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Machines with intelligence have the potential to use their intelligence to make ethical decisions. The field of machine ethics provides machines with ethical principles and procedures for resolving ethical dilemmas. [304] The field of machine ethics is also called computational morality, [304] and was founded at an AAAI symposium in 2005. [305]
The study of functions of a complex variable is known as complex analysis and has enormous practical use in applied mathematics as well as in other branches of mathematics. Often, the most natural proofs for statements in real analysis or even number theory employ techniques from complex analysis (see prime number theorem for an example).
The Math Images Project is a wiki collaboration between Swarthmore College, the Math Forum at Drexel University, and the National Science Digital Library. The project aims to introduce the public to mathematics through beautiful and intriguing images found throughout the fields of math. The Math Images Project runs on MediaWiki software, as ...
A complex system is a system composed of many components which may interact with each other. [1] Examples of complex systems are Earth's global climate, organisms, the human brain, infrastructure such as power grid, transportation or communication systems, complex software and electronic systems, social and economic organizations (like cities), an ecosystem, a living cell, and, ultimately, for ...
Simple machines provide a "vocabulary" for understanding more complex machines. The idea that a machine can be decomposed into simple movable elements led Archimedes to define the lever, pulley and screw as simple machines. By the time of the Renaissance this list increased to include the wheel and axle, wedge and inclined plane.
Much of the mathematics of chaos theory involves the repeated iteration of simple mathematical formulas, which would be impractical to do by hand. Electronic computers made these repeated calculations practical, while figures and images made it possible to visualize these systems.
Sierpiński Carpet - Infinite perimeter and zero area Mandelbrot set at islands The Mandelbrot set: its boundary is a fractal curve with Hausdorff dimension 2. (Note that the colored sections of the image are not actually part of the Mandelbrot Set, but rather they are based on how quickly the function that produces it diverges.)
The time required by a deterministic Turing machine on input is the total number of state transitions, or steps, the machine makes before it halts and outputs the answer ("yes" or "no"). A Turing machine M {\displaystyle M} is said to operate within time f ( n ) {\displaystyle f(n)} if the time required by M {\displaystyle M} on each input of ...