Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Constantin Carathéodory - Mathematics and Politics in Turbulent Times is the biography of a mathematician, born in Berlin in 1873, who became famous during his life time, but has hitherto been ignored by historians for half a century since his death in 1950, in Munich. In a thought-provoking approach, Maria Georgiadou devotes to Constantin Carathéodory all the attention such a personality deserves. With breathtaking detail and the appropriate scrutiny she elucidates his oeuvre, life and turbulent political and historical surroundings. A descendant of the the Greek élite of Constantinople, Carathéodory graduated from the military school of Brussels, became engineer at the Assiout dam in Egypt and finally dedicated a life of effort to mathematics and education. He studied and embarked on an international academic career, haunted by wars, catastrophes and personal tragedies. Over the last years of his life, he stayed in Munich despite World War II, an ambiguous decision upon which the author sheds unprecedented light. Carathéodory's most significant mathematical contributions were to the calculus of variations, the theory of point set measure and the theory of functions of a real variable, pde's, also to complex function theory. The interdisciplinary nature of the text allows easy access for both scholars and readers with a general interest in mathematics, politics and history. The thoroughness of the author’s research and evaluations is certain to leave everyone impressed and more knowledgeable. .

Carathéodory, Constantin --- Mathematicians --- Caratheodory, Constantin, --- Mathematics. --- History. --- History of Mathematical Sciences. --- Annals --- Auxiliary sciences of history --- Math --- Science --- Mathematicians - Greece - Biography --- Caratheodory, Constantin, - 1873-1950

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book presents first-year calculus roughly in the order in which it first was discovered. The first two chapters show how the ancient calculations of practical problems led to infinite series, differential and integral calculus and to differential equations. The establishment of mathematical rigour for these subjects in the 19th century for one and several variables is treated in chapters III and IV. The text is complemented by a large number of examples, calculations and mathematical pictures and will provide stimulating and enjoyable reading for students, teachers, as well as researchers. From the reviews: The aim of this interesting new contribution to the series Readings in Mathematics is an attempt to restore the historical order in the presentation of basic mathematical analysis...such a historical approach can provide a very fruitful and interesting approach to mathematical analysis. - Jean Mawhin, Zentralblatt The authors include a large number of once-traditional subjects which have now vanished from the analysis curriculum, at least in the standard American courses. Thus we find continued fractions, elliptic integrals, the Euler-MacLaurin summation formula, etc., most of which are found only in more compendious works. Many of the exercises are inspired by original papers, with the bibliographic references sometimes given. The work is very well illustrated. The book is definitely an analysis text, rather than a history, but a great deal of reliable historical material is included. For those seeking an alternative to the traditional approach, it seems to me to be of great interest. - Thomas Archibald, Mathematical Reviews The authors...have assembled an impressive array of annotated results, quotations, tables, charts, figures and drawings, many copied from original documents....they write with great enthusiasm and with evident affection for both analysis and history. - John Troutman, American Mathematical Monthly.

Mathematics. --- Functions of real variables. --- History. --- Real Functions. --- History of Mathematical Sciences. --- Mathematical analysis. --- 517.1 Mathematical analysis --- Mathematical analysis --- Math --- Science --- Didactics of mathematics --- Annals --- Auxiliary sciences of history --- Real variables --- Functions of complex variables

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Most Honourable Remembrance provides an in-depth discussion of the life and work of Thomas Bayes, an eighteenth-century Presbyterian minister and lay mathematician who planted the seed of modern Bayesian Statistics in 1763 with his posthumous, An Essay Towards Solving a Problem in the Doctrine of Chances. After biographical details of Bayes' ancestors, consideration is turned to what is known of Thomas Bayes, the time in which he lived, and also the town in which he spent the major part of his professional life, Tunbridge Wells. Bayes' published works, ranging from a theological tract to one on fluxions, are reprinted in full and commented upon. Unpublished works, with commentary, are also included, special attention being given to a manuscript notebook in which some early work on a result from the above mentioned Essay may be found. The book concludes with a chapter on Bunhill Fields Burial Ground, where the Bayes family vault is still to be seen and where many prominent Nonconformists were interred. This book is the first to provide a biography and full discussion of Bayes' works and will be of interest to modern Bayesian statisticians as well as to mathematicians who may well be surprised at some of the mathematical insights shown by Bayes and which are not generally known to be attributable to him.

