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Galois Theory and Advanced Linear Algebra

  • Textbook
  • © 2020

Overview

Authors:
  1. Rajnikant Sinha

    1. Samne Ghat, Varanasi, India

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  • Discusses the fundamental topics in Galois theory and advanced linear algebra

  • Serves as an easy-to-understand textbook for undergraduate students of linear algebra

  • Helps students understand other courses, such as Riemannian geometry

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Table of contents (4 chapters)

  1. Front Matter

    Pages i-ix
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  2. Galois Theory I

    • Rajnikant Sinha
    Pages 1-90

  3. Galois Theory II

    • Rajnikant Sinha
    Pages 91-166

  4. Linear Transformations

    • Rajnikant Sinha
    Pages 167-253

  5. Sylvester’s Law of Inertia

    • Rajnikant Sinha
    Pages 255-349

  6. Back Matter

    Pages 351-351
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Keywords

About this book

This book discusses major topics in Galois theory and advanced linear algebra, including canonical forms. Divided into four chapters and presenting numerous new theorems, it serves as an easy-to-understand textbook for undergraduate students of advanced linear algebra, and helps students understand other courses, such as Riemannian geometry. The book also discusses key topics including Cayley–Hamilton theorem, Galois groups, Sylvester’s law of inertia, Eisenstein criterion, and solvability by radicals. Readers are assumed to have a grasp of elementary properties of groups, rings, fields, and vector spaces, and familiarity with the elementary properties of positive integers, inner product space of finite dimension and linear transformations is beneficial.

Authors and Affiliations

  • Samne Ghat, Varanasi, India

    Rajnikant Sinha

About the author

Rajnikant Sinha is a former Professor of Mathematics at Magadh University, Bodh Gaya, India. A passionate mathematician, Prof. Sinha has published numerous interesting research findings in international journals, and has authored three textbooks with Springer Nature: Smooth Manifolds, Real and Complex Analysis: Volume 1, and Real and Complex Analysis: Volume 2; and a contributed volume on Solutions to Weatherburn’s Elementary Vector Analysis: With Applications to Geometry and Mechanics (with another publisher). His research focuses on topological vector spaces, differential geometry and manifolds.

Bibliographic Information

  • Book Title: Galois Theory and Advanced Linear Algebra

  • Authors: Rajnikant Sinha

  • DOI: https://doi.org/10.1007/978-981-13-9849-0

  • Publisher: Springer Singapore

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Nature Singapore Pte Ltd. 2020

  • Hardcover ISBN: 978-981-13-9848-3Published: 30 January 2020

  • Softcover ISBN: 978-981-13-9851-3Published: 09 March 2021

  • eBook ISBN: 978-981-13-9849-0Published: 28 December 2019

  • Edition Number: 1

  • Number of Pages: IX, 351

  • Number of Illustrations: 9 b/w illustrations

  • Topics: Linear Algebra, Linear and Multilinear Algebras, Matrix Theory

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