id stringlengths 1 6 | contents stringlengths 176 60.2k |
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900 | "Statistics"
The use of modern computers has expedited large-scale statistical computations and has also made possible new methods that are impractical to perform manually. Statistics continues to be an area of active research for example on the problem of how to analyze big data. [37] When full census data cannot be c... |
901 | "Statistics"
A major problem lies in determining the extent that the sample chosen is actually representative. Statistics offers methods to estimate and correct for any bias within the sample and data collection procedures. There are also methods of experimental design for experiments that can lessen these issues at th... |
902 | "Statistics"
The difference in point of view between classic probability theory and sampling theory is, roughly, that probability theory starts from the given parameters of a total population to deduce probabilities that pertain to samples. Statistical inference, however, moves in the opposite direction— inductively in... |
903 | "Statistics"
In both types of studies, the effect of differences of an independent variable (or variables) on the behavior of the dependent variable are observed. The difference between the two types lies in how the study is actually conducted. Each can be very effective. An experimental study involves taking measureme... |
904 | "Statistics"
While the tools of data analysis work best on data from randomized studies, they are also applied to other kinds of data—like natural experiments and observational studies [38] —for which a statistician would use a modified, more structured estimation method (e.g., Difference in differences estimation and ... |
905 | "Statistics"
The researchers first measured the productivity in the plant, then modified the illumination in an area of the plant and checked if the changes in illumination affected productivity. It turned out that productivity indeed improved (under the experimental conditions). However, the study is heavily criticize... |
906 | "Statistics"
[39] An example of an observational study is one that explores the association between smoking and lung cancer. This type of study typically uses a survey to collect observations about the area of interest and then performs statistical analysis. In this case, the researchers would collect observations of b... |
907 | "Statistics"
Various attempts have been made to produce a taxonomy of levels of measurement. The psychophysicist Stanley Smith Stevens defined nominal, ordinal, interval, and ratio scales. Nominal measurements do not have meaningful rank order among values, and permit any one-to-one (injective) transformation. Ordinal ... |
908 | "Statistics"
Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically, sometimes they are grouped together as categorical variables, whereas ratio and interval measurements are grouped together as quantitative variables, which can be either discrete or continuous, d... |
909 | "Statistics"
Other categorizations have been proposed. For example, Mosteller and Tukey (1977) [41] distinguished grades, ranks, counted fractions, counts, amounts, and balances. Nelder (1990) [42] described continuous counts, continuous ratios, count ratios, and categorical modes of data. (See also: Chrisman (1998), [... |
910 | "Statistics"
Whether or not a transformation is sensible to contemplate depends on the question one is trying to answer." [45]: 82 A descriptive statistic (in the count noun sense) is a summary statistic that quantitatively describes or summarizes features of a collection of information, [46] while descriptive statisti... |
911 | "Statistics"
[47] Inferential statistical analysis infers properties of a population, for example by testing hypotheses and deriving estimates. It is assumed that the observed data set is sampled from a larger population. Inferential statistics can be contrasted with descriptive statistics. Descriptive statistics is so... |
912 | "Statistics"
[48] The population being examined is described by a probability distribution that may have unknown parameters. A statistic is a random variable that is a function of the random sample, but not a function of unknown parameters. The probability distribution of the statistic, though, may have unknown paramet... |
913 | "Statistics"
Widely used pivots include the z-score, the chi square statistic and Student's t-value. Between two estimators of a given parameter, the one with lower mean squared error is said to be more efficient. Furthermore, an estimator is said to be unbiased if its expected value is equal to the true value of the u... |
914 | "Statistics"
This still leaves the question of how to obtain estimators in a given situation and carry the computation, several methods have been proposed: the method of moments, the maximum likelihood method, the least squares method and the more recent method of estimating equations. Interpretation of statistical inf... |
