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This is the first in a series of three volumes dealing with important topics in algebra. It offers an introduction to the foundations of mathematics together with the fundamental algebraic structures, namely groups, rings, fields, and arithmetic. Intended as a text for undergraduate and graduate students of mathematics, it discusses all major topics in algebra with numerous motivating illustrations and exercises to enable readers to acquire a good understanding of the basic algebraic structures, which they can then use to find the exact or the most realistic solutions to their problems.
This book, the third book in the four-volume series in algebra, deals with important topics in homological algebra, including abstract theory of derived functors, sheaf co-homology, and an introduction to etale and l-adic co-homology. It contains four chapters which discuss homology theory in an abelian category together with some important and fundamental applications in geometry, topology, algebraic geometry (including basics in abstract algebraic geometry), and group theory. The book will be of value to graduate and higher undergraduate students specializing in any branch of mathematics. The author has tried to make the book self-contained by introducing relevant concepts and results required. Prerequisite knowledge of the basics of algebra, linear algebra, topology, and calculus of several variables will be useful.
This book, the fourth book in the four-volume series in algebra, discusses Lie algebra and representation theory in detail. It covers topics such as semisimple Lie algebras, root systems, representation theory of Lie algebra, Chevalley groups and representation theory of Chevalley groups. Numerous motivating illustrations have been presented along with exercises, enabling readers to acquire a good understanding of topics which they can then use to find the exact or most realistic solutions to their problems.
This is the second in a series of three volumes dealing with important topics in algebra. Volume 2 is an introduction to linear algebra (including linear algebra over rings), Galois theory, representation theory, and the theory of group extensions. The section on linear algebra (chapters 1–5) does not require any background material from Algebra 1, except an understanding of set theory. Linear algebra is the most applicable branch of mathematics, and it is essential for students of science and engineering As such, the text can be used for one-semester courses for these students. The remaining part of the volume discusses Jordan and rational forms, general linear algebra (linear algebra over rings), Galois theory, representation theory (linear algebra over group algebras), and the theory of extension of groups follow linear algebra, and is suitable as a text for the second and third year students specializing in mathematics.
Ruskin Bond, b. 1934, Indo-English litterateur.
In Rajasthan, India, a caste of musicians and mendicants, the Nath-Jogis, sing stories of kings who renounce their thrones to become wandering mendicants. They also sing of a god, Mahadeva, Shiva, who must abandon his world-renouncing life and marry, thus establishing the very caste that tells his story. This is the first detailed ethnomusicological study of the music of this caste, examining how the existential questions of the sung stories--of the conflict between loyalty to families or communities and the transcending desire to renounce the material world--are articulated in musical performances in which the caste's own ethnography is inscribed. Discussing the relationship between the performed repertoire and the caste's identity, the contexts of performance and ways in which familiar stories are effectively retold, the book offers a transcription, translation and musical and ethnographic analysis of one performance, by Kishori Nath, and shows how the questions the performances project are not merely speculative acts of self-identification but also challenges to audiences to consider their own responses.
Dalit assertion has been a central feature of the states in the Hindi heartland since the mid-1980s, leading to the rise of political consciousness and identity-based lower-caste parties. The present study focuses on the different political response of the Congress party to identity assertion in Madhya Pradesh under the leadership of Digvijay Singh. In Uttar Pradesh and Bihar, in response to the strong wave of Dalit assertion that swept the region, parties such as the Bahujan Samaj Party (BSP) and the Rashtriya Janata Dal (RJD) used strategies of political mobilisation to consolidate Dalit/backward votes and capture state power. In Madhya Pradesh, in contrast, the Congress party and Digvijay...