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Navigating Across Mathematical Cultures
And Times: Exploring The Diversity Of Di

Navigating Across Mathematical Cultures And Times: Exploring The Diversity Of Discoveries And Proofs

Synthese Library

This second of a two-volume book prolongs the inquiry of volume 1 by considering other examples apt to better illustrate the ideal of epistemic economy in mathematical recasting. The new examples are drawn from second-order definitions of real numbers and allow the comparison of three different approaches to the definition of these numbers: by domain extension, as ratios of magnitudes, and as bicimal developments. These definitions are presented in detail (by often going further than any available presentation) and compared with respect to their epistemic economy. In doing so, original results and insights are offered, such as a faithful and still consistent rephrasing of Frege’s definitions of reals, and an original and epistemically highly economical definition of real numbers as bicimal developments. This ensures the book is of interest to scholars and students in the philosophy of mathematics and logic.

The Real Numbers

Reals by Abstraction. An Inquiry about Epistemic Economy in Mathematics: Volume II

A Memoir

Building Things

Leibniz from Oxford

This volume gathers together the philosophical journal articles that appeared during Leibniz's lifetime, as a companion to Leibniz: Journal Articles on Natural Philosophy (OUP, 2023). The articles include seminal original works, responses to criticisms, and series of critical discussions of Descartes and Cartesian philosophy.

This volume gathers together the philosophical journal articles that appeared during Leibniz's lifetime, as a companion to Leibniz: Journal Articles on Natural Philosophy (OUP, 2023). The articles include seminal original works, responses to criticisms, and series of critical discussions of Descartes and Cartesian philosophy.

Leibniz: Journal Articles on Philosophy

SUMS Readings

Springer Undergraduate Mathematics Series

This book offers an introduction to the nature of mathematics, its history, and some of the curious individuals who have shaped it. It explores a range of fundamental ideas that can be appreciated without prior mathematical training. &nbsp; Highlighting the human side of mathematics and its shared lineage with philosophy, the book embraces the subject’s colorful history, incorporating original source material in the main text. Based on a course taught to non-science majors, it is intended for anyone with an interest in mathematics—including those whose last experience with algebra was less than enjoyable.

The Unreasonable Elegance of Mathematics

"An interdisciplinary history of trigonometry from the mid-sixteenth century through to the early twentieth century The Doctrine of Triangles offers an interdisciplinary history of trigonometry that spans four centuries, starting in 1550 and concluding in the 1900s. Glen Van Brummelen tells the story of trigonometry as it evolved from an instrument for understanding the heavens to a practical tool, used in fields such as surveying and navigation. In Europe, China, and America, trigonometry aided and was itself transformed by concurrent mathematical revolutions, as well as the rise of science and technology. Following its uses in mid-sixteenth-century Europe as the "foot of the ladder to the stars" and the mathematical helpmate of astronomy, trigonometry became a ubiquitous tool for modeling various phenomena, including animal populations and sound waves. In the late sixteenth century, trigonometry increasingly entered the physical world through the practical disciplines, and its societal reach expanded with the invention of logarithms. Calculus shifted mathematical reasoning from geometric to algebraic patterns of thought, and trigonometry's participation in this new mathematical analysis grew, encouraging such innovations as complex numbers and non-Euclidean geometry. Meanwhile in China, trigonometry was evolving rapidly too, sometimes merging with indigenous forms of knowledge, and with Western discoveries. In the nineteenth century, trigonometry became even more integral to science and industry as a fundamental part of the science and engineering toolbox, and a staple subject in high school classrooms"--

A History of Modern Trigonometry

The Doctrine of Triangles

Springer Biographies

This book is not only about the history of mathematics, but also by telling the story of some of the most distinctive personalities in the history of mathematics, it goes on to reveal the various strange treasures, bright flowers and hidden passions of the mathematical kingdom. Some of these mathematicians were thinkers, writers, poets, musicians, painters, politicians, judges, soldiers, clerks, young men of society or even prisoners. The mathematical world constructed by these geniuses is exquisite, and a walk in such a world not only expands our mathematical horizons and imagination, but also raises our humanistic cultivation to a higher level.Written for general audience, this book will be of interest to anyone who's studied mathematics in university or even high school, while also benefiting researchers in mathematics and the humanities.&nbsp;The readers will also enjoy reading the beautiful and simple language of all the articles and interviews.The author is a poet, essaist as well as a professor of mathematics.

This book is not only about the history of mathematics, but also by telling the story of some of the most distinctive personalities in the history of mathematics, it goes on to reveal the various strange treasures, bright flowers and hidden passions of the mathematical kingdom. Some of these mathematicians were thinkers, writers, poets, musicians, painters, politicians, judges, soldiers, clerks, young men of society or even prisoners. The mathematical world constructed by these geniuses is exquisite, and a walk in such a world not only expands our mathematical horizons and imagination, but also raises our humanistic cultivation to a higher level.Written for general audience, this book will be of interest to anyone who's studied mathematics in university or even high school, while also benefiting researchers in mathematics and the humanities.&nbsp;The readers will also enjoy reading the beautiful and simple language of all the articles and interviews.

