The starting point of this book is the question of to what extent knowledge can be objectively justified and to what extent our statements, in their claim to be true, must necessarily presuppose a reference to a world given independently of our subjective experience. Overall, it is to be shown that, first, every theory of truth must in some way be based on correspondence-theoretical assumptions (i.e., truth is the agreement of a statement or thought with reality). Second, however, that eve...

The book is devoted to the study of the geometrical and topological structure of gauge theories. It consists of the following three building blocks:- Geometry and topology of fibre bundles,- Clifford algebras, spin structures and Dirac operators,- Gauge theory.Written in the style of a mathematical textbook, it combines a comprehensive presentation of the mathematical foundations with a discussion of a variety of advanced topics in gauge theory.The f...

This book provides a systematic, interdisciplinary analysis of the conflicts, issues, and tensions associated with today’s ecological transformation processes from an Environmental Humanities perspective. It explores the notion of ecological ambivalence, where conflicting reactions, beliefs, or feelings toward public policies or private practices for "saving planet Earth" threaten to produce a stalemate.Under the umbrella of the Environmental Humanities, the book brings together sc...

This open access book presents a thorough look at tortuosity and microstructure effects in porous materials. The book delivers a comprehensive review of the subject, summarizing all key results in the field with respect to the underlying theories, empirical data available in the literature, modern methodologies and calculation approaches, and quantitative relationships between microscopic and macroscopic properties. It thoroughly discusses up to 20 different types of tortuosity and introdu...

Boost Your grades with this illustrated Study Guide. You will use it from college all the way to graduate school and beyond.FEATURES:- Clear and concise explanations - Difficult concepts are explained in simple terms - Illustrated with graphs and diagrams TABLE OF CONTENTS:I. Linear equations System of linear equations Determinant Minor Cauchy-Binet formula Cramer's rule Gaussian elimination Gauss-Jordan elimination Strassen algorithm II. Matrices Matrix addition Matrix multiplication Basi...

Linear Algebra is intended for a one-term course at the junior or senior level. It begins with an exposition of the basic theory of vector spaces and proceeds to explain the fundamental structure theorems for linear maps, including eigenvectors and eigenvalues, quadric and hermitian forms, diagonalization of symmetric, hermitian, and unitary linear maps and matrices, triangulation, and Jordan canonical form. The book also includes a useful chapter on convex sets and the finite-dimensional ...

This first volume, a three-part introduction to the subject, is intended for students with a beginning knowledge of mathematical analysis who are motivated to discover the ideas that shape Fourier analysis. It begins with the simple conviction that Fourier arrived at in the early nineteenth century when studying problems in the physical sciences--that an arbitrary function can be written as an infinite sum of the most basic trigonometric functions.The first part implements this ide...

Providing a succinct yet comprehensive treatment of the essentials of modern differential geometry and topology, this book's clear prose and informal style make it accessible to advanced undergraduate and graduate students in mathematics and the physical sciences. The text covers the basics of multilinear algebra, differentiation and integration on manifolds, Lie groups and Lie algebras, homotopy and de Rham cohomology, homology, vector bundles, Riemannian and pseudo-Riemannian geometry, a...

At first sight, finitely generated abelian groups and canonical forms of matrices appear to have little in common. However, reduction to Smith normal form, named after its originator H.J.S.Smith in 1861, is a matrix version of the Euclidean algorithm and is exactly what the theory requires in both cases. Starting with matrices over the integers, Part 1 of this book provides a measured introduction to such groups: two finitely generated abelian groups are isomorphic if and only if their inv...

This lively and accessible book describes the theory and applications of Hilbert spaces and also presents the history of the subject to reveal the ideas behind theorems and the human struggle that led to them. The authors begin by establishing the concept of 'countably infinite', which is central to the proper understanding of separable Hilbert spaces. Fundamental ideas such as convergence, completeness and dense sets are first demonstrated through simple familiar examples and then formali...

Based on lectures given at Zhejiang University in Hangzhou, China, and Johns Hopkins University, this book introduces eigenfunctions on Riemannian manifolds. Christopher Sogge gives a proof of the sharp Weyl formula for the distribution of eigenvalues of Laplace-Beltrami operators, as well as an improved version of the Weyl formula, the Duistermaat-Guillemin theorem under natural assumptions on the geodesic flow. Sogge shows that there is quantum ergodicity of eigenfunctions if the geodesi...

The mathematical methods that physical scientists need for solving substantial problems in their fields of study are set out clearly and simply in this tutorial-style textbook. Students will develop problem-solving skills through hundreds of worked examples, self-test questions and homework problems. Each chapter concludes with a summary of the main procedures and results and all assumed prior knowledge is summarized in one of the appendices. Over 300 worked examples show how to use the te...