Mathematics category: 12022 books

This text systematically presents the basics of quantum mechanics, emphasizing the role of Lie groups, Lie algebras, and their unitary representations. The mathematical structure of the subject is brought to the fore, intentionally avoiding significant overlap with material from standard physics courses...

A quantity can be made smaller and smaller without it ever vanishing. This fact has profound consequences for science, technology, and even the way we think about numbers. In this book, we will explore this idea by moving at an easy pace through an account of elementary real analysis and, in particular,...

Elliptic Tales describes the latest developments in number theory by looking at one of the most exciting unsolved problems in contemporary mathematics—the Birch and Swinnerton-Dyer Conjecture. In this book, Avner Ash and Robert Gross guide readers through the mathematics they need to understand...

This book covers work written by leading scholars from different schools within the research area of paraconsistency. The authors critically investigate how contemporary paraconsistent logics can be used to better understand human reasoning in science and mathematics. Offering a variety of perspectives,...

Intensive research in matrix completions, moments, and sums of Hermitian squares has yielded a multitude of results in recent decades. This book provides a comprehensive account of this quickly developing area of mathematics and applications and gives complete proofs of many recently solved problems....

This book deals with a topic that has been largely neglected by philosophers of science to date: the ability to refer and analyze in tandem. On the basis of a set of philosophical case studies involving both problems in number theory and issues concerning time and cosmology from the era of Galileo,...

This enlightening survey of mathematical concept formation holds a natural appeal to philosophically minded readers, and no formal training in mathematics is necessary to appreciate its clear exposition of mathematic fundamentals. Rather than a system of theorems with completely developed proofs or...

This interdisciplinary study of infinity explores the concept through the prism of mathematics and then offers more expansive investigations in areas beyond mathematical boundaries to reflect the broader, deeper implications of infinity for human intellectual thought. More than a dozen world-renowned...

This volume explores the many different meanings of the notion of the axiomatic method, offering an insightful historical and philosophical discussion about how these notions changed over the millennia. The author, a well-known philosopher and historian of mathematics, first examines Euclid,...

In 1907 Luitzen Egbertus Jan Brouwer defended his doctoral dissertation on the foundations of mathematics and with this event the modem version of mathematical intuitionism came into being. Brouwer attacked the main currents of the philosophy of mathematics: the formalists and the Platonists. In tum,...

This book presents diverse topics in mathematical logic such as proof theory, meta-mathematics, and applications of logic to mathematical structures. The collection spans the first 100 years of modern logic and is dedicated to the memory of Irving Anellis, founder of the journal 'Modern Logic', whose...

The term "fuzzy logic," as it is understood in this book, stands for all aspects of representing and manipulating knowledge based on the rejection of the most fundamental principle of classical logic---the principle of bivalence. According to this principle, each declarative sentence is required to...

Intended for a college senior or first-year graduate-level course in partial differential equations, this text offers students in mathematics, engineering, and the applied sciences a solid foundation for advanced studies in mathematics. Classical topics presented in a modern context include coverage...

Deep comprehension of applied sciences requires a solid knowledge of Mathematical Analysis. For most of high level scientific research, the good understanding of Functional Analysis and weak solutions to differential equations is essential. This book aims to deal with the main topics that are necessary...