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Mathematical psychology is an approach to psychological research that is based on mathematical modeling of perceptual, thought, cognitive and motor processes, and on the establishment of law-like rules that relate quantifiable stimulus characteristics with quantifiable behavior (in practice often constituted by task performance).
Word problem from the Līlāvatī (12th century), with its English translation and solution. In science education, a word problem is a mathematical exercise (such as in a textbook, worksheet, or exam) where significant background information on the problem is presented in ordinary language rather than in mathematical notation.
In mathematical logic, algebraic logic is the reasoning obtained by manipulating equations with free variables.. What is now usually called classical algebraic logic focuses on the identification and algebraic description of models appropriate for the study of various logics (in the form of classes of algebras that constitute the algebraic semantics for these deductive systems) and connected ...
A closely related problem is found in some valid natural language arguments whose most obvious translations are invalid in formal logic. For example, the argument "(1) Fury is a horse; (2) therefore Fury is an animal" is valid but the corresponding argument in formal logic from H ( f ) {\displaystyle H(f)} to A ( f ) {\displaystyle A(f)} is ...
Schanuel's conjecture would solve the first of these problems somewhat as it deals with algebraic independence and would indeed confirm that e + π is transcendental. It still revolves around the exponential function, however, and so would not necessarily deal with numbers such as Apéry's constant or the Euler–Mascheroni constant .
Algebra – Branch of mathematics; Algedonics – Branch of psychology that deals with pleasant and unpleasant states of consciousness; Algology – Branch of biology concerned with the study of algae ; Algology – Medical treatment of pain as practiced in Greece and Turkey
In mathematical logic, an algebraic definition is one that can be given using only equations between terms with free variables. Inequalities and quantifiers are specifically disallowed. Saying that a definition is algebraic is a stronger condition than saying it is elementary.
The language of mathematics has a wide vocabulary of specialist and technical terms. It also has a certain amount of jargon: commonly used phrases which are part of the culture of mathematics, rather than of the subject.