An Invitation to General Algebra and Universal Constructions by George M. Bergman

About this book :-
This book provide the basic notations and results of general algebra; also, it is a detailed and self-contained introduction to general algebra from the point of view of categories and functors. Starting with a survey, in non-category-theoretic terms, of many familiar and not-so-familiar constructions in algebra (plus two from topology for perspective), the reader is guided to an understanding and appreciation of the general concepts and tools unifying these constructions. A Cook's tour of other universal constructions, ordered sets, induction, and the axiom of Choice, Lattices, closure operators, and Galois connections, categories and functors, universal constructions in category-theoretic terms, set theory, varieties of algebras and adjunctions, algebra and co algebra objects in categories, and functors having adjoins. A large number of exercises, from the routine to the challenging, interspersed through the text, develop the reader's grasp of the material, exhibit applications of the general theory to diverse areas of algebra, and in some cases point to outstanding open questions. Graduate students and researchers wishing to gain fluency in important mathematical constructions will welcome this carefully motivated book. The author takes care in writing full proofs throughout the book and he shows also ways of possible applications.

Book Detail :-
Title: An Invitation to General Algebra and Universal Constructions by George M. Bergman
Publisher: George Bergman
Year: 1998
Pages: 398
Type: PDF
Language: English
ISBN-10 #: 0965521141
ISBN-13 #: 9780965521147
License: Linked Content Owned by Author
Amazon: Amazon

About Author :-
The author George Mark Bergman (born 1943 in Brooklyn, New York) is an algebraist mathematician. He attended Stuyvesant High School in New York City and received his Ph.D. from Harvard University in 1968, under the direction of John Tate. The year before he had been appointed Assistant Professor of mathematics at the University of California, Berkeley, where he has taught ever since, being promoted to Associate Professor in 1974 and to Professor in 1978. His primary research area is algebra, in particular associative rings, universal algebra, category theory and the construction of counterexamples. Mathematical logic is an additional research area. Bergman officially retired in 2009, but is still teaching.[3] His interests beyond mathematics include subjects as diverse as third-party politics and the works of James Joyce. He was designated a member of the Inaugural Class of Fellows of the American Mathematical Society in 2013.

Book Contents :-
1. About the course, and these Notes Part-I Motivation and Examples 2. Making Some Things Precise 3. Free Groups 4. A Cook’s Tour Part-II Basic Tools and Concepts 5. Ordered Sets, Induction, and the Axiom of Choice 6. Lattices, Closure Operators, and Galois Connections 7. Categories and Functors 8. Universal Constructions 9. Varieties of Algebras Part-III More on Adjunctions 10. Algebras, Coalgebras, and Adjunctions Word and Phrase Index Symbol Index

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