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Running Total
A running total or rolling total is the summation of a sequence of numbers which is updated each time a new number is added to the sequence, by adding the value of the new number to the previous running total. Another term for it is partial sum. The purposes of a running total are twofold. First, it allows the total to be stated at any point in time without having to sum the entire sequence each time. Second, it can save having to record the sequence itself, if the particular numbers are not individually important. Method Consider the sequence (5, 8, 3, 2). What is the total of this sequence? Answer: 5 + 8 + 3 + 2 = 18. This is arrived at by simple summation of the sequence. Now we insert the number 6 at the end of the sequence to get (5, 8, 3, 2, 6). What is the total of that sequence? Answer: 5 + 8 + 3 + 2 + 6 = 24. This is arrived at by simple summation of the sequence. ''But'' if we regarded 18 as the running total, we need only add 6 to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Summation
In mathematics, summation is the addition of a sequence of numbers, called ''addends'' or ''summands''; the result is their ''sum'' or ''total''. Beside numbers, other types of values can be summed as well: functions, vectors, matrices, polynomials and, in general, elements of any type of mathematical objects on which an operation denoted "+" is defined. Summations of infinite sequences are called series. They involve the concept of limit, and are not considered in this article. The summation of an explicit sequence is denoted as a succession of additions. For example, summation of is denoted , and results in 9, that is, . Because addition is associative and commutative, there is no need for parentheses, and the result is the same irrespective of the order of the summands. Summation of a sequence of only one summand results in the summand itself. Summation of an empty sequence (a sequence with no elements), by convention, results in 0. Very often, the elements of a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Series (mathematics)
In mathematics, a series is, roughly speaking, an addition of Infinity, infinitely many Addition#Terms, terms, one after the other. The study of series is a major part of calculus and its generalization, mathematical analysis. Series are used in most areas of mathematics, even for studying finite structures in combinatorics through generating functions. The mathematical properties of infinite series make them widely applicable in other quantitative disciplines such as physics, computer science, statistics and finance. Among the Ancient Greece, Ancient Greeks, the idea that a potential infinity, potentially infinite summation could produce a finite result was considered paradoxical, most famously in Zeno's paradoxes. Nonetheless, infinite series were applied practically by Ancient Greek mathematicians including Archimedes, for instance in the Quadrature of the Parabola, quadrature of the parabola. The mathematical side of Zeno's paradoxes was resolved using the concept of a limit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sequence (mathematics)
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called ''elements'', or ''terms''). The number of elements (possibly infinite) is called the ''length'' of the sequence. Unlike a set, the same elements can appear multiple times at different positions in a sequence, and unlike a set, the order does matter. Formally, a sequence can be defined as a function from natural numbers (the positions of elements in the sequence) to the elements at each position. The notion of a sequence can be generalized to an indexed family, defined as a function from an ''arbitrary'' index set. For example, (M, A, R, Y) is a sequence of letters with the letter "M" first and "Y" last. This sequence differs from (A, R, M, Y). Also, the sequence (1, 1, 2, 3, 5, 8), which contains the number 1 at two different positions, is a valid sequence. Sequences can be '' finite'', as in these examples, or '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Difference Operator
In mathematics, a recurrence relation is an equation according to which the nth term of a sequence of numbers is equal to some combination of the previous terms. Often, only k previous terms of the sequence appear in the equation, for a parameter k that is independent of n; this number k is called the ''order'' of the relation. If the values of the first k numbers in the sequence have been given, the rest of the sequence can be calculated by repeatedly applying the equation. In ''linear recurrences'', the th term is equated to a linear function of the k previous terms. A famous example is the recurrence for the Fibonacci numbers, F_n=F_+F_ where the order k is two and the linear function merely adds the two previous terms. This example is a linear recurrence with constant coefficients, because the coefficients of the linear function (1 and 1) are constants that do not depend on n. For these recurrences, one can express the general term of the sequence as a closed-form expression of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Darts
Darts is a competitive sport in which two or more players bare-handedly throw small projectile point, sharp-pointed projectile, projectiles known as dart (missile), darts at a round shooting target, target known as a #Dartboard, dartboard. Points can be scored by hitting specific marked areas of the board, though unlike in sports such as archery, these areas are distributed all across the board and do not follow a principle of points increasing toward the board's Bullseye (target), bullseye. Though a number of similar games using various boards and rules exist, the term "darts" usually now refers to a standardised game involving a specific board design and set of rules. Darts is both a professional throwing sport and a traditional pub game. Darts is commonly played in the British Isles, and recreationally enjoyed around the world. History In 1908, darts was declared to be a game of skill and was thus allowed to be played in pubs. This came about after the landlord of the Adelph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cash Register
A cash register, sometimes called a till or automated money handling system, is a mechanical or electronic device for registering and calculating transactions at a point of sale. It is usually attached to a Cash register#Cash drawer, drawer for storing cash and other valuables. A modern cash register is usually attached to a printer that can print out receipts for record-keeping purposes. History An early mechanical cash register was invented by James Ritty and John Birch following the American Civil War. James was the owner of a Bar (establishment), saloon in Dayton, Ohio, Dayton, Ohio, US, and wanted to stop employees from pilfering his profits. The Ritty Model I was invented in 1879 after seeing a tool that counted the revolutions of the propeller on a steamship. With the help of James' brother John Ritty, they patented it in 1879. It was called ''Ritty's Incorruptible Cashier'' and it was invented to stop cashiers from pilfering and eliminate employee theft and embezzlemen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Central Processing Unit
