History of Elementary Algebra - Modern Algebra - Abstract Algebra

Abstract Algebra

The ability to do algebra is a skill cultivated in mathematics education. As explained by Andrew Warwick, Cambridge University students in the early 19th century practiced "mixed mathematics", doing exercises based on physical variables such as space, time, and weight. Over time the association of variables with physical quantities faded away as mathematical technique grew. Eventually mathematics was concerned completely with abstract polynomials, complex numbers, hypercomplex numbers and other concepts. Application to physical situations was then called applied mathematics or mathematical physics, and the field of mathematics expanded to include abstract algebra. For instance, the issue of constructible numbers showed some mathematical limitations, and the field of Galois theory was developed.

Read more about this topic:  History Of Elementary Algebra, Modern Algebra

Other articles related to "algebra, abstract algebra, algebras":

Algebra
... Algebra is related to mathematics, but for historical reasons, the word "algebra" has three meanings as a bare word, depending on the context ... As a single word, "algebra" can mean Use of letters and symbols to represent values and their relations, especially for solving equations ... This is also called "Elementary algebra" ...
Field With One Element
... F1 are only suggestive, as there is no field with one element in classical abstract algebra ... that there should be a way to replace sets and operations, the traditional building blocks for abstract algebra, with other, more flexible objects ... Instead, most proposed theories of F1 replace abstract algebra entirely ...
Abstract Algebra - Applications
... Because of its generality, abstract algebra is used in many fields of mathematics and science ... are Lie groups, and the study of Lie groups and Lie algebras reveals much about the physical system for instance, the number of force carriers in a theory is equal to ...
Emmy Noether - Biography - Seminal Work in Abstract Algebra
... upon physics, among mathematicians she is best remembered for her seminal contributions to abstract algebra ... to Noether's Collected Papers, The development of abstract algebra, which is one of the most distinctive innovations of twentieth century mathematics, is largely due to her – in published ... Noether's groundbreaking work in algebra began in 1920 ...

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