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Maor Eli: Pentagons and Pentagrams

Pentagons and Pentagrams

An Illustrated History

Elements in the Philosophy of Mathematics

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

A melodic odyssey through the interwoven worlds of music, physics and mathematics.

Music, Mathematics and Science

A Perfect Harmony

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.

Leibniz: Journal Articles on Philosophy

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

This book covers computational group theory (CGT), an active, rapidly expanding field at the interface of mathematics and computer science. It is the first systematic effort to establish computing with infinite matrix groups on the same footing as the rest of CGT. The book emphasizes practical methods based on results of linear group theory, solutions of fundamental algorithmic problems, and provision of software. Additionally, the book sets out a research program to make further progress in the area.

Linear Groups and Computation

Discussing various versions of two medieval arguments for the impossibility of infinity, this Element sheds light on early stages of the evolution of the notion of INFINITIES OF DIFFERENT SIZES. The first argument is called 'the Equality Argument' and relies on the premise that all infinities are equal. The second argument is called 'the Mapping Argument' and relies on the assumption that if one thing is mapped/ superposed upon another thing and neither exceeds the other, the two things are equal to each other. Although these arguments were initially proposed in the context of discussions against the possibility of infinities, they have played pivotal roles in the historical evolution of the notion of INFINITIES OF DIFFERENT SIZES.

Medieval Finitism

Husserl's Philosophy of Mathematical Practice explores the applicability of the phenomenological method to philosophy of mathematical practice. The first section elaborates on Husserl's own understanding of the method of radical sense-investigation (Besinnung), with which he thought the mathematics of his time should be approached. The second section shows how Husserl himself practiced it, tracking both constructive and platonistic features in mathematical practice. Finally, the third section situates Husserlian phenomenology within the contemporary philosophy of mathematical practice, where the examined styles are more diverse. Husserl's phenomenology is presented as a method, not a fixed doctrine, applicable to study and unify philosophy of mathematical practice and the metaphysics implied in it. In so doing, this Element develops Husserl's philosophy of mathematical practice as a species of Kantian critical philosophy and asks after the conditions of possibility of social and self-critical mathematical practices.

Husserl's Philosophy of Mathematical Practice

Rules to Infinity defends the thesis that mathematics contributes to the explanatory power of science by expressing conceptual rules that allow for the transformation of empirical descriptions. It claims that mathematics should not be thought of as describing, in any substantive sense, an abstract realm of eternal mathematical objects, as traditional Platonists have thought.

The Normative Role of Mathematics in Scientific Explanation

Rules to Infinity

Kyle D. Evans - maths gift books

***A Strong Words 2023 Book of the Year*** 'A highly enjoyable and serendipitous read!' - Rob Eastaway, bestselling co-author of Headscratchers: The New Scientist Puzzle Book Did you know: -Only around 100 people have ever lived beyond a million hours (that's about 114 years) -Around 7% of everyone who has ever lived is currently alive -The '12 days of Christmas' song, when sung in full, results in 364 gifts being given - one for every day... except Christmas Broken down into 12 chapters that correspond roughly to months of the year - from going 'back to school' with arithmetic and times tables through prime numbers and all the way to the 12 Days of Chris-maths, this book features a collection of 365 fascinating numerical 'nuggets', accompanied by clear, bite-size explanations of the mathematics that underpin them.

365 Astonishing Maths Facts

A Year in Numbers

Textbooks in Mathematics

This is the only available student solutions manual prepared by the author of Contemporary Abstract Algebra, Eleventh Edition and the only official one. It is designed to supplement the text and the author's original approach to instruction.

Student Solutions Manual for Gallian's Contemporary Abstract Algebra

Annals of Mathematics Studies

A comprehensive new theory of adelic line bundles on quasi-projective varieties over finitely generated fieldsThis book introduces a comprehensive theory of adelic line bundles on quasi-projective varieties over finitely generated fields, developed in both geometric and arithmetic contexts. In the geometric setting, adelic line bundles are defined as limits of line bundles on projective compactifications under the boundary topology. In the arithmetic setting, they are defined as limits of Hermitian line bundles on projective arithmetic compactifications, also under the boundary topology. After establishing these foundational definitions, the book uses the theory to explore key concepts such as intersection theory, effective sections, volumes, and positivity of adelic line bundles. It also applies these results to study height functions of algebraic points and prove an equidistribution theorem on quasi-projective varieties. This theory has broad applications in the study of numerical, dynamical, and Diophantine properties of moduli spaces, quasi-projective varieties, and varieties over finitely generated fields.

Adelic Line Bundles on Quasi-projective Varieties

"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

Pentagons and Pentagrams

Informations bibliographiques

Mots-clés

Informations bibliographiques

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