Knowledge of Different Perspectives on Algebra

"Candidates emphasize relationships among quantities including functions, ways of representing mathematical relationships, and the analysis of change."

Reflection on the Standard:

One of the courses I have taken to fulfill this standard is Linear Algebra. This course covered systems of linear equations, matrix theory, vector spaces, linear transformations, determinants, eigenvalues, and eigenvectors. In this course I applied the fundamental ideas of linear algebra (meeting indicator 10.2) and used technological tools, especially Maple, to explore algebraic ideas and representations (meeting indicator 10.5).

Another course I have taken to fulfill this standard is Abstract Algebra. This course covered algebraic structures, elementary properties of numbers, polynomials, groups, rings, integral domains, and fields. In this course I applied the major concepts of abstract algebra to prove algebraic operations and formally analyze algebraic structures (meeting indicator 10.3) and gained an understanding of the historical development of algebra by reading Unknown Quantity (Derbyshire, 2006) (meeting indicator 10.6).


To illustrate this standard, I have selected a research paper on symmetric polynomials that I wrote in Abstract Algebra. Please click the artifact icon below to view this paper:

Explanation of Artifact in Relation to the Standard:

In my paper, I describe the influence of Isaac Newton's ideas about symmetric and elementary polynomials on the development of the Fundamental Theorem of Symmetric Polynomials, an important theorem in algebra (meeting indicator 10.6).

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