Knowledge Sharing:
1. A mathematical model is a description of a system using mathematical concepts and language.
2. Mathematical models are used in the natural sciences (such as physics, biology, earth science, meteorology) and engineering disciplines (such as computer science, artificial intelligence), as well as in the social sciences (such as economics, psychology, sociology, political science).
3. Physicists, engineers, statisticians, operations research analysts, and economists use mathematical models most extensively.
4. A model may help to explain a system and to study the effects of different components, and to make predictions about behaviour.
5. In many cases, the quality of a scientific field depends on how well the mathematical models developed on the theoretical side agree with results of repeatable experiments.
6. Lack of agreement between theoretical mathematical models and experimental measurements often leads to important advances as better theories are developed.
7. Mathematical models can take many forms, including but not limited to dynamical systems, statistical models, differential equations, or game theoretic models.
8. Mathematical models are usually composed of relationships and variables. Relationships can be described by operators, such as algebraic operators, functions, differential operators, etc. Variables are abstractions of system parameters of interest, that can be quantified.
9. In mathematics, computer science and operations research, mathematical optimization (alternatively, optimization or mathematical programming) is the selection of a best element (with regard to some criteria) from some set of available alternatives.
10. optimization includes finding "best available" values of some objective function given a defined domain (or a set of constraints), including a variety of different types of objective functions and different types of domains.
11. In a mathematical programming model, if the objective functions and constraints are represented entirely by linear equations, then the model is regarded as a linear model. If one or more of the objective functions or constraints are represented with a nonlinear equation, then the model is known as a nonlinear model.
12. A dynamic model accounts for time-dependent changes in the state of the system, while a static (or steady-state) model calculates the system in equilibrium, and thus is time-invariant. Dynamic models typically are represented by differential equations.
14. A discrete model treats objects as discrete, such as the particles in a molecular model or the states in a statistical model; while a continuous model represents the objects in a continuous manner, such as the velocity field of fluid in pipe flows, temperatures and stresses in a solid, and electric field that applies continuously over the entire model due to a point charge.
15. A deductive model is a logical structure based on a theory. An inductive model arises from empirical findings and generalization from them. The floating model rests on neither theory nor observation, but is merely the invocation of expected structure.
16. Mathematical economics is the application of mathematical methods to represent theories and analyze problems in economics.
17. Much of economic theory is currently presented in terms of mathematical economic models, a set of stylized and simplified mathematical relationships asserted to clarify assumptions and implications.
18.
About Game Theory:
1. Game theory is mainly used in economics, political science, and psychology, as well as logic, computer science, biology and Poker
2. To be fully defined, a game must specify the following elements: the players of the game, the information and actions available to each player at each decision point, and the payoffs for each outcome.
3. These equilibrium strategies determine an equilibrium to the game—a stable state in which either one outcome occurs or a set of outcomes occur with known probability.
4.
People:
John von Neumann /vɒn ˈnɔɪmən/ (Hungarian: Neumann János (Hungarian pronunciation: [ˈnɒjmɒn ˈjaːnoʃ ˈlɒjoʃ]); December 28, 1903 – February 8, 1957) was a Hungarian-American pure and applied mathematician, physicist, inventor, and polymath.
Types:
dynamical systems,
statistical models,
differential equations,
game theoretic models.
Keys:
Linear vs Nonlinear
Static vs Dynamic
Explicit vs Implicit
Discrete vs Continuous
Deterministic vs Probabilistic
Deductive, Inductive, or Floating
References:
https://en.wikipedia.org/wiki/Mathematical_model
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