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A Physicist's Introduction to Algebraic Structures

A Physicist's Introduction to Algebraic Structures
Vector Spaces, Groups, Topological Spaces and More

c.$89.99 (P)

  • Publication planned for: December 2021
  • availability: Not yet published - available from December 2021
  • format: Paperback
  • isbn: 9781108729116

c.$ 89.99 (P)

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About the Authors
  • An algebraic structure consists of a set of elements, with some rule of combining them, or some special property of selected subsets of the entire set. Many algebraic structures, such as vector space and group, come to everyday use of a modern physicist. Catering to the needs of graduate students and researchers in the field of mathematical physics and theoretical physics, this comprehensive and valuable text discusses the essential concepts of algebraic structures such as metric space, group, modular numbers, algebraic integers, field, vector space, Boolean algebra, measure space and Lebesgue integral. Important topics including finite and infinite dimensional vector spaces, finite groups and their representations, unitary groups and their representations and representations of the Lorentz group, homotopy and homology of topological spaces are covered extensively. Rich pedagogy includes various problems interspersed throughout the book for better understanding of concepts.

    • Includes detailed proofs of important theorems
    • Offers more than 400 problems to test the understanding of concepts, including answers to many of them
    • In-depth coverage of topics includes vector space, group, and topological space
    • Topology is introduced after group theory, helping students understand the topological properties of group parameter spaces
    Read more

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    Product details

    • Publication planned for: December 2021
    • format: Paperback
    • isbn: 9781108729116
    • length: 550 pages
    • dimensions: 228 x 152 mm
    • availability: Not yet published - available from December 2021
  • Table of Contents

    Part I. General Introduction:
    1. Rules of logic
    2. Sets and functions
    3. Algebraic structures
    Part II. Vector Spaces:
    4. Basics
    5. Operators on vector spaces
    6. Infinite dimensional vector spaces
    Part III. Group Theory:
    7. General properties of groups
    8. Finite groups
    9. Representation of finite groups
    10. Symmetries of regular geometrical objects
    11. Countably infinite groups
    12. General properties of Lie groups
    13. Rotations and translations
    14. Unitary groups and their representations
    15. Orthogonal groups and their representations
    16. Parameter space of Lie groups
    17. Representations of the Lorentz group
    18. Roots and weights
    19. Some other groups and algebras
    Part IV. Topology:
    20. Continuity of functions
    21. Topological spaces
    22. Homotopy theory
    23. Homology

  • Author

    Palash B. Pal, Saha Institute of Nuclear Physics, India
    Palash B. Pal is Senior Professor in the Theory Division at the Saha Institute of Nuclear Physics, Kolkata. His current research includes elementary particle physics, with specializations in neutrinos, grand unified theories, and particles in electromagnetic fields. He has published more than 100 papers in journals of international repute. He has taught courses on mathematical methods, particle physics, quantum field theory, theoretical physics and classical field theory at graduate level. He carried out postdoctoral research at the University of Maryland, University of Massachusetts, University of Oregon and University of Texas.

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