Experimental
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1.
Experimental mathematics is an approach to mathematics in which numerical computation is used to investigate mathematical objects and identify properties and patterns. It has been defined as "that branch of mathematics that concerns itself ultimately with the codification and transmission of insights within the mathematical community through the use of experimental (in either the Galilean, Baconian, Aristotelian or Kantian sense) exploration of conjectures and more informal beliefs and a careful analysis of the data acquired in this pursuit. 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", like defined as follows discovering new patterns and relationships, using graphical displays to suggest underlying mathematical principles, etc. Experimental mathematics makes use of numerical methods to calculate approximate values for integrals and infinite series.If a counterexample is being sought or a large-scale proof by exhaustion is being attempted, distributed computing techniques may be used to divide the calculations between multiple computers. Experimental mathematics software usually includes error detection and correction mechanisms, integrity checks and redundant calculations designed to minimise the possibility of results being invalidated by a hardware or software error. Applications and examples of experimental mathematics include searching for a counterexample to a conjecture, Finding new examples of numbers or objects with particular properties, Finding serendipitous numerical patterns, Use of computer programs to check a large but finite number of cases to complete a computer-assisted proof by exhaustion, etc.
2. a. Computational science (also scientific computing or scientific computation) is concerned with constructing mathematical models and quantitative analysis techniques and using computers to analyze and solve scientific problems. In practical use, it is typically the application of computer simulation and other forms of computation from numerical analysis and theoretical computer science to problems in various scientific disciplines. b. Computational science is the application of computational and numerical techniques to solve large and complex problems. c. Computational science refers to the use of computers, networks, storage devices, software, and algorithms to solve problems, do simulations, build things, or create new knowledge.
Experimental mathematics is an approach to mathematics in which numerical computation is used to investigate mathematical objects and identify properties and patterns. It has been defined as "that branch of mathematics that concerns itself ultimately with the codification and transmission of insights within the mathematical community through the use of experimental (in either the Galilean, Baconian, Aristotelian or Kantian sense) exploration of conjectures and more informal beliefs and a careful analysis of the data acquired in this pursuit. 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", like defined as follows discovering new patterns and relationships, using graphical displays to suggest underlying mathematical principles, etc. Experimental mathematics makes use of numerical methods to calculate approximate values for integrals and infinite series.If a counterexample is being sought or a large-scale proof by exhaustion is being attempted, distributed computing techniques may be used to divide the calculations between multiple computers. Experimental mathematics software usually includes error detection and correction mechanisms, integrity checks and redundant calculations designed to minimise the possibility of results being invalidated by a hardware or software error. Applications and examples of experimental mathematics include searching for a counterexample to a conjecture, Finding new examples of numbers or objects with particular properties, Finding serendipitous numerical patterns, Use of computer programs to check a large but finite number of cases to complete a computer-assisted proof by exhaustion, etc.
2. a. Computational science (also scientific computing or scientific computation) is concerned with constructing mathematical models and quantitative analysis techniques and using computers to analyze and solve scientific problems. In practical use, it is typically the application of computer simulation and other forms of computation from numerical analysis and theoretical computer science to problems in various scientific disciplines. b. Computational science is the application of computational and numerical techniques to solve large and complex problems. c. Computational science refers to the use of computers, networks, storage devices, software, and algorithms to solve problems, do simulations, build things, or create new knowledge.
