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Algebra is the branch of mathematics that studies certain abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic operations other than the standard arithmetic operations, such as addition and multiplication.
Probably the hardest part of writing a Wikipedia article on a mathematical topic, and generally any Wikipedia article, is addressing a reader's level of knowledge. For example, when writing about a field in the context of abstract algebra, is it best to assume that a reader is already familiar with group theory? A general approach to writing an ...
Secondary students are taught structured essay formats to improve their writing skills; admission essays are often used by universities in selecting applicants, and in the humanities and social sciences essays are often used as a way of assessing the performance of students during final exams.
Equally important as the use or lack of symbolism in algebra was the degree of the equations that were addressed. Quadratic equations played an important role in early algebra; and throughout most of history, until the early modern period, all quadratic equations were classified as belonging to one of three categories.
Academic writing often features prose register that is conventionally characterized by "evidence...that the writer(s) have been persistent, open-minded and disciplined in the study"; that prioritizes "reason over emotion or sensual perception"; and that imagines a reader who is "coolly rational, reading for information, and intending to formulate a reasoned response."
[1] Elementary algebra, also known as high school algebra or college algebra, [2] encompasses the basic concepts of algebra. It is often contrasted with arithmetic : arithmetic deals with specified numbers , [ 3 ] whilst algebra introduces variables (quantities without fixed values).
One example is the parallel postulate, which is neither provable nor refutable from the remaining axioms of Euclidean geometry. Mathematicians have shown there are many statements that are neither provable nor disprovable in Zermelo–Fraenkel set theory with the axiom of choice (ZFC), the standard system of set theory in mathematics (assuming ...