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Author(s):

Sharanjan Kumar Gargari
Keywords:

Group Theory, Clock Arithmetic, Modular Arithmetic, Cyclic Group, Real-Life Applications
Abstract:
Group Theory Is One Of The Most Fundamental Branches Of Modern Algebra And Plays An Important Role In Various Areas Of Mathematics And Science. However, At The Undergraduate Level, It Is Often Perceived As A Highly Abstract Subject With Little Connection To Real-life Situations. This Paper Aims To Reduce This Gap By Presenting A Simple And Intuitive Real-life Example Of Group Theory Through The Working Of A Clock. By Modeling The Clock Using Addition Modulo 12, The Study Demonstrates That The Set Of Clock Hours Forms A Cyclic Abelian Group. The Paper Systematically Verifies All Group Axioms And Explains How Everyday Time Calculations Naturally Follow Group-theoretic Principles. The Objective Is Not To Introduce New Theoretical Results, But To Strengthen Conceptual Understanding And Show That Group Theory Is Essentially The Study Of Patterns That Appear In Daily Life. This Work Is Written At A B.Sc. Level And Is Intended To Help Beginners Appreciate The Practical Relevance Of Abstract Algebra.