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Term algebra. In universal algebra and mathematical logic, a term algebra is a freely generated algebraic structure over a given signature. [ 1][ 2] For example, in a signature consisting of a single binary operation, the term algebra over a set X of variables is exactly the free magma generated by X. Other synonyms for the notion include ...
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values true and false, usually denoted 1 and 0, whereas in elementary algebra the values of the variables are numbers. Second, Boolean algebra uses logical operators such ...
Uniformed Services University of the Health Sciences (USU) is a health science university and professional school of the U.S. federal government.The primary mission of the school is to prepare graduates for service to the U.S. at home and abroad as uniformed health professionals, scientists and leaders; by conducting cutting-edge, military-relevant research; by leading the Military Health ...
Universal generalization / instantiation. Existential generalization / instantiation. In propositional logic and Boolean algebra, De Morgan's laws, [ 1][ 2][ 3] also known as De Morgan's theorem, [ 4] are a pair of transformation rules that are both valid rules of inference. They are named after Augustus De Morgan, a 19th-century British ...
In elementary algebra, FOIL is a mnemonic for the standard method of multiplying two binomials [ 1] —hence the method may be referred to as the FOIL method. The word FOIL is an acronym for the four terms of the product: The general form is. Note that a is both a "first" term and an "outer" term; b is both a "last" and "inner" term, and so forth.
Algebra. Elementary algebra studies which values solve equations formed using arithmetical operations. Abstract algebra studies algebraic structures, like the ring of integers given by the set of integers together with operations of addition ( ) and multiplication ( ). Algebra is the branch of mathematics that studies certain abstract systems ...
The complex numbers form a 2-dimensional commutative algebra over the real numbers. The quaternions form a 4-dimensional associative algebra over the reals (but not an algebra over the complex numbers, since the complex numbers are not in the center of the quaternions). Every polynomial ring R[x 1, ..., x n] is a commutative R-algebra.
Fundamentals. The algebra of sets is the set-theoretic analogue of the algebra of numbers. Just as arithmetic addition and multiplication are associative and commutative, so are set union and intersection; just as the arithmetic relation "less than or equal" is reflexive, antisymmetric and transitive, so is the set relation of "subset".