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MATH 4033
Abstract Algebra I

Lecture Notes

The following are lecture notes designed for the abstract algebra class at ATU. The topics follow the partition of the textbook "Modern Algebra" by John R. Durbin. These notes have been improved and will continue to be. Please feel free to browse through them.

To Students: BEWARE! The notes posted here are those that I write for myself to bring to class so that if you miss class, you can see approximately what we covered. I will NOT be posting notes as they would appear in class. There will be many missing examples and explanations. This is not a replacement for coming to class and taking notes yourself.
§ 0 Preliminary Notions
§ 1 The Concept of a Mapping
§ 2 Composition. Invertible Mappings
§ 3 Binary Operations
§ 4 Composition of Mappings as a Binary Operation
§ 5 Definition and Examples of Groups
§ 6 Permutation Groups
§ 7 Subgroups
§ 8 Symmetry Groups
§ 9 Equivalence Relations
§ 10 The Division Algorithm. Congruence Modulo n
§ 11 Arithmetic Modulo n
§ 12 Greatest Common Divisors. The Euclidean Algorithm.
§ 13 The Fundamental Theorem of Arithmetic. Euler's Phi Function.
§ 14 Elementary Properties of Groups.
§ 15 Generated Subgroups. Direct Product of Groups.
§ 16 Cosets.
§ 17 Lagrange's Theorem.
§ 18 Isomorphism
§ 19 More Properties of Isomorphisms
§ 20 Cayley's Theorem
§ 21 Homomorphisms and Normal Subgroups
§ 22 Quotient Groups
§ 23 Isomorphism Theorems
§ 24 Rings: Definition and Basic Results
§ 25 Integral Domains. Subrings
§ 26 Ideals and Quotient Rings

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Last updated:April 08, 2017