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Rigor is a cornerstone quality of mathematics, and can play an important role in preventing mathematics from degenerating into fallacies. well-behaved An object is well-behaved (in contrast with being Pathological ) if it satisfies certain prevailing regularity properties, or if it conforms to mathematical intuition (even though intuition can ...
Also called infinitesimal calculus A foundation of calculus, first developed in the 17th century, that makes use of infinitesimal numbers. Calculus of moving surfaces an extension of the theory of tensor calculus to include deforming manifolds. Calculus of variations the field dedicated to maximizing or minimizing functionals. It used to be called functional calculus. Catastrophe theory a ...
An academic discipline or field of study is a branch of knowledge, taught and researched as part of higher education.A scholar's discipline is commonly defined by the university faculties and learned societies to which they belong and the academic journals in which they publish research.
Theoretical astronomy, theoretical physics, theoretical and applied mechanics, continuum mechanics, mathematical chemistry, actuarial science, computer science, computational science, data science, operations research, quantitative biology, control theory, econometrics, geophysics and mathematical geosciences are likewise other fields often ...
Mathematicians study and research in all the different areas of mathematics. The publication of new discoveries in mathematics continues at an immense rate in hundreds of scientific journals, many of them devoted to mathematics and many devoted to subjects to which mathematics is applied (such as theoretical computer science and theoretical ...
An academic discipline or academic field is a subdivision of knowledge that is taught and researched at the college or university level. Disciplines are defined (in part) and recognized by the academic journals in which research is published, and the learned societies and academic departments or faculties within colleges and universities to which their practitioners belong.
Mathematics, in the broadest sense, is just a synonym of formal science; but traditionally mathematics means more specifically the coalition of four areas: arithmetic, algebra, geometry, and analysis, which are, to some degree, the study of quantity, structure, space, and change respectively.
These results include previously proved theorems, axioms, and—in case of abstraction from nature—some basic properties that are considered true starting points of the theory under consideration. [1] Mathematics is essential in the natural sciences, engineering, medicine, finance, computer science, and the social sciences. Although ...