Binary Operations - Introductory Abstract Algebra (Undergraduate Advanced)
[University] Introduction to Abstract AlgebraMaster the foundational structures of modern mathematics. This learning track provides a direct path through abstract algebra, from basic sets to groups, rings, and fields. It delivers the analytical framework essential for advanced theoretical work.
This programme is for undergraduate students in mathematics, computer science, or theoretical physics. It is also essential for professionals requiring a rigorous grasp of algebraic structures for work in cryptography, algorithm design, or quantum computing.
Construct rigorous proofs and analyse the properties of groups, rings, and fields. This programme directly prepares you for postgraduate studies in pure mathematics and for advanced technical roles in cryptography and algorithm theory.
Master the foundational structures of modern mathematics. This learning track provides a direct path through abstract algebra, from basic sets to groups, rings, and fields. It delivers the analytical framework essential for advanced theoretical work. This programme is for undergraduate students in mathematics, computer science, or theoretical physics. It is also essential for professionals requiring a rigorous grasp of algebraic structures for work in cryptography, algorithm design, or quantum computing. Construct rigorous proofs and analyse the properties of groups, rings, and fields. This programme directly prepares you for postgraduate studies in pure mathematics and for advanced technical roles in cryptography and algorithm theory.
Course Chapters
1. Introduction
Definition of binary operations, signs and symbols, binary operation on a set.
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2. Closure
Definition of closure property, examples of closure in binary operations.
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3. Asssociativity
Definition of associativity, notational conventions, examples of associative operations.
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4. Commutativity
Definition of commutativity, examples of commutative operations.
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5. Distributivity
Definition of distributivity, examples involving one operation distributing over another.
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6. Identity Element
Definition of identity element, examples in various binary operations.
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7. Inverse Element
Definition of inverse element, examples of invertibility under binary operations.
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8. Cayley Tables
Meaning and construction of Cayley tables, Latin square property, related structural concepts.
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