century, who were at the forefront of research in the closely related fields of mathematics and physics, often in the face of various kinds of anti-Semitism. Some were caught up in the trauma of the Nazi accession to power in Germany and the Second World War. Wolfgang Pauli, described as 'greater than Einstein' by his contemporary Max Born, became a German national following the Nazi annexation of Austria in 1938 but was able to escape to the United States for the duration of the war. Already hampered by anti-Semitism in his native Poland, logician and mathematician Alfred Tarski found himself stranded in the USA at the outbreak of war and did not see his wife and sons until the war's end. The Italian mathematician Vito Volterra publicly opposed Mussolini's Fascist regime at considerable personal risk. Others such as George Pólya and Emmy Noether found that their left-wing political beliefs hindered their careers.
Book Synopsis Geometry of Sets and Measures in Euclidean Spaces by : Pertti Mattila
Download or read book Geometry of Sets and Measures in Euclidean Spaces written by Pertti Mattila and published by Cambridge University Press. This book was released on 1999-02-25 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies the geometric properties of general sets and measures in euclidean space.
Book Synopsis Labyrinth of Thought by : Jose Ferreiros
Download or read book Labyrinth of Thought written by Jose Ferreiros and published by Springer Science & Business Media. This book was released on 2001-11-01 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: "José Ferreirós has written a magisterial account of the history of set theory which is panoramic, balanced, and engaging. Not only does this book synthesize much previous work and provide fresh insights and points of view, but it also features a major innovation, a full-fledged treatment of the emergence of the set-theoretic approach in mathematics from the early nineteenth century. This takes up Part One of the book. Part Two analyzes the crucial developments in the last quarter of the nineteenth century, above all the work of Cantor, but also Dedekind and the interaction between the two. Lastly, Part Three details the development of set theory up to 1950, taking account of foundational questions and the emergence of the modern axiomatization." (Bulletin of Symbolic Logic)
Book Synopsis The Multidimensionality of Hermeneutic Phenomenology by : Babette Babich
Download or read book The Multidimensionality of Hermeneutic Phenomenology written by Babette Babich and published by Springer Science & Business Media. This book was released on 2014-01-15 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers new reflections on the life world, from both phenomenological and hermeneutic perspectives. It presents a prism for a new philosophy of science and technology, especially including the social sciences but also the environment as well as questions of ethics and philosophical aesthetics in addition to exploring the themes of theology and religion. Inspired by the many contributions made by the philosopher Joseph Kockelmans, this book examines the past, present and future prospects of hermeneutic phenomenology. It raises key questions of truth and method as well as highlights both continental and analytic traditions of philosophy. Contributors to The Multidimensionality of Hermeneutic Phenomenology include leading scholars in the field as well as new voices representing analytic philosophers of science, hermeneutic and phenomenological philosophers of science, scholars of comparative literature, theorists of environmental studies, specialists in phenomenological ethics and experts in classical hermeneutics.
