Search results for ""Hindustan Book Agency""

Treats Probability Theory as a branch of Measure Theory. Probability measures in product spaces are introduced at the start by way of laying the ground work to later claim the existence of stochastic processes with prescribed finite dimensional distributions. Other topics include supports of probability measures, functional central limit theorem and functional law of the iterated logarithm for independent variables, and the use of analytic functions of a complex variable in the study of geometric ergodicity in Markov chains.

Read more less

Several generations of students of algebraic geometry have learned the subject from David Mumford's fabled "Red Book" containing notes of his lectures at Harvard University. Their genesis and evolution are described in the preface as:Initially notes to the course were mimeographed and bound and sold by the Harvard math department with a red cover. These old notes were picked up by Springer and are now sold as the "Red book of Varieties and Schemes". However, every time I taught the course, the content changed and grew. I had aimed to eventually publish more polished notes in three volumes...This book contains what Mumford had then intended to be Volume II. It covers the material in the "Red Book" in more depth with several more topics added. The notes have been brought to the present form in collaboration with T. Oda.

Read more less

This is part two of a two-volume introduction to real analysis and is intended for honours undergraduates who have already been exposed to calculus. The emphasis is on rigour and on foundations. The material starts at the very beginning--the construction of the number systems and set theory--then goes on to the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and finally to the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. There are also appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of twenty-five to thirty lectures each.The course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory.The fourth edition incorporates a large number of additional corrections reported since the release of the third edition, as well as some additional new exercises.

Read more less