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Author: Ekkehard Kopp Publisher: Open Book Publishers ISBN: 1800640978 Category : Mathematics Languages : en Pages : 280
Book Description
Making up Numbers: A History of Invention in Mathematics offers a detailed but accessible account of a wide range of mathematical ideas. Starting with elementary concepts, it leads the reader towards aspects of current mathematical research. The book explains how conceptual hurdles in the development of numbers and number systems were overcome in the course of history, from Babylon to Classical Greece, from the Middle Ages to the Renaissance, and so to the nineteenth and twentieth centuries. The narrative moves from the Pythagorean insistence on positive multiples to the gradual acceptance of negative numbers, irrationals and complex numbers as essential tools in quantitative analysis. Within this chronological framework, chapters are organised thematically, covering a variety of topics and contexts: writing and solving equations, geometric construction, coordinates and complex numbers, perceptions of ‘infinity’ and its permissible uses in mathematics, number systems, and evolving views of the role of axioms. Through this approach, the author demonstrates that changes in our understanding of numbers have often relied on the breaking of long-held conventions to make way for new inventions at once providing greater clarity and widening mathematical horizons. Viewed from this historical perspective, mathematical abstraction emerges as neither mysterious nor immutable, but as a contingent, developing human activity. Making up Numbers will be of great interest to undergraduate and A-level students of mathematics, as well as secondary school teachers of the subject. In virtue of its detailed treatment of mathematical ideas, it will be of value to anyone seeking to learn more about the development of the subject.
Author: Ekkehard Kopp Publisher: Open Book Publishers ISBN: 1800640978 Category : Mathematics Languages : en Pages : 280
Book Description
Making up Numbers: A History of Invention in Mathematics offers a detailed but accessible account of a wide range of mathematical ideas. Starting with elementary concepts, it leads the reader towards aspects of current mathematical research. The book explains how conceptual hurdles in the development of numbers and number systems were overcome in the course of history, from Babylon to Classical Greece, from the Middle Ages to the Renaissance, and so to the nineteenth and twentieth centuries. The narrative moves from the Pythagorean insistence on positive multiples to the gradual acceptance of negative numbers, irrationals and complex numbers as essential tools in quantitative analysis. Within this chronological framework, chapters are organised thematically, covering a variety of topics and contexts: writing and solving equations, geometric construction, coordinates and complex numbers, perceptions of ‘infinity’ and its permissible uses in mathematics, number systems, and evolving views of the role of axioms. Through this approach, the author demonstrates that changes in our understanding of numbers have often relied on the breaking of long-held conventions to make way for new inventions at once providing greater clarity and widening mathematical horizons. Viewed from this historical perspective, mathematical abstraction emerges as neither mysterious nor immutable, but as a contingent, developing human activity. Making up Numbers will be of great interest to undergraduate and A-level students of mathematics, as well as secondary school teachers of the subject. In virtue of its detailed treatment of mathematical ideas, it will be of value to anyone seeking to learn more about the development of the subject.
Author: Stewart Shapiro Publisher: Oxford University Press, USA ISBN: 0198809646 Category : Mathematics Languages : en Pages : 593
Book Description
Mathematical and philosophical thought about continuity has changed considerably over the ages, from Aristotle's insistence that a continuum is a unified whole, to the dominant account today, that a continuum is composed of infinitely many points. This book explores the key ideas and debates concerning continuity over more than 2500 years.
Author: Shair Ahmad Publisher: Springer ISBN: 3319164082 Category : Mathematics Languages : en Pages : 337
Book Description
This book offers readers a primer on the theory and applications of Ordinary Differential Equations. The style used is simple, yet thorough and rigorous. Each chapter ends with a broad set of exercises that range from the routine to the more challenging and thought-provoking. Solutions to selected exercises can be found at the end of the book. The book contains many interesting examples on topics such as electric circuits, the pendulum equation, the logistic equation, the Lotka-Volterra system, the Laplace Transform, etc., which introduce students to a number of interesting aspects of the theory and applications. The work is mainly intended for students of Mathematics, Physics, Engineering, Computer Science and other areas of the natural and social sciences that use ordinary differential equations, and who have a firm grasp of Calculus and a minimal understanding of the basic concepts used in Linear Algebra. It also studies a few more advanced topics, such as Stability Theory and Boundary Value Problems, which may be suitable for more advanced undergraduate or first-year graduate students. The second edition has been revised to correct minor errata, and features a number of carefully selected new exercises, together with more detailed explanations of some of the topics. A complete Solutions Manual, containing solutions to all the exercises published in the book, is available. Instructors who wish to adopt the book may request the manual by writing directly to one of the authors.
