This book will contain lectures given by four eminent speakers at the Recent Advances in Operator Theory and Operator Algebras conference held at the Indian Statistical Institute, Bangalore, India in 2014. The main aim of this book is to bring together various results in one place with cogent introduction and references for further study.

The Foundations of GeometryGeometry, like arithmetic, requires for its logical development only a small number of simple, fundamental principles. These fundamental principles are called the axioms of geometry. The choice of the axioms and the investigation of their relations to one another is a problem which, since the time of Euclid, has been discussed in numerous excellent memoirs to be found in the mathematical literature.This problem is tantamount to the ...

This textbook is distinguished from other texts on the subject by the depth of the presentation and the discussion of the calculus of moving surfaces, which is an extension of tensor calculus to deforming manifolds.Designed for advanced undergraduate and graduate students, this text invites its audience to take a fresh look at previously learned material through the prism of tensor calculus. Once the framework is mastered, the student is introduced to new material which includes di...

What do proteins and pop-up cards have in common? How is opening a grocery bag different from opening a gift box? How can you cut out the letters for a whole word all at once with one straight scissors cut? How many ways are there to flatten a cube? With the help of 200 colour figures, author Joseph O'Rourke explains these fascinating folding problems starting from high school algebra and geometry and introducing more advanced concepts in tangible contexts as they arise. He shows how varia...

In a sense, trigonometry sits at the center of high school mathematics. It originates in the study of geometry when we investigate the ratios of sides in similar right triangles, or when we look at the relationship between a chord of a circle and its arc. It leads to a much deeper study of periodic functions, and of the so-called transcendental functions, which cannot be described using finite algebraic processes. It also has many applications to physics, astronomy, and other branches of s...

Since Benoit Mandelbrot's pioneering work in the late 1970s, scores of research articles and books have been published on the topic of fractals. Despite the volume of literature in the field, the general level of theoretical understanding has remained low; most work is aimed either at too mainstream an audience to achieve any depth or at too specialized a community to achieve widespread use. Written by celebrated mathematician and educator A.A. Kirillov, A Tale of Two Fractals is ...

The featured review of the AMS describes the author’s earlier work in the field of approach spaces as, ‘A landmark in the history of general topology’. In this book, the author has expanded this study further and taken it in a new and exciting direction.The number of conceptually and technically different systems which characterize approach spaces is increased and moreover their uniform counterpart, uniform gauge spaces, is put into the picture. An extensive study of completions, b...

Reversibility is a thread woven through many branches of mathematics. It arises in dynamics, in systems that admit a time-reversal symmetry, and in group theory where the reversible group elements are those that are conjugate to their inverses. However, the lack of a lingua franca for discussing reversibility means that researchers who encounter the concept may be unaware of related work in other fields. This text is the first to make reversibility the focus of attention. The authors fix s...

This volume presents an extensive overview of all major modern trends in applications of probability and stochastic analysis. It will be a great source of inspiration for designing new algorithms, modeling procedures and experiments. Accessible to researchers, practitioners, as well as graduate and postgraduate students, this volume presents a variety of new tools, ideas and methodologies in the fields of optimization, physics, finance, probability, hydrodynamics, reliability, decision mak...

This book presents applications of geometric optimal control to real life biomedical problems with an emphasis on cancer treatments. A number of mathematical models for both classical and novel cancer treatments are presented as optimal control problems with the goal of constructing optimal protocols. The power of geometric methods is illustrated with fully worked out complete global solutions to these mathematically challenging problems. Elaborate constructions of optimal controls and cor...

This volume contains nine survey articles based on the invited lectures given at the 24th British Combinatorial Conference, held at Royal Holloway, University of London in July 2013. This biennial conference is a well-established international event, with speakers from around the world. The volume provides an up-to-date overview of current research in several areas of combinatorics, including graph theory, matroid theory and automatic counting, as well as connections to coding theory and B...

This book presents a method for solving linear ordinary differential equations based on the factorization of the differential operator. The approach for the case of constant coefficients is elementary, and only requires a basic knowledge of calculus and linear algebra. In particular, the book avoids the use of distribution theory, as well as the other more advanced approaches: Laplace transform, linear systems, the general theory of linear equations with variable coefficients and variation...