915 | "Statistics"
The indictment comes because of suspicion of the guilt. The H 0 (status quo) stands in opposition to H 1 and is maintained unless H 1 is supported by evidence "beyond a reasonable doubt". However, "failure to reject H 0 " in this case does not imply innocence, but merely that the evidence was insufficient ... |
916 | "Statistics"
What statisticians call an alternative hypothesis is simply a hypothesis that contradicts the null hypothesis. Working from a null hypothesis, two broad categories of error are recognized: Standard deviation refers to the extent to which individual observations in a sample differ from a central value, such... |
917 | "Statistics"
Mean squared error is used for obtaining efficient estimators, a widely used class of estimators. Root mean square error is simply the square root of mean squared error. Many statistical methods seek to minimize the residual sum of squares, and these are called " methods of least squares " in contrast to L... |
918 | "Statistics"
Also in a linear regression model the non deterministic part of the model is called error term, disturbance or more simply noise. Both linear regression and non-linear regression are addressed in polynomial least squares, which also describes the variance in a prediction of the dependent variable (y axis) ... |
919 | "Statistics"
The presence of missing data or censoring may result in biased estimates and specific techniques have been developed to address these problems. [51] Most studies only sample part of a population, so results don't fully represent the whole population. Any estimates obtained from the sample only approximate ... |
920 | "Statistics"
This does not imply that the probability that the true value is in the confidence interval is 95%. From the frequentist perspective, such a claim does not even make sense, as the true value is not a random variable. Either the true value is or is not within the given interval. However, it is true that, bef... |
921 | "Statistics"
In principle confidence intervals can be symmetrical or asymmetrical. An interval can be asymmetrical because it works as lower or upper bound for a parameter (left-sided interval or right sided interval), but it can also be asymmetrical because the two sided interval is built violating symmetry around the... |
922 | "Statistics"
The standard approach [48] is to test a null hypothesis against an alternative hypothesis. A critical region is the set of values of the estimator that leads to refuting the null hypothesis. The probability of type I error is therefore the probability that the estimator belongs to the critical region given... |
923 | "Statistics"
Referring to statistical significance does not necessarily mean that the overall result is significant in real world terms. For example, in a large study of a drug it may be shown that the drug has a statistically significant but very small beneficial effect, such that the drug is unlikely to help the pati... |
924 | "Statistics"
Therefore, the smaller the significance level, the lower the probability of committing type I error. Some problems are usually associated with this framework (See criticism of hypothesis testing ): Some well-known statistical tests and procedures are: Exploratory data analysis ( EDA ) is an approach to ana... |
925 | "Statistics"
For instance, social policy, medical practice, and the reliability of structures like bridges all rely on the proper use of statistics. Even when statistical techniques are correctly applied, the results can be difficult to interpret for those lacking expertise. The statistical significance of a trend in t... |
926 | "Statistics"
There is a general perception that statistical knowledge is all-too-frequently intentionally misused by finding ways to interpret only the data that are favorable to the presenter. [53] A mistrust and misunderstanding of statistics is associated with the quotation, " There are three kinds of lies: lies, da... |
927 | "Statistics"
Warne, Lazo, Ramos, and Ritter (2012)). [54] Ways to avoid misuse of statistics include using proper diagrams and avoiding bias. [55] Misuse can occur when conclusions are overgeneralized and claimed to be representative of more than they really are, often by either deliberately or unconsciously overlookin... |
928 | "Statistics"
[56] To make data gathered from statistics believable and accurate, the sample taken must be representative of the whole. [57] According to Huff, "The dependability of a sample can be destroyed by [bias]... allow yourself some degree of skepticism." [58] To assist in the understanding of statistics Huff pr... |
929 | "Statistics"
For example, a study of annual income that also looks at age of death might find that poor people tend to have shorter lives than affluent people. The two variables are said to be correlated; however, they may or may not be the cause of one another. The correlation phenomena could be caused by a third, pre... |
930 | "Statistics"
