Algebra - The Gateway to Higher Mathematics



The Gateway - Danilo Rizzuti

 

Algebraic methods not only solve many real life problems, but also are the portal to all higher branches of mathematics. For this reason, algebra rules.

The importance of algebra hinges on its being the gateway to higher mathematics. Indeed, calculus, analysis, and linear algebra, to name a few of the more advanced branches of mathematics, all depend heavily on the rudiments laid out in this discipline. In many respects, calculus is a sort of "glorified algebra," its differential and integral branches being supported by algebraic manipulations and circumnavigations; analysis springs forth from algebraic extensions and requires algebra to prove its underlying theorems; and linear algebra, as it contains the very same word, relies predominantly on the use of algebraic concepts and ideas.

Algebra the Great

Algebra is not just a subject that hides behind a mask of letters and symbols, parading around like some costumed guest at a masquerade ball. Algebra is the arena in which patterns in nature are allowed to be expressed in terms of human quantifiers: the very functions which underpin a vast part of this subject. Indeed a pattern can be thought of as a rule, a model, a relationship between two letters, which transform into the independent and dependent variables of a function. Such is algebra: the intertwining of letters, variables, or changing quantities, that describes nature in all of its resplendence. (...)

Jul 4, 2011
Joe Pagano

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