A central processing unit (CPU), also called a central processor, main processor, or just processor, is the primary Processor (computing), processor in a given computer. Its electronic circuitry executes Instruction (computing), instructions of a computer program, such as arithmetic, logic, controlling, and input/output (I/O) operations. This role contrasts with that of external components, such as main memory and I/O circuitry, and specialized coprocessors such as graphics processing units (GPUs). The form, CPU design, design, and implementation of CPUs have changed over time, but their fundamental operation remains almost unchanged. Principal components of a CPU include the arithmetic–logic unit (ALU) that performs arithmetic operation, arithmetic and Bitwise operation, logic operations, processor registers that supply operands to the ALU and store the results of ALU operations, and a control unit that orchestrates the #Fetch, fetching (from memory), #Decode, decoding and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Accumulator (computing)
In a computer's central processing unit (CPU), the accumulator is a register in which intermediate arithmetic logic unit results are stored. Without a register like an accumulator, it would be necessary to write the result of each calculation (addition, multiplication, shift, etc.) to cache or main memory, perhaps only to be read right back again for use in the next operation. Accessing memory is slower than accessing a register like an accumulator because the technology used for the large main memory is slower (but cheaper) than that used for a register. Early electronic computer systems were often split into two groups, those with accumulators and those without. Modern computer systems often have multiple general-purpose registers that can operate as accumulators, and the term is no longer as common as it once was. However, to simplify their design, a number of special-purpose processors still use a single accumulator. Basic concept Mathematical operations often take ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Accumulator (bet)
A parlay, accumulator (or acca), combo bet, or multi is a single bet that links together two or more individual wagers, usually seen in sports betting. Winning the parlay is dependent on all of those wagers winning together. If any of the bets in the parlay lose, the entire parlay loses. If any of the plays in the parlay ties, or "pushes", the parlay reverts to a lower number of wagers with the payout odds reducing accordingly. Parlay bets are high-risk, high-reward; linking the possibilities drastically reduces the chance of the bet paying off overall. The benefit of the parlay is that there are much higher pay-offs, although as usual, casinos and bookkeepers offering parlays often exploit the poor calculation of gamblers by not increasing the pay-out as much as the odds truly demand, with the effect of the house edge increasing in parlays. Although a variety of bets can be used to build a parlay bet, correlated parlays are usually not allowed by traditional bookmakers. Co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Running Average
In statistics, a moving average (rolling average or running average or moving mean or rolling mean) is a calculation to analyze data points by creating a series of averages of different selections of the full data set. Variations include: simple, cumulative, or weighted forms. Mathematically, a moving average is a type of convolution. Thus in signal processing it is viewed as a low-pass finite impulse response filter. Because the boxcar function outlines its filter coefficients, it is called a boxcar filter. It is sometimes followed by downsampling. Given a series of numbers and a fixed subset size, the first element of the moving average is obtained by taking the average of the initial fixed subset of the number series. Then the subset is modified by "shifting forward"; that is, excluding the first number of the series and including the next value in the series. A moving average is commonly used with time series data to smooth out short-term fluctuations and highlight longer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prefix Sum
In computer science, the prefix sum, cumulative sum, inclusive scan, or simply scan of a sequence of numbers is a second sequence of numbers , the summation, sums of Prefix (computer science), prefixes (running totals) of the input sequence: : : : :... For instance, the prefix sums of the natural numbers are the triangular numbers: : Prefix sums are trivial to compute in sequential models of computation, by using the formula to compute each output value in sequence order. However, despite their ease of computation, prefix sums are a useful primitive in certain algorithms such as counting sort,. and they form the basis of the scan higher-order function in functional programming languages. Prefix sums have also been much studied in parallel algorithms, both as a test problem to be solved and as a useful primitive to be used as a subroutine in other parallel algorithms.. Abstractly, a prefix sum requires only a semigroup, binary associative operator ⊕, making it useful for many a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Digital Equipment Corporation
Digital Equipment Corporation (DEC ), using the trademark Digital, was a major American company in the computer industry from the 1960s to the 1990s. The company was co-founded by Ken Olsen and Harlan Anderson in 1957. Olsen was president until he was forced to resign in 1992, after the company had gone into precipitous decline. The company produced many different product lines over its history. It is best known for the work in the minicomputer market starting in the early 1960s. The company produced a series of machines known as the Programmed Data Processor, PDP line, with the PDP-8 and PDP-11 being among the most successful minis in history. Their success was only surpassed by another DEC product, the late-1970s VAX "supermini" systems that were designed to replace the PDP-11. Although a number of competitors had successfully competed with Digital through the 1970s, the VAX cemented the company's place as a leading vendor in the computer space. As microcomputers improved in t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
