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Dept. of Mathematics, Ramakrishna Mission Vivekananda Educational and Research Institute (RKMVERI) has organised an colloquia on “Transition from High-School Algebra to College Algebra” by Professor Amartya Kumar Dutta on 23 September 2024.

Title: Transition from High-School Algebra to College Algebra

Abstract

The algebra taught up to the higher secondary stage is a part of “Classical Algebra” which is primarily a study of polynomials: solutions of polynomial equations, relations between the roots and coefficients of polynomials.  At the college level, students get introduced to “Modern Algebra” or “Abstract Algebra” which is primarily a study of abstract structures like groups, fields, rings and ideals.  The late Prof. S.S. Abhyankar gave the names “High-School Algebra” and “College Algebra” to “Classical Algebra” and “Abstract Algebra” respectively.

Though we use the common name “Algebra”, the High-School Algebra and College Algebra may appear to the students to be completely different branches of study,  mysteriously linked  by a common name.  In this talk we  shall try to indicate a link between the two: First, we will discuss the solution of the cubic polynomial and how the investigations on the higher degree polynomials brought into the forefront the idea of “permutation” of roots and thus, implicitly, the idea of “group action”.  Next, we will indicate how  the ideas of groups and fields emerged from these investigations.