This work delves into the intricate contributions of Henri Poincaré across mathematics, physics, and philosophy. It explores his groundbreaking ideas and theories, highlighting his influence on modern science and thought. The book examines Poincaré's approach to topics such as topology, celestial mechanics, and the foundations of mathematics, while also addressing his philosophical insights regarding the nature of knowledge and reality. Through this comprehensive analysis, readers gain a deeper understanding of Poincaré's legacy and its enduring impact on various fields.
Based on a course for third-year university students, the book contains
numerous historical and mathematical exercises, offers extensive advice to the
student on how to write essays, and can easily be used in whole or in part as
a course in the history of mathematics.
Though little known outside of his field, Bernhard Riemann was one of the most important and influential mathematicians of the modern era. His early work prepared the way for Einstein's general theory of relativity, and his breakthroughs in geometry, topology, analysis, and number theory continue to inspire and challenge mathematicians today. In Simply Riemann, author Jeremy Gray takes us into the mind of a great mathematician, exploring the ideas beneath the technicalities, and providing an insightful portrait of a would-be pastor who found himself increasingly "called" by the abstract beauty of numbers.
"This textbook provides an accessible account of the history of abstract algebra, tracing a range of topics in modern algebra and number theory back to their modest presence in the seventeenth and eighteenth centuries, and exploring the impact of ideas on the development of the subject. Beginning with Gauss's theory of numbers and Galois's ideas, the book progresses to Dedekind and Kronecker, Jordan and Klein, Steinitz, Hilbert, and Emmy Noether. Approaching mathematical topics from a historical perspective, the author explores quadratic forms, quadratic reciprocity, Fermat's Last Theorem, cyclotomy, quintic equations, Galois theory, commutative rings, abstract fields, ideal theory, invariant theory, and group theory. Readers will learn what Galois accomplished, how difficult the proofs of his theorems were, and how important Camille Jordan and Felix Klein were in the eventual acceptance of Galois's approach to the solution of equations. The book also describes the relationship between Kummer's ideal numbers and Dedekind's ideals, and discusses why Dedekind felt his solution to the divisor problem was better than Kummer's. Designed for a course in the history of modern algebra, this book is aimed at undergraduate students with an introductory background in algebra but will also appeal to researchers with a general interest in the topic. With exercises at thei end of each chapter and appendices providing material difficult to find elsewhere, this book is self-contained and therefore suitable for self-study"--Page 4 of cover
Focusing on the evolution of complex function theory, this book explores key developments such as elliptic function theory and differential equations in the complex domain. It also delves into geometric function theory and the foundational years of multi-variable complex function theory, providing a comprehensive overview of these significant mathematical advancements.
In a dystopian Boston, three friends navigate survival amidst gang violence and government oppression. A caterer's error leads to dire consequences, while sociopathic firefighters wreak havoc on the West Coast. A young girl faces the fears lurking in her backyard, shaping her destiny, and a troubled veteran uses sculpture to preserve memories, taking drastic measures to share them. "Scale the Sycamore" weaves these narratives together through poetry and action, exploring themes of death, survival, and the harsh realities of an impending future.
This book contains a history of real and complex analysis in the nineteenth
century, from the work of Lagrange and Fourier to the origins of set theory
and the modern foundations of analysis.
Approximately fifty articles that were published in The Mathematical Intelligencer during its first eighteen years. The selection demonstrates the wide variety of attractive articles that have appeared over the years, ranging from general interest articles of a historical nature to lucid expositions of important current discoveries. Each article is introduced by the editors. "...The Mathematical Intelligencer publishes stylish, well-illustrated articles, rich in ideas and usually short on proofs. ...Many, but not all articles fall within the reach of the advanced undergraduate mathematics major. ... This book makes a nice addition to any undergraduate mathematics collection that does not already sport back issues of The Mathematical Intelligencer." D.V. Feldman, University of New Hamphire, CHOICE Reviews, June 2001.
Based on the latest historical research, Worlds Out of Nothing is the first
book to provide a course on the history of geometry in the 19th century.
Topics include projective geometry, especially the concept of duality, non-
Euclidean geometry, and more.
Focusing on the 19th-century development of geometric function theory, this study explores the intersection of hypergeometric and related linear differential equations, group theory, and non-Euclidean geometry. It delves into how these mathematical areas converged to create a unified vision, highlighting the significance of these concepts in advancing mathematical thought during that era.
