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TI-95
The TI-95, also called the TI-95 PROCALC, is a keystroke programmable calculator and was introduced in 1987 by Texas Instruments. It was rather large, measuring 3.7" by 8" by 1" and had a 16-character alphanumeric display for the main display, and a set of five 3-character displays for use as menu items. It had 8 kB of onboard RAM, capable of being partitioned by the user between program steps for the built-in program editor, numerically-labelled registers, and file memory. It could also be connected to PC-324 compatible printers. The calculator came with a hard carrying case which closes around it. Compatible ROM and extra RAM could be placed in the expansion slot in the upper right corner of the device, which came from the factory with a dummy protector cartridge labelled "ROM/RAM". Texas Instruments would release three compatible ROM cartridges, one containing advanced mathematics functions such as the Gamma function and Newton's method labeled Mathematics, a second contain ...
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Texas Instruments
Texas Instruments Incorporated (TI) is an American multinational semiconductor company headquartered in Dallas, Texas. It is one of the top 10 semiconductor companies worldwide based on sales volume. The company's focus is on developing analog chips and embedded processors, which account for more than 80% of its revenue. TI also produces digital light processing (DLP) technology and education technology products including calculators, microcontrollers, and multi-core processors. Texas Instruments emerged in 1951 after a reorganization of Geophysical Service Incorporated, a company founded in 1930 that manufactured equipment for use in the seismic industry, as well as defense electronics. TI produced the world's first commercial silicon transistor in 1954, and the same year designed and manufactured the first transistor radio. Jack Kilby invented the integrated circuit in 1958 while working at TI's Central Research Labs. TI also invented the hand-held calculator in 1967, and intr ...
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Complex Number
In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the form a + bi, where and are real numbers. Because no real number satisfies the above equation, was called an imaginary number by René Descartes. For the complex number is called the , and is called the . The set of complex numbers is denoted by either of the symbols \mathbb C or . Despite the historical nomenclature, "imaginary" complex numbers have a mathematical existence as firm as that of the real numbers, and they are fundamental tools in the scientific description of the natural world. Complex numbers allow solutions to all polynomial equations, even those that have no solutions in real numbers. More precisely, the fundamental theorem of algebra asserts that every non-constant polynomial equation with real or complex coefficie ...
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Kendall's Tau
In statistics, the Kendall rank correlation coefficient, commonly referred to as Kendall's τ coefficient (after the Greek letter τ, tau), is a statistic used to measure the ordinal association between two measured quantities. A τ test is a non-parametric statistics, non-parametric hypothesis test for statistical dependence based on the τ coefficient. It is a measure of rank correlation: the similarity of the orderings of the data when ranked by each of the quantities. It is named after Maurice Kendall, who developed it in 1938, though Gustav Fechner had proposed a similar measure in the context of time series in 1897. Intuitively, the Kendall correlation between two variables will be high when observations have a similar (or identical for a correlation of 1) Ranking, rank (i.e. relative position label of the observations within the variable: 1st, 2nd, 3rd, etc.) between the two variables, and low when observations have a dissimilar (or fully different for a correlation of −1 ...
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Student's T-test
Student's ''t''-test is a statistical test used to test whether the difference between the response of two groups is statistically significant or not. It is any statistical hypothesis test in which the test statistic follows a Student's ''t''-distribution under the null hypothesis. It is most commonly applied when the test statistic would follow a normal distribution if the value of a scaling term in the test statistic were known (typically, the scaling term is unknown and is therefore a nuisance parameter). When the scaling term is estimated based on the data, the test statistic—under certain conditions—follows a Student's ''t'' distribution. The ''t''-test's most common application is to test whether the means of two populations are significantly different. In many cases, a ''Z''-test will yield very similar results to a ''t''-test because the latter converges to the former as the size of the dataset increases. History The term "''t''-statistic" is abbreviated from " ...
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Analysis Of Variance
Analysis of variance (ANOVA) is a family of statistical methods used to compare the Mean, means of two or more groups by analyzing variance. Specifically, ANOVA compares the amount of variation ''between'' the group means to the amount of variation ''within'' each group. If the between-group variation is substantially larger than the within-group variation, it suggests that the group means are likely different. This comparison is done using an F-test. The underlying principle of ANOVA is based on the law of total variance, which states that the total variance in a dataset can be broken down into components attributable to different sources. In the case of ANOVA, these sources are the variation between groups and the variation within groups. ANOVA was developed by the statistician Ronald Fisher. In its simplest form, it provides a statistical test of whether two or more population means are equal, and therefore generalizes the Student's t-test#Independent two-sample t-test, ''t''- ...
