This book is based on a graduate course taught by the author at the University of Maryland, USA. The lecture notes have been revised and augmented by examples. The work falls into two strands. The first two chapters develop the elementary theory of Artin Braid groups both geometrically and via homotopy theory, and discuss the link between knot ...
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 ...
Many advanced mathematical disciplines, such as dynamical systems, calculus of variations, differential geometry and the theory of Lie groups, have a common foundation in general topology and calculus in normed vector spaces. In this work, mathematically inclined engineering students are offered an opportunity to go into some depth with ...
This work offers insights on various facets of geometry through development of four geometric themes: ellipse, the shape or shadow cast by a cirlce; all three types of conic sections - the ellipse, the parabola and the hyperbola; certain properties of geometric figures related to the problem of finding the largest areas that can be enclosed by a ...
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