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The objectives of experimental mathematics are "to generate understanding and insight; to generate and confirm or confront conjectures; and generally to make mathematics more tangible, lively and fun for both the professional researcher and the novice". [5] The uses of experimental mathematics have been defined as follows: [6]
Scientific method – body of techniques for investigating phenomena and acquiring new knowledge, as well as for correcting and integrating previous knowledge. It is based on observable , empirical , reproducible , measurable evidence , and subject to the laws of reasoning .
The history of scientific method considers changes in the methodology of scientific inquiry, not the history of science itself. The development of rules for scientific reasoning has not been straightforward; scientific method has been the subject of intense and recurring debate throughout the history of science, and eminent natural philosophers and scientists have argued for the primacy of ...
The effects of inbreeding depression, while still relatively small compared to other factors (and thus difficult to control for in a scientific experiment), become more noticeable if isolated and maintained for several generations. [402] Having sex before a sporting event or contest is not physiologically detrimental to performance. [403]
Design of Experiments: A systematic, rigorous approach to engineering problem-solving that applies principles and techniques at the data collection stage so as to ensure the generation of valid, defensible, and supportable engineering conclusions [1] Design Point: A single combination of settings for the independent variables of an experiment.
Inductive reasoning refers to a variety of methods of reasoning in which broad generalizations or principles are derived from a set of observations. [1] [2] Unlike deductive reasoning (such as mathematical induction), where the conclusion is certain, given the premises are correct, inductive reasoning produces conclusions that are at best probable, given the evidence provided.
Francis Bacon, articulating inductivism in England, is often falsely stereotyped as a naive inductivist. [11] [12] Crudely explained, the "Baconian model" advises to observe nature, propose a modest law that generalizes an observed pattern, confirm it by many observations, venture a modestly broader law, and confirm that, too, by many more observations, while discarding disconfirmed laws. [13]
Inductive probability attempts to give the probability of future events based on past events. It is the basis for inductive reasoning, and gives the mathematical basis for learning and the perception of patterns.