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Elwes R: The Story of Huge Numbers

The Story of Huge Numbers

Elements in the Philosophy of Mathematics

The aim of this Element is to provide an overview of abstractionism in the philosophy of mathematics. It distinguishes between mathematical abstractionism and philosophical abstractionism. It also discusses the most recent developments in the debate that pull abstractionism in different directions.

Abstractionism

"Galileo famously wrote that the book of nature is written in mathematical language. The Language of Mathematics is a wide-ranging and beautifully illustrated collection of short, colorful histories of the most commonly used symbols in mathematics, providing readers with an engaging introduction to the origins, evolution, and conceptual meaning of each one. In dozens of lively and informative entries, Raâul Rojas shows how today's mathematics stands on the shoulders of giants, mathematicians from around the world who developed mathematical notation through centuries of collective effort. He tells the stories of such figures as al-Khwarizmi, Renâe Descartes, Joseph-Louis Lagrange, Carl Friedrich Gauss, Augustin-Louis Cauchy, Karl Weierstrass, Sofia Kovalevskaya, David Hilbert, and Kenneth Iverson. Topics range from numbers and variables to sets and functions, constants, and combinatorics. Rojas describes the mathematical problems associated with different symbols and reveals how mathematical notation has sometimes been an accidental process. The entries are self-contained and can be read in any order, each one examining one or two symbols, their history, and the variants they may have had over time. An essential companion for math enthusiasts, The Language of Mathematics shows how mathematics is a living and evolving entity, forever searching for the best symbolism to express relationships between abstract concepts and to convey meaning"--

The Stories behind the Symbols

The Language of Mathematics

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

A Mathematical Tour

Can one prove that 1 + 1 = 2? Which US president proved Pythagoras' theorem? How long is the coastline of Britain? These and many other questions are answered in this book on famous equations and their historical development. The equations come from a range of mathematical disciplines, and cover 4,000 years from early counting to fractal geometry.

Can one prove that 1 + 1 = 2? Which US president proved Pythagoras' theorem? How long is the coastline of Britain? These and many other questions are answered in this book on famous equations and their historical development. The equations come from a range of mathematical disciplines, and cover 4,000 years from early counting to fractal geometry.

Equations and Their Origins

Sum Stories

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.

This Element explores the preference for pure proofs in mathematics since antiquity, focusing on geometry and number theory. It discusses different types of purity, reasons for preferring pure proofs, and the importance of local purity. It also touches on translation issues and the relationship between purity and local considerations.

Elements of Purity

AK Peters/CRC Recreational Mathematics Series

A Greatly-Expanded, Much-Abridged Edition of The Symmetries of Things

The Magic Theorem

This book introduces students and researchers to the philosophical issues at play in the growing field of Bayesian epistemology. It focuses not on how to do particular calculations but instead on the philosophical foundations at the convergence of belief and mathematical representation. Its central questions are: What is the nature of quantifying belief? What is the source of its norms? How is it reasonable to represent belief numerically? Accessible to those without any mathematical background, this book will become a much used classic in the field.

This book introduces students and researchers to the philosophical issues at play in the growing field of formal (or Bayesian) epistemology. It focuses not on how to do particular calculations but instead on the philosophical foundations at the convergence of belief and mathematical representation. Its central questions are: What is the nature of quantifying belief? What is the source of its norms? How is it reasonable to represent belief numerically? Accessible to those without any mathematical background, this book will become a much used classic in the field.

A Philosophical Introduction

The Foundations of Bayesian Epistemology

This second edition continues to present meaningful and practical solutions for teaching mathematics and statistics online, focusing on the problems observed by mathematics instructors currently working in the field. With its set of standard practices, instructors will benefit from learning many new techniques and approaches.

This second edition continues to present meaningful and practical solutions for teaching mathematics and statistics online, focusing on the problems observed by mathematics instructors currently working in the field. With its set of standard practices, instructors will benefit from learning many new techniques and approaches.

Teaching and Learning Mathematics Online

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.

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

This book examines positions that challenge the Fregean logic-first view. It will be a resource for academics, researchers, and advanced students of philosophy, linguistics, mathematics, and computer science.

Critical Views of Logic

Routledge Studies in the History of Economics

John Maynard Keynes is best known for his contributions to economics, yet he spent nearly two decades exploring the concept of probability. His extensive work culminated in the Treatise on Probability (1921), where he developed a unique notion of probability that continues to divide scholars regarding its relevance to economic theory.

John Maynard Keynes is best known for his contributions to economics, yet he spent nearly two decades exploring the concept of probability. His extensive work culminated in the Treatise on Probability (1921), where he developed a unique notion of probability that continues to divide scholars regarding its relevance to economic theory.

The Influence of Locke, Leibniz, and Hume

J.M. Keynes and the History of Probability

The Story of Huge Numbers

Bibliografische Angaben

Schlagworte

Bibliografische Angaben

Schlagworte

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