Author: Jan Surman Publisher: Purdue University Press ISBN: 1612495621 Category : History Languages : en Pages : 473
Book Description
Combining history of science and a history of universities with the new imperial history, Universities in Imperial Austria 1848–1918: A Social History of a Multilingual Space by Jan Surman analyzes the practice of scholarly migration and its lasting influence on the intellectual output in the Austrian part of the Habsburg Empire. The Habsburg Empire and its successor states were home to developments that shaped Central Europe's scholarship well into the twentieth century. Universities became centers of both state- and nation-building, as well as of confessional resistance, placing scholars if not in conflict, then certainly at odds with the neutral international orientation of academe. By going beyond national narratives, Surman reveals the Empire as a state with institutions divided by language but united by legislation, practices, and other influences. Such an approach allows readers a better view to how scholars turned gradually away from state-centric discourse to form distinct language communities after 1867; these influences affected scholarship, and by examining the scholarly record, Surman tracks the turn. Drawing on archives in Austria, the Czech Republic, Poland, and Ukraine, Surman analyzes the careers of several thousand scholars from the faculties of philosophy and medicine of a number of Habsburg universities, thus covering various moments in the history of the Empire for the widest view. Universities in Imperial Austria 1848–1918 focuses on the tension between the political and linguistic spaces scholars occupied and shows that this tension did not lead to a gradual dissolution of the monarchy’s academia, but rather to an ongoing development of new strategies to cope with the cultural and linguistic multitude.
Author: Detlef Laugwitz Publisher: Springer Science & Business Media ISBN: 0817647775 Category : Mathematics Languages : en Pages : 372
Book Description
The name of Bernard Riemann is well known to mathematicians and physicists around the world. His name is indelibly stamped on the literature of mathematics and physics. This remarkable work, rich in insight and scholarship, is addressed to mathematicians, physicists, and philosophers interested in mathematics. It seeks to draw those readers closer to the underlying ideas of Riemann’s work and to the development of them in their historical context. This illuminating English-language version of the original German edition will be an important contribution to the literature of the history of mathematics.
Author: Gillian Rose Publisher: A&C Black ISBN: 1441122060 Category : Philosophy Languages : en Pages : 270
Book Description
This original and challenging book presents a radical revision of traditional assessments of Hegel. Gillian Rose argues that the classical origins of contemporary non-Marxist and Marxist sociology rest on the 'neo-Kantian' paradigm and that Hegel's thought anticipates and criticises the limitations of this paradigm and the problems of methodologism and moralism in sociological method. Hegel's major mature works are expounded in the light of his early radical writings. From this unusual perspective Dr Rose shows that Hegel's speculative discourse is a powerful critique of bourgeois property relations and law, or art and religion as misrepresentation and of the inversions and end of culture. The book concludes with a discussion of the end of philosophy, the repetition of sociology and the culture and fate of Marxism.
Author: Carl Friedrich Gauss Publisher: Springer ISBN: 1493975609 Category : Mathematics Languages : en Pages : 491
Book Description
Carl Friedrich Gauss’s textbook, Disquisitiones arithmeticae, published in 1801 (Latin), remains to this day a true masterpiece of mathematical examination. .
Author: Catherine Goldstein Publisher: Springer Science & Business Media ISBN: 3540347208 Category : Mathematics Languages : en Pages : 579
Book Description
Since its publication, C.F. Gauss's Disquisitiones Arithmeticae (1801) has acquired an almost mythical reputation, standing as an ideal of exposition in notation, problems and methods; as a model of organisation and theory building; and as a source of mathematical inspiration. Eighteen authors - mathematicians, historians, philosophers - have collaborated in this volume to assess the impact of the Disquisitiones, in the two centuries since its publication.
Author: Robert Edouard Moritz Publisher: Theclassics.Us ISBN: 9781230267388 Category : Languages : en Pages : 140
Book Description
This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1914 edition. Excerpt: ...identical, is as much at home in the art of reasoning as anywhere else: and this is why no science, whether biology or any other, can offer any kind of reasoning, of which mathematics does not supply a simpler and purer counterpart. Thus, we are enabled to eliminate the only remaining portion of the old philosophy which could even appear to offer any real utility; the logical part, the value of which is irrevocably absorbed by mathematical science.--Comte, A. Positive Philosophy, Martineau, (London, 1875), Vol. 1, pp. 321-322. 1316. We know that mathematicians care no more for logic than logicians for mathematics. The two eyes of exact science are mathematics and logic: the mathematical sect puts out the logical eye, the logical sect puts out the mathematical eye; each believing that it can see better with one eye than with two. De Morgan, A. Quoted in F. Cajori: History of Mathematics (New York, 1897), p. 316. 1316. The progress of the art of rational discovery depends in a great part upon the art of characteristic (ars characteristica). The reason why people usually seek demonstrations only in numbers and lines and things represented by these is none other than that there are not, outside of numbers, convenient characters corresponding to the notions.--Leibnitz, G. W. Philosophische Schriften Gerhardt Bd. 8, p. 198. 1317. The influence of the mathematics of Leibnitz upon his philosophy appears chiefly in connection with his law of continuity and his prolonged efforts to establish a Logical Calculus.... To find a Logical Calculus (implying a universal philosophical language or system of signs) is an attempt to apply in theological and philosophical investigations an analytic method analogous to that which had proved so successful in...
Author: Ekkehard Kopp
Author: Ekkehard Kopp
Author: Stewart Shapiro
Author: Shair Ahmad
Author: Bernard Bolzano
Author: Jan Surman
Author: Detlef Laugwitz
Author: Gillian Rose
Author: Carl Friedrich Gauss
Author: Catherine Goldstein
Author: Robert Edouard Moritz