[60] [61] Theoretical statistics concerns the logical arguments underlying justification of approaches to statistical inference, as well as encompassing mathematical statistics. Mathematical statistics includes not only the manipulation of probability distributions necessary for deriving results related to... |
931 | "Statistics"
Business statistics applies statistical methods in econometrics, auditing and production and operations, including services improvement and marketing research. [62] A study of two journals in tropical biology found that the 12 most frequent statistical tests are: Analysis of Variance (ANOVA), Chi-Square Te... |
932 | "Statistics"
[63] The rapid and sustained increases in computing power starting from the second half of the 20th century have had a substantial impact on the practice of statistical science. Early statistical models were almost always from the class of linear models, but powerful computers, coupled with suitable numeri... |
933 | "Statistics"
The computer revolution has implications for the future of statistics with a new emphasis on "experimental" and "empirical" statistics. A large number of both general and special purpose statistical software are now available. Examples of available software capable of complex statistical computation includ... |
934 | "Statistics"
( Econometrics is the application of statistical methods to economic data in order to give empirical content to economic relationships.) A typical "Business Statistics" course is intended for business majors, and covers [67] descriptive statistics ( collection, description, analysis, and summary of data), ... |
935 | "Statistics"
Traditionally, statistics was concerned with drawing inferences using a semi-standardized methodology that was "required learning" in most sciences. [68] This tradition has changed with the use of statistics in non-inferential contexts. What was once considered a dry subject, taken in many fields as a degr... |
936 | "Statistics"
These disciplines include: In addition, there are particular types of statistical analysis that have also developed their own specialised terminology and methodology: Statistics form a key basis tool in business and manufacturing as well. It is used to understand measurement systems variability, control pr... |
937 | "Theoretical computer science"
Theoretical computer science ( TCS ) is a subset of general computer science and mathematics that focuses on mathematical aspects of computer science such as the theory of computation, lambda calculus, and type theory. It is difficult to circumscribe the theoretical areas precisely. The A... |
938 | "Theoretical computer science"
Work in this field is often distinguished by its emphasis on mathematical technique and rigor. While logical inference and mathematical proof had existed previously, in 1931 Kurt Gödel proved with his incompleteness theorem that there are fundamental limitations on what statements could b... |
939 | "Theoretical computer science"
With the development of quantum mechanics in the beginning of the 20th century came the concept that mathematical operations could be performed on an entire particle wavefunction. In other words, one could compute functions on multiple states simultaneously. This led to the concept of a q... |
940 | "Theoretical computer science"
Algorithms are used for calculation, data processing, and automated reasoning. An algorithm is an effective method expressed as a finite list [2] of well-defined instructions [3] for calculating a function. [4] Starting from an initial state and initial input (perhaps empty ), [5] the ins... |
941 | "Theoretical computer science"
It is a theory in theoretical computer science, under discrete mathematics (a section of mathematics and also of computer science ). Automata comes from the Greek word αὐτόματα meaning "self-acting". Automata Theory is the study of self-operating virtual machines to help in the logical un... |
942 | "Theoretical computer science"
This typically involves the removal of redundancy and the correction (or detection) of errors in the transmitted data. Computational biology involves the development and application of data-analytical and theoretical methods, mathematical modeling and computational simulation techniques t... |
943 | "Theoretical computer science"
Computational complexity theory is a branch of the theory of computation that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other. A computational problem is understood to be a task that is in principle amenable to... |
944 | "Theoretical computer science"
Other complexity measures are also used, such as the amount of communication (used in communication complexity ), the number of gates in a circuit (used in circuit complexity ) and the number of processors (used in parallel computing ). One of the roles of computational complexity theory ... |
945 | "Theoretical computer science"
