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Abstract Algebra I
Abstract algebra is a fascinating area of study within mathematics that explores the intricacies of algebraic structures such as groups, rings, and fields. These structures are defined using abstract axioms, and the focus is on understanding their properties independently of any specific mathematical objects or physical systems. It is a highly abstract and theoretical field, but one that has practical applications in areas such as computer science, physics, chemistry and engineering.
- Author
- Pamini Thangarajah
- Publisher
- Mount Royal University
- Source
- LibreTexts
- License
- CC BY-NC-SA
- Language
- EN
- Category
- Basic Sciences
Contents· 50 sections
- Chapter 0: Preliminaries
- 0.0: Introduction to proofs
- 0.1: Sets
- 0.2: Relations
- 0.3: Functions
- 0.5: Proof Templates (Summary)
- 0E: Exercises
- Chapter 1: Integers
- 1.1: Division Algorithm
- 1.2: Greatest common divisor and least common multiple
- 1.3: Primes
- 1.4: Integers modulo n
- 1.5 Linear Congruence
- 1E: Exercises
- Chapter 2: Groups
- 2.1: Introduction to Group
- 2.2: Properties of Group Elements
- 2.3: Subgroups
- 2.4: Cyclic groups
- 2E: Exercises
- Chapter 3: Permutation Groups
- 3.1: Symmetric Groups
- 3.2: Alternating Groups
- 3.3: Dihedral Groups (Group of Symmetries)
- 3E: Exercises
- Chapter 4: Cosets, special groups, and homomorphisms
- 4.1: Cosets and Lagranges Theorem
- 4.2: Normal Supgroups and Factor Groups
- 4.3: Homomorphisms
- 4.4: On Special Groups
- 4.5: Isomorphism Theorems
- 4.6: Classification of Groups
- 4E: Exercises
- Chapter 5: Rings
- 5.1: Introduction to Rings
- 5.2: Ideals and Factor Rings
- 5.3: Ring Homomorphisms
- 5E: Excercises
- Mock Exams (Celebration of Learning)
- Sample final
- Sample test 1
- Sample test 2
- Sample test 4
- Sample Assignments with solution
- Assignment 1
- Assignment 2
- Assignment 3
- Assignment 4
- Assignment 5
- Assignment 6