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The use of multiple representations supports and requires tasks that involve decision-making and other problem-solving skills. [2] [3] [4] The choice of which representation to use, the task of making representations given other representations, and the understanding of how changes in one representation affect others are examples of such mathematically sophisticated activities.
Automated theorem proving (also known as ATP or automated deduction) is a subfield of automated reasoning and mathematical logic dealing with proving mathematical theorems by computer programs. Automated reasoning over mathematical proof was a major motivating factor for the development of computer science.
Reasoning mechanisms are based on graph notions, basically the classical notion of graph homomorphism; this allows, in particular, to link basic reasoning problems to other fundamental problems in computer science (e.g., problems concerning conjunctive queries in relational databases, or constraint satisfaction problems).
McNamara's interest in quantitative figures is also seen in Project 100,000 aka McNamara's Folly: by lowering admission standards to the military, enlistment was increased. Key to this decision was the idea that one soldier is, in the abstract, more or less equal to another, and that with the right training and superior equipment, he would ...
Quantitative research is a research strategy that focuses on quantifying the collection and analysis of data. [1] It is formed from a deductive approach where emphasis is placed on the testing of theory, shaped by empiricist and positivist philosophies.
The field of numerical analysis predates the invention of modern computers by many centuries. Linear interpolation was already in use more than 2000 years ago. Many great mathematicians of the past were preoccupied by numerical analysis, [5] as is obvious from the names of important algorithms like Newton's method, Lagrange interpolation polynomial, Gaussian elimination, or Euler's method.
Uncertainty quantification (UQ) is the science of quantitative characterization and estimation of uncertainties in both computational and real world applications. It tries to determine how likely certain outcomes are if some aspects of the system are not exactly known.
In the philosophy of Immanuel Kant, analytic reasoning represents judgments made upon statements that are based on the virtue of the statement's own content. No particular experience, beyond an understanding of the meanings of words used, is necessary for analytic reasoning. [3] For example, "John is a bachelor." is a given