The main impetus for the development of computational geometry as a discipline was progress in computer graphics and computer-aided design and manufacturing ( CAD / CAM ), but many problems in computational geometry are classical in nature, and may come from mathematical visualization. Ot... |
946 | "Theoretical computer science"
For example, the samples might be descriptions of mushrooms, and the labels could be whether or not the mushrooms are edible. The algorithm takes these previously labeled samples and uses them to induce a classifier. This classifier is a function that assigns labels to samples including t... |
947 | "Theoretical computer science"
The best known problem in the field is integer factorization. Cryptography is the practice and study of techniques for secure communication in the presence of third parties (called adversaries ). [11] More generally, it is about constructing and analyzing protocols that overcome the influ... |
948 | "Theoretical computer science"
It is theoretically possible to break such a system, but it is infeasible to do so by any known practical means. These schemes are therefore termed computationally secure; theoretical advances, e.g., improvements in integer factorization algorithms, and faster computing technology require... |
949 | "Theoretical computer science"
[14] [15] Different kinds of data structures are suited to different kinds of applications, and some are highly specialized to specific tasks. For example, databases use B-tree indexes for small percentages of data retrieval and compilers and databases use dynamic hash tables as look up t... |
950 | "Theoretical computer science"
Distributed computing studies distributed systems. A distributed system is a software system in which components located on networked computers communicate and coordinate their actions by passing messages. [16] The components interact with each other in order to achieve a common goal. Thr... |
951 | "Theoretical computer science"
[17] There are many alternatives for the message passing mechanism, including RPC-like connectors and message queues. An important goal and challenge of distributed systems is location transparency. Information-based complexity (IBC) studies optimal algorithms and computational complexity... |
952 | "Theoretical computer science"
[19] Formal methods are best described as the application of a fairly broad variety of theoretical computer science fundamentals, in particular logic calculi, formal languages, automata theory, and program semantics, but also type systems and algebraic data types to problems in software a... |
953 | "Theoretical computer science"
[27] Applications of fundamental topics of information theory include lossless data compression (e.g. ZIP files ), lossy data compression (e.g. MP3s and JPEGs ), and channel coding (e.g. for Digital Subscriber Line (DSL) ). The field is at the intersection of mathematics, statistics, comp... |
954 | "Theoretical computer science"
Machine learning is a scientific discipline that deals with the construction and study of algorithms that can learn from data. [28] Such algorithms operate by building a model based on inputs [29]: 2 and using that to make predictions or decisions, rather than following only explicitly pr... |
955 | "Theoretical computer science"
Machine learning is sometimes conflated with data mining, [31] although that focuses more on exploratory data analysis. [32] Machine learning and pattern recognition "can be viewed as two facets of the same field." [29]: vii Parallel computing is a form of computation in which many calcul... |
956 | "Theoretical computer science"
[34] As power consumption (and consequently heat generation) by computers has become a concern in recent years, [35] parallel computing has become the dominant paradigm in computer architecture, mainly in the form of multi-core processors. [36] Parallel computer programs are more difficul... |
957 | "Theoretical computer science"
In programming language theory, semantics is the field concerned with the rigorous mathematical study of the meaning of programming languages. It does so by evaluating the meaning of syntactically legal strings defined by a specific programming language, showing the computation involved. ... |
958 | "Theoretical computer science"
A quantum computer is a computation system that makes direct use of quantum-mechanical phenomena, such as superposition and entanglement, to perform operations on data. [38] Quantum computers are different from digital computers based on transistors. Whereas digital computers require data... |
959 | "Theoretical computer science"
The field of quantum computing was first introduced by Yuri Manin in 1980 [39] and Richard Feynman in 1982. [40] [41] A quantum computer with spins as quantum bits was also formulated for use as a quantum space–time in 1968. [42] As of 2014 [update], quantum computing is still in its infa... |
960 | "Theoretical computer science"
[44] Computer algebra, also called symbolic computation or algebraic computation is a scientific area that refers to the study and development of algorithms and software for manipulating mathematical expressions and other mathematical objects. Although, properly speaking, computer algebra... |
