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Modern proof theory treats proofs as inductively defined data structures, not requiring an assumption that axioms are "true" in any sense. This allows parallel mathematical theories as formal models of a given intuitive concept, based on alternate sets of axioms, for example axiomatic set theory and non-Euclidean geometry.
Qualitative research is a type of research that aims to gather and analyse non-numerical (descriptive) data in order to gain an understanding of individuals' social reality, including understanding their attitudes, beliefs, and motivation.
It reintroduces the basic assumptions of positivism: the possibility and desirability of objective truth, and the use of experimental methodology. The work of philosophers Nancy Cartwright and Ian Hacking are representative of these ideas. [citation needed] Postpositivism of this type is described in social science guides to research methods. [7]
For qualitative research, the sample size is usually rather small, while quantitative research tends to focus on big groups and collecting a lot of data. After the collection, the data needs to be analyzed and interpreted to arrive at interesting conclusions that pertain directly to the research question.
The team even defeats the Moscow team. Inference: The small city in Siberia is not a small city anymore. The Soviets are working on their own nuclear or high-value secret weapons program. Knowns: The Soviet Union is a command economy: people and material are told where to go and what to do. The small city was remote and historically had never ...
These approaches are a form of qualitative positivism or small q qualitative research, [22] which combine the use of qualitative data with data analysis processes and procedures based on the research values and assumptions of (quantitative) positivism – emphasising the importance of establishing coding reliability and viewing researcher ...
One of the popular examples in computer science is the mathematical models of various machines, an example is the deterministic finite automaton (DFA) which is defined as an abstract mathematical concept, but due to the deterministic nature of a DFA, it is implementable in hardware and software for solving various specific problems. For example ...
Mathematical psychology is an approach to psychological research that is based on mathematical modeling of perceptual, thought, cognitive and motor processes, and on the establishment of law-like rules that relate quantifiable stimulus characteristics with quantifiable behavior (in practice often constituted by task performance).