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Chi-squared Distribution
In probability theory and statistics, the \chi^2-distribution with k Degrees of freedom (statistics), degrees of freedom is the distribution of a sum of the squares of k Independence (probability theory), independent standard normal random variables. The chi-squared distribution \chi^2_k is a special case of the gamma distribution and the univariate Wishart distribution. Specifically if X \sim \chi^2_k then X \sim \text(\alpha=\frac, \theta=2) (where \alpha is the shape parameter and \theta the scale parameter of the gamma distribution) and X \sim \text_1(1,k) . The scaled chi-squared distribution s^2 \chi^2_k is a reparametrization of the gamma distribution and the univariate Wishart distribution. Specifically if X \sim s^2 \chi^2_k then X \sim \text(\alpha=\frac, \theta=2 s^2) and X \sim \text_1(s^2,k) . The chi-squared distribution is one of the most widely used probability distributions in inferential statistics, notably in hypothesis testing and in constru ...
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Gamma Function
In mathematics, the gamma function (represented by Γ, capital Greek alphabet, Greek letter gamma) is the most common extension of the factorial function to complex numbers. Derived by Daniel Bernoulli, the gamma function \Gamma(z) is defined for all complex numbers z except non-positive integers, and for every positive integer z=n, \Gamma(n) = (n-1)!\,.The gamma function can be defined via a convergent improper integral for complex numbers with positive real part: \Gamma(z) = \int_0^\infty t^ e^\textt, \ \qquad \Re(z) > 0\,.The gamma function then is defined in the complex plane as the analytic continuation of this integral function: it is a meromorphic function which is holomorphic function, holomorphic except at zero and the negative integers, where it has simple Zeros and poles, poles. The gamma function has no zeros, so the reciprocal gamma function is an entire function. In fact, the gamma function corresponds to the Mellin transform of the negative exponential functi ...
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Numerical Integration
In analysis, numerical integration comprises a broad family of algorithms for calculating the numerical value of a definite integral. The term numerical quadrature (often abbreviated to quadrature) is more or less a synonym for "numerical integration", especially as applied to one-dimensional integrals. Some authors refer to numerical integration over more than one dimension as cubature; others take "quadrature" to include higher-dimensional integration. The basic problem in numerical integration is to compute an approximate solution to a definite integral :\int_a^b f(x) \, dx to a given degree of accuracy. If is a smooth function integrated over a small number of dimensions, and the domain of integration is bounded, there are many methods for approximating the integral to the desired precision. Numerical integration has roots in the geometrical problem of finding a square with the same area as a given plane figure ('' quadrature'' or ''squaring''), as in the quadrature of t ...
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Keystroke Programming
Keystroke programming describes a specific way of programming by which each keystroke on a device or application is recorded in some way and then played back so that the recorded key-presses can be repeated multiple times. Keystroke programming is most commonly but not exclusively found in programmable calculators—there are keystroke-programmable software applications, too, such as Vim. TI calculator example The Texas Instruments TI-58/TI-58C/TI-59 calculators were programmable, and program storage took the form of a sequence of codes which (mostly) corresponded to the position of keys on the calculator keypad. Here is a simplified diagram of the basic key layout: Each key is assigned a two-digit code; for most (but not all) keys, the tens digit comes from the row number (as indicated down the left of the table) and the units digit comes from the column number (as indicated across the top of the table). Now consider a very simple program, which adds 2 to the number being ...
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Pocket Computer
A pocket computer is a class of handheld computer characterized by very short displays (typically accommodating only one or a handful of lines of text) and calculator-style alphanumeric keypads. Pocket computers occupy a small footprint, allowing the unit to be comfortably stashed in one's pocket when on the go, and usually weigh less than . Many feature a port for an expansion chassis, allowing the computers to be used with external peripherals. Pocket computers had their peak of popularity in the early 1980s, but sales quickly plateaued and declined in Western markets as consumers became aware of their limitations. In Japan, where they were invented, pocket computers maintained their popularity and continued to be used as teaching aids into the 21st century. History The first pocket computer was the Sharp PC-1211, introduced in March 1980 by Sharp Corporation and sold exclusively in Japan. Later in 1980, the PC-1211 was resold and rebranded by Tandy Corporation in the Unite ...
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Chemical Engineering
Chemical engineering is an engineering field which deals with the study of the operation and design of chemical plants as well as methods of improving production. Chemical engineers develop economical commercial processes to convert raw materials into useful products. Chemical engineering uses principles of chemistry, physics, mathematics, biology, and economics to efficiently use, produce, design, transport and transform energy and materials. The work of chemical engineers can range from the utilization of nanotechnology and nanomaterials in the laboratory to large-scale industrial processes that convert chemicals, raw materials, living cells, microorganisms, and energy into useful forms and products. Chemical engineers are involved in many aspects of plant design and operation, including safety and hazard assessments, process engineering, process design and analysis, modeling and simulation, modeling, control engineering, chemical reaction engineering, nuclear engineering, biologi ...
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