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Dunham W: A Mathematician's Scrapbook

A Mathematician's Scrapbook

Highlights and Surprises from Across a Career

Universitext

The theory of elliptic functions and modular forms is rich and storied, though it has a reputation for difficulty. In this textbook, the authors successfully bridge foundational concepts and advanced material. Following Weierstrass’s approach to elliptic functions, they also cover elliptic curves and complex multiplication. The sections on modular forms, which can be read independently, include discussions of Hecke operators and Dirichlet series. Special emphasis is placed on theta series, with some advanced results included. With detailed proofs and numerous exercises, this book is well-suited for self-study or use as a reference. A companion website provides videos and a discussion forum on the topic.

Elliptic Functions and Modular Forms

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

Mathematics and the Built Environment

This collection of essays reflects the author's decades-long dedication to studying the interplay between mechanics and architecture. It explores how advancements in mechanics have influenced architectural innovation and how the need for new architectural solutions has driven theoretical progress in engineering. By examining the historical roots of these fields, these essays provide a deep analysis of key developments.

This interdisciplinary work will appeal to scholars, students, and anyone interested in the complex relationship between the theoretical and practical aspects of architecture and civil engineering.

This collection of essays reflects the author's decades-long dedication to studying the interplay between mechanics and architecture. It explores how advancements in mechanics have influenced architectural innovation and how the need for new architectural solutions has driven theoretical progress in engineering. By examining the historical roots of these fields, these essays provide a deep analysis of key developments.This interdisciplinary work will appeal to scholars, students, and anyone interested in the complex relationship between the theoretical and practical aspects of architecture and civil engineering.

The Mathematical Search for Stability in Architecture

Between Mechanics and Architecture

Compact Textbooks in Mathematics

This textbook combines the history of synthetic geometry, centered on the years 1800-1855, with a theorem-proof exposition of the geometry developed in those years. The book starts with the background needed from Euclid’s&nbsp;Elements, followed by chapters on transformations, including dilation (similitude), homology, homogeneous coordinates, projective geometry, inversion, the Möbius transformation, and transformation geometry as in French schoolbooks of 1910. Projective geometry is presented by tracing its path through the work of J. V. Poncelet, J. Steiner, and K. G. C. von Staudt. Extensive exercises are included, many from the period studied. The prerequisites for approaching this course are knowledge of high school geometry and enthusiasm for mathematical demonstration.This textbook is ideal for a college geometry course, for self-study, or as preparation for the study of modern geometry.

This textbook combines the history of synthetic geometry, centered on the years 1800-1855, with a theorem-proof exposition of the geometry developed in those years. The book starts with the background needed from Euclid’s&nbsp;Elements, followed by chapters on transformations, including dilation (similitude), homology, homogeneous coordinates, projective geometry, inversion, the Möbius transformation, and transformation geometry as in French schoolbooks of 1910. Projective geometry is presented by tracing its path through the work of J. V. Poncelet, J. Steiner, and K. G. C. von Staudt. Extensive exercises are included, many from the period studied. The prerequisites for approaching this course are knowledge of high school geometry and enthusiasm for mathematical demonstration.This textbook is ideal for a college geometry course, for self-study, or as preparation for the study of modern geometry.&nbsp;

Lessons Centered on the History from 1800-1855

Geometry by Its Transformations

Problem Solving in Mathematics and Beyond

Appreciating Geometry Through Extraordinary Relationships

Magic Numbers to Better Understand a Race Car

Race Car Handling Optimization

Selected Chapters Of Number Theory: Special Numbers

Eulerian Numbers

Geometry Workbook for Anyone: Learn, Recap, Practice, Discover, Enjoy!This new volume focuses on problem-solving in plane geometry topics and is suitable for any reader with elementary geometrical knowledge at the secondary school level. The author has assembled an exceptional collection of geometry exercises with approximately equal weight allocated among different types of problems: proofs, calculations, and geometric straightedge-and-compass constructions.The book is divided into seven chapters, with sets of problems arranged in approximate order of increasing difficulty. The first chapter is devoted to a discussion of several useful strategies and techniques for approaching geometric problems. The next chapter presents warm-up exercises to 'stretch' geometric muscles and refresh the very basic facts about topics covered in subsequent chapters. Each of the following chapters: 'Triangles, ' 'Quadrilaterals, ' 'Circles, ' and 'Areas' has three sections (A, B, and C), starting with simple problems and questions (section A), progressing to intermediate problems (section B), and ending with more advanced and complex challenges (section C), some of which were offered in math Olympiads and various math contests. The final chapter is a mixture of challenging problems comprising material covered in previous chapters.At the end of the book, the 'Solutions and Answers' section provides detailed explanations and solutions for all the problems. In that section, for many interesting problems, the author reveals not just one but multiple alternative solutions, compares them, and discusses their effectiveness. The emphasis is on how to acquire insight and develop different strategies for tackling geometrical challenges. By solving these problems, readers discover fascinating links between them, unlock geometrical secrets, build self-confidence, and -- for many skeptics -- discover that learning geometry can be fun and enjoyable!

Learning Geometry Through Problem Solving

Frontiers in Mathematics

This monograph presents the work of the authors in metrical theory of continued fractions in the last two decades. The monograph cuts a particular path through this extensive theory and describes the theory in its current form for three families of continued fractions, namely, θ-continued fractions, N-continued fractions, and generalized Rényi continued fractions. The book systematically lays out the required preliminaries, making the book easy to read. This monograph provides a solid introduction into the theory of continued fractions.The book is intended for researchers in metrical theory, as well as advanced graduate students and mathematicians interested in this field.

Metrical and Ergodic Theory of Continued Fraction Algorithms

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

ZAG Handbook of Algebraic Geometry provides an expansive collection of extended summaries of all the research talks given at the worldwide ZAG (Zoom Algebraic Geometry) Seminar as well as contributed short notes.

ZAG Handbook of Modern Algebraic Geometry

Routledge Focus on Mental Health

In The Mind of Complex Numbers and the Subject in Analyses, Raul Moncayo uses the complex plane to evaluate analytic outcomes. Moncayo's approach provides a study of the process and outcome of singular analyses that does not rely on the methods and questionnaires of psychotherapy or medical research.

The Mind of Complex Numbers and the Subject in Analyses

A Mathematician's Scrapbook

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