Algebra: Abstract and Concrete by Frederick M. Goodman
Algebra: Abstract and Concrete - Table of Contents
- 1. Algebraic Themes and Geometric Patterns
- 2. Basic Theory of Groups and Homomorphisms
- 3. Products of Groups (Direct & Semidirect)
- 4. Symmetries of Polyhedra
- 5. Actions of Groups and Orbits
- 6. Rings, Ideals, and Quotients
- 7. Field Extensions – First Look
- 8. Modules and Vector Spaces over PIDs
- 9. Field Extensions – Second Look & Splitting
- 10. Solvability by Radicals and Galois Groups
- 11. Isometry Groups and Euclidean Transformations
What You Will Learn in Algebra: Abstract and Concrete
Algebra: Abstract and Concrete by Frederick M. Goodman is an authoritative, open-access textbook published by SemiSimple Press that bridges concrete geometric structures and group actions with modern ring and field theory. This comprehensive volume guides readers through algebraic themes, basic group theory, direct and semidirect group products, polyhedral symmetry groups, G-set group actions, commutative and non-commutative rings, principal ideal domains, modules over PIDs, field extension degree theory, Galois solvability by radicals, and geometric isometry groups with exceptional visual clarity and logical rigor.
Designed for undergraduate mathematics majors, graduate self-study learners, theoretical physicists, and research algebraists, this foundational text bridges concrete geometric transformations directly with formal algebraic proof techniques. Goodman details step-by-step group action orbits, polyhedral rotations, module decomposition theorems, field splitting constructions, and isometry classifications. Whether you are building background for quantum mechanics symmetry operators, preparing for doctoral algebra qualifying exams, or studying modern Galois theory, this book offers an indispensable roadmap.
Recognized globally for its emphasis on concrete geometric motivation prior to abstract generalization, it stands as one of the best open-access textbooks for learning abstract algebra through symmetry. By unifying geometric isometry operations directly with ring modules and field extensions, it serves as an essential tool for mastering abstract and concrete algebra with confidence.
Book Details & Specifications
Title:
Algebra: Abstract and Concrete by Frederick M. Goodman
Publisher:
Frederick Goodman
Year:
2015
Pages:
587
Type:
PDF
Language:
English
ISBN-10 #:
0130673420
ISBN-13 #:
9780130673428
License:
External Educational Resource
Amazon:
Amazon
About the Author: Frederick M. Goodman
The author Frederick M. Goodman
is Professor Emeritus of Mathematics at the University of Iowa, internationally celebrated for his research in subfactors, operator algebras, quantum groups, and active open-access mathematical pedagogy.
Through Algebra: Abstract and Concrete, Goodman delivers a masterfully illustrated, systematically structured approach to modern abstract algebra. His emphasis on visual polyhedral symmetry, geometric group actions, and accessible proof paths make this text a classic reference for group theory, modules, and field extensions trusted by students and educators worldwide.
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