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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

"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.

A Guide

The Deflationary Approach to Truth

Engineers, designers, applied mathematicians, physicists, and historians of science can now directly access James Clerk Maxwell's seminal ideas in structural mechanics. Annotations of his texts combined with summaries of the latest research show how this often-overlooked aspect of Maxwell's work has immediate relevance for 21st-century design.

James Clerk Maxwell and 21st-Century Structural Mechanics

The Geometry of Equilibrium

Elements in the Philosophy of Mathematics

This Element provides a framework for studying mathematical notations, aimed at researchers and students in philosophy, history, cognitive science, and mathematics education. It discusses the characteristics of mathematical notations, their language, cognitive resources, tasks, material basis, and historical context.

Mathematical Notations

Huge Numbers

"This Element introduces a young field, the 'philosophy of mathematical practice'. We first offer a general characterisation of the approach to the philosophy of mathematics that takes mathematical practice seriously and contrast it with 'mathematical philosophy'. The latter is traced back to Bertrand Russell and the orientation referred to as 'scientific philosophy' that was active between 1850 and 1930. To give a better sense of the field, the Element further contains two examples of topics studied, that of mathematical structuralism and visual thinking in mathematics. These are in part presented from a methodological point of view, focussing on mathematics as an activity and questions related to how mathematics develops. In addition, the Element contains several examples from mathematics, both historical and contemporary, to illustrate and support the philosophical points"--

Introducing the Philosophy of Mathematical Practice

A proof of a theorem can be said to be pure if it draws only on what is 'close' or 'intrinsic' to that theorem. In this Element we will investigate the apparent preference for pure proofs that has persisted in mathematics since antiquity, alongside a competing preference for impurity. In Section 1, we present two examples of purity, from geometry and number theory. In Section 2, we give a brief history of purity in mathematics. In Section 3, we discuss several different types of purity, based on different measures of distance between theorem and proof. In Section 4 we discuss reasons for preferring pure proofs, for the varieties of purity constraints presented in Section 3. In Section 5 we conclude by reflecting briefly on purity as a preference for the local and how issues of translation intersect with the considerations we have raised throughout this work.

Elements of Purity

Series on Advances in Mathematics for Applied Sciences

This is the first book on the problems of mathematical modelling that combines a generalised approach to the problem of mathematical modelling processes and phenomena in the real world with developing modelling methods in relation to specific objects and processes. Some of the problems discussed here include the stability and bifurcation of simplified models of supply and demand, and resultants of various approaches, such as standardisation, unification, partial ordering and data packaging.As well as touching upon the general principles of modelling, the book studies the stability of mathematical models using the generalised direct Lyapunov method based on matrix-valued auxiliary functions. It has significant potential for application in the design of new moving objects (nano-robots, manipulators, drones, etc.) and processes related to artificial intelligence (multidimensional interaction of related data arrays) that can be described by differential equations of different types.Written by two respected specialists in the field of the qualitative theory of equations and problems of modelling real-world phenomena, this book is primarily targeted at specialists in the field of engineering sciences, but is also suitable for graduate courses.

Mathematical Modelling: Selected Objects And Processes

A TLS BOOK OF THE YEAR 'Anaximander is a delight and so is this book' -- James McConnachie, Sunday Times Now widely available in English for the first time, this is Carlo Rovelli's first book: the thrilling story of a little-known man who created one of the greatest intellectual revolutions Over two thousand years ago, one man changed the way we see the world. Since the dawn of civilization, humans had believed in the heavens above and the Earth below. Then, on the Ionian coast, a Greek philosopher named Anaximander set in motion a revolution. He not only conceived that the Earth floats in space, but also that animals evolve, that storms and earthquakes are natural, not supernatural, that the world can be mapped and, above all, that progress is made by the endless search for knowledge. Carlo Rovelli's first book, now widely available in English, tells the origin story of scientific thinking: our rebellious ability to reimagine the world, again and again. Translated by Marion Lignana Rosenberg

And the Nature of Science

Anaximander

AK Peters/CRC Recreational Mathematics Series

Overlooked and Omitted Topics in Mathematics

I Wish They'd Taught Me That

A Mathematical Tour introduces readers to a selection of mathematical topics chosen for their centrality, importance, historical significance, and intrinsic appeal and beauty.

A Mathematical Tour

Princeton Mathematical Series

Princeton Legacy Library

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

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

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