Mathematics


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1 The art and science of mathematics, its branches or divisions, the origin and development of mathematics.
2 The distinction of mathematics from physics and metaphysics, its relation to logic.
3 The service of mathematics to dialectic and philosophy, its place in liberal education.
4 The certainty and exactitude of mathematical knowledge, truth in mathematics, the a priori foundations of arithmetic and geometry.
5 The ideal of a universal mathematics, the unification of arithmetic and geometry.
6 The objects of mathematics, ideas or abstractions, number, figure, extension, relation, order.
7 The apprehension of mathematical objects, by intuition, imagination, construction, the forms of time and space.
8 The being of mathematical objects, their real, ideal, or mental existence.
9 Kinds of quantity, magnitude and multitude, continuous and discrete quantities, the problem of the irrational.
10 Method in mathematics, the model of mathematical thought.
11 The conditions and character of demonstration in mathematics, the use of definitions, postulates, axioms, hypotheses, theorems, proofs.
12 The role of construction, its bearing on proof, mathematical existence, and the scope of mathematical inquiry.
13 Analysis and synthesis, function and variable.
14 Symbols and formulas, the attainment of generality.
15 Mathematical techniques.
16 The arithmetic and algebraic processes, algebraic form.
17 The operations of geometry.
18 The use of proportions and equations.
19 The method of exhaustion, the theory of limits and the calculus.
20 The applications of mathematics to physical phenomena, the utility of mathematics.
21 The art of measurement.
22 Mathematical physics, the mathematical structure of nature.
23 The distinction between pure and applied mathematics.


All text from the Outlines is Copyright ©1990 Encyclopedia Britannica Inc.; this electronic edition is Copyright© 2005 by Michael R. Lissack and reproduced by permission.