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Markov Chain

Latest info is most relevant info. What happened today is more important than what happened yesterday. A Markov chain or Markov process is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event .[1][2][3] A countably infinite sequence, in which the chain moves state at discrete time steps, gives a discrete-time Markov chain (DTMC). A continuous-time process is called a continuous-time Markov chain (CTMC). It is named after the Russian mathematician Andrey Markov. Markov chains have many applications as statistical models of real-world processes,[1][4][5][6] such as studying cruise control systems in motor vehicles, queues or lines of customers arriving at an airport, currency exchange rates and animal population dynamics.[7] Markov processes are the basis for general stochastic simulation methods known as Markov chain Monte Carlo, which are used for simulating sampling from comp...
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Algebraic Curve

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Algebraic Curve An algebraic curve over a field is an equation , where is a polynomial in and with coefficients in . A nonsingular algebraic curve is an algebraic curve over which has no singular points over . A point on an algebraic curve is simply a solution of the equation of the curve. A - rational point is a point on the curve, where and are in the field . The following table lists the names of algebraic curves of a given degree.
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Surreal Numbers

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In mathematics , the surreal number system is a totally ordered class containing the real numbers as well as infinite and infinitesimal numbers , respectively larger or smaller in absolute value than any positive real number. The surreals share many properties with the reals, including the usual arithmetic operations (addition, subtraction, multiplication, and division); as such, they form an ordered field . [a] If formulated in Von Neumann–Bernays–Gödel set theory , the surreal numbers are the largest possible ordered field; all other ordered fields, such as the rationals, the reals, the rational functions , the Levi-Civita field , the superreal numbers , and the hyperreal numbers , can be realized as subfields of the surreals. [1] It has also been shown (in Von Neumann–Bernays–Gödel set theory ) that the maximal class hyperreal field is isomorphic to the maximal class surreal field; in theories without the axiom of global choice , this need not be the case, and in such the...
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Sequences & Series

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Arithmetic Mean   In mathematics and statistics, the arithmetic mean (/ˌærɪθˈmɛtɪk ˈmiːn/), or simply the mean or average when the context is clear, is the sum of a collection of numbers divided by the number of numbers in the collection ‎ Definition · ‎ Motivating properties · ‎ Contrast with median · ‎ Generalizations   Arithmetic Sequence   In mathematics, an arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15 … is an arithmetic progression with common difference of 2   Arithmetic Series   noun noun: arithmetic series ; plural noun: arithmetic series a sequence of numbers in which each differs from the preceding by a constant quantity (e.g., 3, 6, 9, 12, etc.; 9, 7, 5, 3, etc.). the relationship between numbers in an arithmetic progression. "the numbers a...
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Mathematicians Top 100

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For example:   Pierre de Fermat was the most brilliant mathematician of his era and, along with Descartes, one of the most influential. Although mathematics was just his hobby (Fermat was a government lawyer), Fermat practically founded Number Theory, and also played key roles in the discoveries of Analytic Geometry and Calculus. Lagrange considered Fermat, rather than Newton or Leibniz, to be the inventor of calculus. Fermat was first to study certain interesting curves, e.g. the "Witch of Agnesi". He was also an excellent geometer (e.g. discovering a triangle's Fermat point), and (in collaboration with Blaise Pascal) discovered probability theory. Fellow geniuses are the best judges of genius, and Blaise Pascal had this to say of Fermat: "For my part, I confess that [Fermat's researches about numbers] are far beyond me, and I am competent only to admire them." E.T. Bell wrote "it can be argued that Fermat was at least Newton's equal as a pure m...
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MIT Mathlets

http://universalcalculus.blogspot.com/2016/10/mit-mathlets.html
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Probability Distribution

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In probability and statistics , a probability distribution is a mathematical function that, stated in simple terms, can be thought of as providing the probability of occurrence of different possible outcomes in an experiment . For instance, if the random variable X is used to denote the outcome of a coin toss ('the experiment'), then the probability distribution of X would take the value 0.5 for X=Heads {\displaystyle {\text{X=Heads}}} , and 0.5 for X=Tails {\displaystyle {\text{X=Tails}}} . In more technical terms, the probability distribution is a description of a random phenomenon in terms of the probabilities of events . Examples of random phenomena can include the results of an experiment or survey . A probability distribution is defined in terms of an underlying sample space , which is the set of all possible outcomes of the random...
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