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Maor Eli: Pentagons and Pentagrams

Pentagons and Pentagrams

An Illustrated History

The DnA of Statistics

Indo-Arabic Numerals and the Making of Practical Knowledge in Early Modern Europe

Working Numbers

Annals of Mathematics Studies

A comprehensive new theory of adelic line bundles on quasi-projective varieties over finitely generated fields This 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

How We Gave Computers the Power to Choose for Us

The Irrational Decision

This book discusses, analyzes, and reflects on how "self-different" fractals can create and change innovation. Concentrating on the potential benefits and opportunities that self-different fractals have on innovating systems, this book provides academic researchers and practitioners with the knowledge of how competing and contradictory principles co-produce the productive chaos that causes change, development, and evolution to occur. Covering both linear and non-linear designs, the authors will analyze the way selfdifferent fractals promote innovation and how creative designs are not only possible, but also necessary for the innovation system that drives society and social systems.

Self-Different Fractals and Innovation

Beading With Algorithms: Cellular Automata In Peyote Stitch

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.

Surveys and Tutorials in the Applied Mathematical Sciences

Mechanics is one of the oldest and most foundational subjects in undergraduate curricula for mathematicians, physicists, and engineers. Traditionally taught through a classical, or "analytical," approach, modern advancements have introduced a "geometric" perspective that has found applications in diverse fields such as machine learning, climate research, satellite navigation, and more.This book bridges the gap between classical mechanics and its modern, geometric counterpart. Designed for students and educators, it presents the essential topics typically required in mechanics courses while integrating a geometric approach to deepen understanding.Key features include:*Clear explanations of core concepts, including Lagrangian mechanics, variational methods, canonical transformations, and systems with constraints.*Numerous solved problems and real-world examples to solidify understanding.*Sample midterms and final exams to help students prepare for coursework and assessments.*Every chapter includes a ‘looking forward’ section outlining modern applications of the materialThe book minimizes mathematical abstraction, introducing only the necessary concepts to make the material accessible and practical. Whether you're a student looking to master the essentials or an instructor seeking a fresh perspective, this book provides a comprehensive, approachable, and modern exploration of mechanics.

Mechanics is one of the oldest and most foundational subjects in undergraduate curricula for mathematicians, physicists, and engineers. Traditionally taught through a classical, or "analytical," approach, modern advancements have introduced a "geometric" perspective that has found applications in diverse fields such as machine learning, climate research, satellite navigation, and more.This book bridges the gap between classical mechanics and its modern, geometric counterpart. Designed for students and educators, it presents the essential topics typically required in mechanics courses while integrating a geometric approach to deepen understanding.Key features include:*Clear explanations of core concepts, including Lagrangian mechanics, variational methods, canonical transformations, and systems with constraints.*Numerous solved problems and real-world examples to solidify understanding.*Sample midterms and final exams to help students prepare for coursework and assessments.*Every chapter includes a ‘looking forward’ section outlining modern applications of the material.The book minimizes mathematical abstraction, introducing only the necessary concepts to make the material accessible and practical. Whether you're a student looking to master the essentials or an instructor seeking a fresh perspective, this book provides a comprehensive, approachable, and modern exploration of mechanics.

A Concise Introduction to Classical Mechanics

Problem Solving in Mathematics and Beyond

Our physical world is embedded in a geometric environment. Plane geometry has many amazing wonders beyond those that are briefly touched on at school. The circle, one of the basic aspects of geometry, has a plethora of unexpected curiosities, which the authors present in an easily understandable fashion requiring nothing more than the very basics of school geometry to appreciate these curiosities and their justifications or proofs.

The book is intended to be widely appreciated by a general readership, whose love for geometry should be greatly enhanced through exploring these many unexpected relationships. Geometric Gems is also suitable for mathematics teachers, to enhance the education of their students with these highly motivating circle properties.

Geometric Gems: An Appreciation For Geometric Curiosities - Volume Iii: The Wonders Of Circles

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

A Memoir

Building Things

Learning Geometry Through Problem Solving

Pentagons and Pentagrams

Bibliografische Angaben

Schlagworte

Bibliografische Angaben

Schlagworte

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