The revised edition of the book fills in the urgent need of a treatise on the fundamental laws of operation with numbers so that the readers can understand points of similarity and difference between the Algebra of Matrices and of numbers. The subject is equally important to mathematical disciplines such as Geometry and Modern Algebra and to sciences. The book provides a well rounded and complete account of important concepts of Group, Ring, Field Isomorphism, Equivalence, Congruence and reduction of real quadratic and Hermitian forms to canonical form. Elementary treatment of Vector spaces and linear independence and dependence of vector systems helps in discussing Ranks of matrices and in formulation of results of a system of equations and characteristic vector of a matrix. Illustration of every idea and theorem with abundant solved examples and lucid language are the unique features of this legendary textbook. It is a must read for Mathematics and Science students of undergraduate programmes. Aspirants trying for competitive examinations will also find the book equally useful.
This book is an attempt to make presentation of Elements of Real Analysis more lucid. The book contains examples and exercises meant to help a proper understanding of the text. For B.A., B.Sc. and Honours (Mathematics and Physics), M.A. and M.Sc. (Mathematics) students of various Universities/ Institutions.As per UGC Model Curriculum and for I.A.S. and Various other competitive exams.
Born in 1925, Shanti Bhushan was witness to the formative years of the Indian republic. Courting Destiny traces the remarkable story of his life---the family's origins in the town of Bijnor in the United Provinces, the experience of growing up in a joint family in Allahabad, initial encounters with the law when the Constitution of India was being framed, the distinguished career as a lawyer and law minister, culminating in the campaign for judicial accountability. These memoirs provide a participant's account of some of the most interesting and seminal cases that laid the foundations of India's constitutional history. They include the Keshav Singh case of 1964 which led to the first standoff between the executive and the judiciary; Indira Gandhi's election case which unseated her as prime minister, leading to the imposition of the Emergency; the habeas corpus case where the Supreme Court declared that during an emergency there is no right to life or liberty and hence no recourse against illegal detention; and the parliament attack case in which the Supreme Court, while acquitting Shaukat Guru of all charges of conspiracy, convicted him on a charge for which he was never accused. Together, they offer a broad perspective of the evolution of Indian law and the interpretation of the Constitution. Courting Destiny affords us a glimpse of the many fundamental and far-reaching political and constitutional changes that took place in the decades following independence. The descriptions of Shanti Bhushan's brief involvement in party politics and his time as law minister in the post-Emergency Janata government make for a fascinating insider's account of an important phase of the nation's life. In this narration of the author's life and work, the personal, the professional and the public unfold seamlessly, never at the cost of one or the other. Written in a direct and engaging style, laced with gentle humour, Courting Destiny will appeal to all those interested in India's legal, constitutional and political history. At a time when both the Bar and the Bench are under a cloud, the illustrious sixty-year career of Shanti Bhushan will be a source of inspiration for young advocates.
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