961 | "Theoretical computer science"
Very-large-scale integration ( VLSI ) is the process of creating an integrated circuit (IC) by combining thousands of transistors into a single chip. VLSI began in the 1970s when complex semiconductor and communication technologies were being developed. The microprocessor is a VLSI device... |
962 | "Algebra"
Algebra (from Arabic الجبر ( al-jabr ) 'reunion of broken parts, [1] bonesetting ') [2] is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; [3] it is a unifying thread of almost all of mathematics. [... |
963 | "Algebra"
There are many areas of mathematics that belong to algebra, some having "algebra" in their name, such as commutative algebra and some not, such as Galois theory. The word algebra is not only used for naming an area of mathematics and some subareas; it is also used for naming some sorts of algebraic structures... |
964 | "Algebra"
'reunion of broken parts, [1] bonesetting [2] ' from the title of the early 9th century book c Ilm al-jabr wa l-muqābala "The Science of Restoring and Balancing" by the Persian mathematician and astronomer al-Khwarizmi. In his work, the term al-jabr referred to the operation of moving a term from one side of ... |
965 | "Algebra"
The mathematical meaning was first recorded (in English) in the 16th century. [6] The word "algebra" has several related meanings in mathematics, as a single word or with qualifiers. Algebra began with computations similar to those of arithmetic, with letters standing for numbers. [7] This allowed proofs of p... |
966 | "Algebra"
That is to say, to find all the solutions of the equation. Historically, and in current teaching, the study of algebra starts with the solving of equations, such as the quadratic equation above. Then more general questions, such as "does an equation have a solution?", "how many solutions does an equation have... |
967 | "Algebra"
Even though some methods, which had been developed much earlier, may be considered nowadays as algebra, the emergence of algebra and, soon thereafter, of infinitesimal calculus as subfields of mathematics only dates from the 16th or 17th century. From the second half of the 19th century on, many new fields of... |
968 | "Algebra"
Today algebra includes section 08-General algebraic systems, 12- Field theory and polynomials, 13- Commutative algebra, 15- Linear and multilinear algebra; matrix theory, 16- Associative rings and algebras, 17- Nonassociative rings and algebras, 18- Category theory; homological algebra, 19- K-theory and 20- G... |
969 | "Algebra"
Al-jabr referred to a method for transforming equations by subtracting like terms from both sides, or passing one term from one side to the other, after changing its sign. Therefore, algebra referred originally to the manipulation of equations, and, by extension, to the theory of equations. This is still what... |
970 | "Algebra"
This includes but is not limited to the theory of equations. At the beginning of the 20th century, algebra evolved again by considering operations that act not only on numbers but also on elements of so-called mathematical structures such as groups, fields and vector spaces. This new algebra was called modern... |
971 | "Algebra"
The Babylonians developed formulas to calculate solutions for problems typically solved today by using linear equations, quadratic equations, and indeterminate linear equations. By contrast, most Egyptians of this era, as well as Greek and Chinese mathematics in the 1st millennium BC, usually solved such equa... |
972 | "Algebra"
[10] By the time of Plato, Greek mathematics had undergone a drastic change. The Greeks created a geometric algebra where terms were represented by sides of geometric objects, usually lines, that had letters associated with them. [7] Diophantus (3rd century AD) was an Alexandrian Greek mathematician and the a... |
973 | "Algebra"
[12] The Hellenistic mathematicians Hero of Alexandria and Diophantus [13] as well as Indian mathematicians such as Brahmagupta, continued the traditions of Egypt and Babylon, though Diophantus' Arithmetica and Brahmagupta's Brāhmasphuṭasiddhānta are on a higher level. [14] [ better source needed ] For exampl... |
974 | "Algebra"
He solved linear and quadratic equations without algebraic symbolism, negative numbers or zero, thus he had to distinguish several types of equations. [17] In the context where algebra is identified with the theory of equations, the Greek mathematician Diophantus has traditionally been known as the "father of... |
975 | "Algebra"
Those who support Diophantus point to the fact that the algebra found in Al-Jabr is slightly more elementary than the algebra found in Arithmetica and that Arithmetica is syncopated while Al-Jabr is fully rhetorical. [25] Those who support Al-Khwarizmi point to the fact that he introduced the methods of " red... |
976 | "Algebra"
