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In proof by exhaustion, the conclusion is established by dividing it into a finite number of cases and proving each one separately. The number of cases sometimes can become very large. For example, the first proof of the four color theorem was a proof by exhaustion with 1,936 cases. This proof was controversial because the majority of the cases ...
Each entry below is an outline, an introduction to a subject structured as a hierarchical list of the essential points. Each of these outlines focuses on a mathematics or logic. Along with Wikipedia:Contents/Outlines, the outlines on Wikipedia form an all
The following outline is provided as an overview of and topical guide to the scientific method: . Scientific method – body of techniques for investigating phenomena and acquiring new knowledge, as well as for correcting and integrating previous knowledge.
In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. [1] [2] [3] Some conjectures, such as the Riemann hypothesis or Fermat's conjecture (now a theorem, proven in 1995 by Andrew Wiles), have shaped much of mathematical history as new areas of mathematics are developed in order to ...
Examples of unexpected applications of mathematical theories can be found in many areas of mathematics. A notable example is the prime factorization of natural numbers that was discovered more than 2,000 years before its common use for secure internet communications through the RSA cryptosystem. [127]
Neyman believed that hypothesis testing represented a generalization and improvement of significance testing. The rationale for their methods can be found in their collaborative papers. [10] Hypothesis testing involves considering multiple hypotheses and selecting one among them, akin to making a multiple-choice decision.
The Jane Schaffer method is a formula for essay writing that is taught in some U.S. middle schools and high schools.Developed by a San Diego teacher named Jane Schaffer, who started offering training and a 45-day curriculum in 1995, it is intended to help students who struggle with structuring essays by providing a framework.
A statistical significance test starts with a random sample from a population. If the sample data are consistent with the null hypothesis, then you do not reject the null hypothesis; if the sample data are inconsistent with the null hypothesis, then you reject the null hypothesis and conclude that the alternative hypothesis is true. [3]