Algebra: Abstract and Concrete by Frederick M. Goodman
Book Contents :-
1. Algebraic Themes
2. Basic Theory of Groups
3. Products of Groups
4. Symmetries of Polyhedra
5. Actions of Groups
6. Rings
7. Field Extensions – First Look
8. Modules
9. Field Extensions – Second Look
10. Solvability
11. Isometry Groups
About this book :-
"Algebra: Abstract and Concrete" by "Frederick M. Goodman" is a widely respected textbook that introduces modern algebra by connecting "abstract" ideas with "concrete" examples. Written for advanced undergraduates and early graduate students, the book focuses on building intuition before formal definitions, making difficult concepts easier to grasp.
The text covers core topics such as "groups", "rings", "fields", and linear algebra, using "symmetry" as a unifying theme. Goodman presents examples first and then develops theory, helping students understand why definitions and structures matter. The conversational writing style encourages active thinking rather than passive reading, which supports deeper learning and long-term retention.
A major strength of the book is its extensive collection of "exercises", ranging from computational problems to proof-based challenges. Helpful appendices review logic, set theory, and linear algebra, making the book suitable for "self-study" as well as classroom use. Overall, "Algebra: Abstract and Concrete" is valued for its clarity, depth, and balanced approach to learning algebra meaningfully.
Book Detail :-
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 Author :-
The author
Frederick M. Goodman
is an American mathematician known for his work in "algebra", "representation theory", and mathematical "symmetry". He is also widely respected as an educator who focuses on helping students understand difficult ideas through clear explanations and meaningful examples. Goodman’s teaching philosophy emphasizes "intuition" and "conceptual clarity" over rote formalism. In "Algebra: Abstract and Concrete", he blends theory with examples to support "active learning", making abstract algebra more accessible for advanced undergraduate and beginning graduate students.
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