Statisticians --- Bayes, Thomas, --- Bayes, Thomas --- Statisticiens --- Biography --- Biographie --- EPUB-LIV-FT SPRINGER-B --- Mathematics. --- History. --- Statistics. --- History of Mathematical Sciences. --- Statistical Theory and Methods. --- Mathematical statistics. --- Biography. --- Statistics . --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Annals --- Auxiliary sciences of history --- Math --- Science

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The book offers a collection of essays on various aspects of Leibniz's scientific thought, written by historians of science and world-leading experts on Leibniz. The essays deal with a vast array of topics on the exact sciences: Leibniz's logic, mereology, the notion of infinity and cardinality, the foundations of geometry, the theory of curves and differential geometry, and finally dynamics and general epistemology. Several chapters attempt a reading of Leibniz's scientific works through modern mathematical tools, and compare Leibniz's results in these fields with 19th- and 20th-Century conceptions of them. All of them have special care in framing Leibniz's work in historical context, and sometimes offer wider historical perspectives that go much beyond Leibniz's researches. A special emphasis is given to effective mathematical practice rather than purely epistemological thought. The book is addressed to all scholars of the exact sciences who have an interest in historical research and Leibniz in particular, and may be useful to historians of mathematics, physics, and epistemology, mathematicians with historical interests, and philosophers of science at large.

Philosophy of science --- Leibniz, von, Gottfried W. --- Philosophy and science --- Philosophy, Modern --- Mathematics --- History --- Logic, symbolic and mathematical --- Physics --- Philosophy and science. --- Modern philosophy. --- Mathematics. --- History. --- Mathematical logic. --- Physics. --- Philosophy of Science. --- Modern Philosophy. --- History of Mathematical Sciences. --- Mathematical Logic and Foundations. --- History and Philosophical Foundations of Physics.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

In his first book, Philosophy of Arithmetic, Edmund Husserl provides a carefully worked out account of number as a categorial or formal feature of the objective world, and of arithmetic as a symbolic technique for mastering the infinite field of numbers for knowledge. It is a realist account of numbers and number relations that interweaves them into the basic structure of the universe and into our knowledge of reality. It provides an answer to the question of how arithmetic applies to reality, and gives an account of how, in general, formalized systems of symbols work in providing access to the world. The "appendices" to this book provide some of Husserl's subsequent discussions of how formalisms work, involving David Hilbert's program of completeness for arithmetic. "Completeness" is integrated into Husserl's own problematic of the "imaginary", and allows him to move beyond the analysis of "representations" in his understanding of the logic of mathematics.Husserl's work here provides an alternative model of what "conceptual analysis" should be - minus the "linguistic turn", but inclusive of language and linguistic meaning. In the process, he provides case after case of "Phenomenological Analysis" - fortunately unencumbered by that title - of the convincing type that made Husserl's life and thought a fountainhead of much of the most important philosophical work of the twentieth Century in Europe. Many Husserlian themes to be developed at length in later writings first emerge here: Abstraction, internal time consciousness, polythetic acts, acts of higher order ('founded' acts), Gestalt qualities and their role in knowledge, formalization (as opposed to generalization), essence analysis, and so forth.This volume is a window on a period of rich and illuminating philosophical activity that has been rendered generally inaccessible by the supposed "revolution" attributed to "Analytic Philosophy" so-called. Careful exposition and critique is given to every serious alternative account of number and number relations available at the time. Husserl's extensive and trenchant criticisms of Gottlob Frege's theory of number and arithmetic reach far beyond those most commonly referred to in the literature on their views.

Mathematical logic --- Arithmetic. --- Mathematics --- Number concept. --- Philosophy. --- Mathematics. --- Modern philosophy. --- Phenomenology. --- History. --- Number theory. --- Number Theory. --- History of Mathematical Sciences. --- Modern Philosophy. --- Arithmetic --- Arithmétique --- Concept du nombre --- Getal (Begrip) --- Getal (Concept) --- Getalbegrip --- Getalconcept --- Nombre (Concept) --- Number concept --- Rekenkunde --- Apperception --- Psychology --- Logic of mathematics --- Mathematics, Logic of --- Set theory --- Calculators --- Numbers, Real --- Philosophy --- Phenomenology . --- Modern philosophy --- Annals --- Auxiliary sciences of history --- Math --- Science --- Philosophy, Modern --- Number study --- Numbers, Theory of --- Algebra --- Mathematics - Philosophy.