Making up Numbers: A History of Invention in Mathematics

Making up Numbers: A History of Invention in Mathematics
Author: Ekkehard Kopp
Publisher: Open Book Publishers
Total Pages: 280
Release: 2020-10-23
Genre: Mathematics
ISBN: 1800640978

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.

A Textbook on Ordinary Differential Equations

A Textbook on Ordinary Differential Equations
Author: Shair Ahmad
Publisher: Springer
Total Pages: 337
Release: 2015-06-05
Genre: Mathematics
ISBN: 3319164082

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.

Bernhard Riemann 1826–1866

Bernhard Riemann 1826–1866
Author: Detlef Laugwitz
Publisher: Springer Science & Business Media
Total Pages: 372
Release: 2009-06-08
Genre: Mathematics
ISBN: 0817647775

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.

Universities in Imperial Austria 1848–1918

Universities in Imperial Austria 1848–1918
Author: Jan Surman
Publisher: Purdue University Press
Total Pages: 473
Release: 2018-12-15
Genre: History
ISBN: 1612495621

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.

Hegel: Contra Sociology

Hegel: Contra Sociology
Author: Gillian Rose
Publisher: A&C Black
Total Pages: 270
Release: 2000-12-01
Genre: Philosophy
ISBN: 1441122060

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.

Disquisitiones Arithmeticae

Disquisitiones Arithmeticae
Author: Carl Friedrich Gauss
Publisher: Springer
Total Pages: 491
Release: 2018-02-07
Genre: Mathematics
ISBN: 1493975609

Carl Friedrich Gauss’s textbook, Disquisitiones arithmeticae, published in 1801 (Latin), remains to this day a true masterpiece of mathematical examination. .

Topological (in) Hegel

Topological (in) Hegel
Author: Borislav G. Dimitrov
Publisher: Borislav Dimitrov
Total Pages: 520
Release: 2018-01-23
Genre: Philosophy
ISBN: 1370071213

The aim of this book is to critically examine whether it is methodologically possible to combine mathematical rigor – topology with a systematic dialectical methodology in Hegel, and if so, to provide as result of my interpretation the outline of Hegel’s Analysis Situs, also with the proposed models (build on the topological manifold, cobordism, topological data analysis, persistent homology, simplicial complexes and graph theory, to provide an indication of how the merger of Hegel’s dialectical logic and topology may be instrumental to a systematic logician and of how a systematic dialectical logic perspective may help mathematical model builders.

The Shaping of Arithmetic after C.F. Gauss's Disquisitiones Arithmeticae

The Shaping of Arithmetic after C.F. Gauss's Disquisitiones Arithmeticae
Author: Catherine Goldstein
Publisher: Springer Science & Business Media
Total Pages: 579
Release: 2007-02-03
Genre: Mathematics
ISBN: 3540347208

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.

Paradoxes of the Infinite (Routledge Revivals)

Paradoxes of the Infinite (Routledge Revivals)
Author: Bernard Bolzano
Publisher: Routledge
Total Pages: 202
Release: 2014-03-18
Genre: Philosophy
ISBN: 1317748581

Paradoxes of the Infinite presents one of the most insightful, yet strangely unacknowledged, mathematical treatises of the 19th century: Dr Bernard Bolzano’s Paradoxien. This volume contains an adept translation of the work itself by Donald A. Steele S.J., and in addition an historical introduction, which includes a brief biography as well as an evaluation of Bolzano the mathematician, logician and physicist.