This book is based on a graduate course taught by the author at the University of Maryland. The lecture notes have been revised and augmented by examples. The first two chapters develop the elementary theory of Artin Braid groups, both geometrically and via homotopy theory, and discuss the link between knot theory and the combinatorics of braid groups through Markou's Theorem. The final two chapters give a detailed investigation of polynomial covering maps, which may be viewed as a homomorphism of the fundamental group of the base space into the Artin Braid group on n strings.
This book is based on a graduate course taught by the author at the University of Maryland. The lecture notes have been revised and augmented by examp...
The aim of this book is to throw light on various facets of geometry through development of four geometrical themes.
The first theme is about the ellipse, the shape of the shadow east by a circle. The next, a natural continuation of the first, is a study of all three types of conic sections, the ellipse, the parabola and the hyperbola.
The third theme is about certain properties of geometrical figures related to the problem of finding the largest area that can be enclosed by a curve of given length. This problem is called the isoperimetric problem. In itself, this topic contains...
The aim of this book is to throw light on various facets of geometry through development of four geometrical themes.
Many advanced mathematical disciplines have a foundation in general topology and calculus in normed vector spaces. This study offers an opportunity to go into some depth with fundamental notions from mathematical analysis that occur frequently in theoretical parts of the engineering sciences.
Many advanced mathematical disciplines have a foundation in general topology and calculus in normed vector spaces. This study offers an opportunity to...
This book presents basic elements of the theory of Hilbert spaces and operators on Hilbert spaces, culminating in a proof of the spectral theorem for compact, self-adjoint operators on separable Hilbert spaces. It exhibits a construction of the space of pth power Lebesgue integrable functions by a completion procedure with respect to a suitable norm in a space of continuous functions, including proofs of the basic inequalities of H?lder and Minkowski. The Lp-spaces thereby emerges in direct analogy with a construction of the real numbers from the rational numbers. This allows grasping the...
This book presents basic elements of the theory of Hilbert spaces and operators on Hilbert spaces, culminating in a proof of the spectral theorem for ...
This book presents basic elements of the theory of Hilbert spaces and operators on Hilbert spaces, culminating in a proof of the spectral theorem for compact, self-adjoint operators on separable Hilbert spaces. It exhibits a construction of the space of pth power Lebesgue integrable functions by a completion procedure with respect to a suitable norm in a space of continuous functions, including proofs of the basic inequalities of Hölder and Minkowski. The Lp-spaces thereby emerges in direct analogy with a construction of the real numbers from the rational numbers. This allows grasping...
This book presents basic elements of the theory of Hilbert spaces and operators on Hilbert spaces, culminating in a proof of the spectral theorem for ...