From Thales to Erdős

Mathematical Legends

"Deflationary" theories are views about truth that are often, but not always, characterized as accounts that accept the utility of the truth predicate without granting the metaphysical or epistemological assumptions that usually go along with it. The Deflationary Approach to Truth: A Guide presents a detailed, up-to-date, and historically informed survey and critical explication of the deflationary approach to the topic of truth, paying special attention to the wide range of different deflationary theories.

"Deflationary" theories are views about truth that are often, but not always, characterized as accounts that accept the utility of the truth predicate without granting the metaphysical or epistemological assumptions that usually go along with it. The Deflationary Approach to Truth: A Guide presents a detailed, up-to-date, and historically informed survey and critical explication of the deflationary approach to the topic of truth, paying special attention to the wide range of various deflationary theories. 

In Part One, Bradley Armour-Garb and James A. Woodbridge explain what the deflationary approach to truth involves and develop a useful framework that clarifies how it differs from the traditional, "inflationary" approach. The framework illuminates certain general deflationary themes in terms of what Armour-Garb and Woodbridge call broad four-dimensional deflationism. This analysis reveals four different dimensions that any deflationary account must satisfy: Linguistic Deflationism, Metaphysical Deflationism, Conceptual Deflationism, and Paradox Treatment Deflationism. Armour-Garb and Woodbridge examine the degree to which these dimensions are displayed in early, "proto-deflationary" accounts before explaining the different contemporary deflationary views and assessing the degree to which these accounts adhere to the four deflationary dimensions, differ from inflationism, and differ from each other. 

In Part Two, Armour-Garb and Woodbridge examine various challenges to deflationism, systematizing them by considering each deflationary dimension and grouping the challenges in terms of which dimension they target. For each challenge, they explain its historical development and investigate the extent to which the most prominent contemporary deflationary accounts answer, or fail to answer, that challenge. In Part Three, Armour-Garb and Woodbridge explore fruitful new directions for deflationism and develop a version of the approach that they think best handles the challenges that are examined in Part Two. The result is an accessible yet comprehensive overview of the challenges to and merits of the deflationary approach to truth.

A Guide

The Deflationary Approach to Truth

Epistemic Economy and The Natural Numbers

Reals by Abstraction. An Inquiry about Epistemic Economy in Mathematics: Volume I

How We Gave Computers the Power to Choose for Us

The Irrational Decision

A Statistical Guide to Certainty in an Uncertain World

What Are the Odds?

Princeton Legacy Library

Princeton Mathematical Series

An authoritative introduction to the essential features of étale cohomology A. Grothendieck’s work on algebraic geometry is one of the most important mathematical achievements of the twentieth century. In the early 1960s, he and M. Artin introduced étale cohomology to extend the methods of sheaf-theoretic cohomology from complex varieties to more general schemes. This work found many applications, not only in algebraic geometry but also in several different branches of number theory and in the representation theory of finite and p-adic groups. In this classic book, James Milne provides an invaluable introduction to étale cohomology, covering the essential features of the theory. Milne begins with a review of the basic properties of flat and étale morphisms and the algebraic fundamental group. He then turns to the basic theory of étale sheaves and elementary étale cohomology, followed by an application of the cohomology to the study of the Brauer group. After a detailed analysis of the cohomology of curves and surfaces, Milne proves the fundamental theorems in étale cohomology—those of base change, purity, Poincaré duality, and the Lefschetz trace formula—and applies these theorems to show the rationality of some very general L-series.

Étale Cohomology

Diese etablierte Formelsammlung enthält und erklärt mathematische Formeln innerhalb ökonomischer Zusammenhänge, wie sie in den Wirtschaftswissenschaften und in der wirtschaftswissenschaftlichen Praxis unbedingt notwendig sind. Das Verständnis der Formeln und deren praktische Anwendung werden durch nützliche Hilfen und erklärliche Beispiele sinnvoll unterstützt, so dass der Kontext wirtschaftsmathematischer Formeln klar und verständlich dargestellt wird. Diese Formelsammlung ist ein unverzichtbares Tool für Studierende der Wirtschaftswissenschaften, aber auch ein nützliches Nachschlagewerk für Verantwortliche aus Wirtschaft, Politik und Lehre.Die Inhalte wurden für die 7. Auflage teilweise überarbeitet und ergänzt. Der Inhalt<ul><li>Mathematische Zeichen und Symbole</li><li>Logik</li><li>Arithmetik</li><li>Algebra</li><li>Kombinatorik</li><li>Finanzmathematik</li><li>Optimierung linearer Modelle</li><li>Funktionen</li><li>Differentialrechnung</li><li>Integralrechnung</li><li>Elastizitäten</li><li>Ökonomische Funktionen</li><li>Peren-Theorem</li></ul>Der Autor Prof. Dr. rer. pol. Franz W. Peren, Ph.D., ist Professor der Betriebswirtschaftslehre, insbesondere quantitative Methoden. Er lehrt Wirtschaftsmathematik, Wirtschaftsstatistik sowie quantitative Methoden der Planung, der Steuerung und der Kontrolle innerhalb des operativen und strategischen Managements an der Hochschule Bonn-Rhein-Sieg. Peren lehrte und forschte zudem an der University of Victoria in Kanada sowie an der Columbia University in New York, USA.

Wissen kompakt für Studierende und Praktiker

Formelsammlung Wirtschaftsmathematik

Navigating Across Mathematical Cultures And Times: Exploring The ...

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