[22] His algebra was also no longer concerned "with a series of problems to be resolved, but an exposition which starts with primitive terms in which the combinations must give all possible prototypes for equations, which henceforward explicitly constitute the true object of study". He also studied an equatio... |
977 | "Algebra"
His book Treatise on Demonstrations of Problems of Algebra (1070), which laid down the principles of algebra, is part of the body of Persian mathematics that was eventually transmitted to Europe. [29] Yet another Persian mathematician, Sharaf al-Dīn al-Tūsī, found algebraic and numerical solutions to various ... |
978 | "Algebra"
Abū al-Ḥasan ibn ʿAlī al-Qalaṣādī (1412–1486) took "the first steps toward the introduction of algebraic symbolism". He also computed Σ n 2, Σ n 3 and used the method of successive approximation to determine square roots. [33] François Viète 's work on new algebra at the close of the 16th century was an impor... |
979 | "Algebra"
Gabriel Cramer also did some work on matrices and determinants in the 18th century. Permutations were studied by Joseph-Louis Lagrange in his 1770 paper " Réflexions sur la résolution algébrique des équations " devoted to solutions of algebraic equations, in which he introduced Lagrange resolvents. Paolo Ruff... |
980 | "Algebra"
Augustus De Morgan discovered relation algebra in his Syllabus of a Proposed System of Logic. Josiah Willard Gibbs developed an algebra of vectors in three-dimensional space, and Arthur Cayley developed an algebra of matrices (this is a noncommutative algebra). [35] Some subareas of algebra have the word alge... |
981 | "Algebra"
In arithmetic, only numbers and their arithmetical operations (such as +, −, ×, ÷) occur. In algebra, numbers are often represented by symbols called variables (such as a, n, x, y or z ). This is useful because: A polynomial is an expression that is the sum of a finite number of non-zero terms, each term cons... |
982 | "Algebra"
For example, ( x − 1)( x + 3) is a polynomial expression, that, properly speaking, is not a polynomial. A polynomial function is a function that is defined by a polynomial, or, equivalently, by a polynomial expression. The two preceding examples define the same polynomial function. Two important and related p... |
983 | "Algebra"
A related class of problems is finding algebraic expressions for the roots of a polynomial in a single variable. It has been suggested that elementary algebra should be taught to students as young as eleven years old, [36] though in recent years it is more common for public lessons to begin at the eighth grad... |
984 | "Algebra"
Sets: Rather than just considering the different types of numbers, abstract algebra deals with the more general concept of sets: collections of objects called elements. All collections of the familiar types of numbers are sets. Other examples of sets include the set of all two-by-two matrices, the set of all ... |
985 | "Algebra"
Binary operations: The notion of addition (+) is generalized to the notion of binary operation (denoted here by ∗). The notion of binary operation is meaningless without the set on which the operation is defined. For two elements a and b in a set S, a ∗ b is another element in the set; this condition is calle... |
986 | "Algebra"
Zero is the identity element for addition and one is the identity element for multiplication. For a general binary operator ∗ the identity element e must satisfy a ∗ e = a and e ∗ a = a, and is necessarily unique, if it exists. This holds for addition as a + 0 = a and 0 + a = a and multiplication a × 1 = a an... |
987 | "Algebra"
Inverse elements: The negative numbers give rise to the concept of inverse elements. For addition, the inverse of a is written − a, and for multiplication the inverse is written a −1. A general two-sided inverse element a −1 satisfies the property that a ∗ a −1 = e and a −1 ∗ a = e, where e is the identity el... |
988 | "Algebra"
This property is shared by most binary operations, but not subtraction or division or octonion multiplication. Commutativity: Addition and multiplication of real numbers are both commutative. That is, the order of the numbers does not affect the result. For example: 2 + 3 = 3 + 2. In general, this becomes a ∗... |
989 | "Algebra"
For example, the set of integers under the operation of addition is a group. In this group, the identity element is 0 and the inverse of any element a is its negation, − a. The associativity requirement is met, because for any integers a, b and c, ( a + b ) + c = a + ( b + c ) The non-zero rational numbers fo... |
990 | "Algebra"
The integers under the multiplication operation, however, do not form a group. This is because, in general, the multiplicative inverse of an integer is not an integer. For example, 4 is an integer, but its multiplicative inverse is 1 / 4, which is not an integer. The theory of groups is studied in group theor... |
991 | "Algebra"
They comprise a set and a closed binary operation but do not necessarily satisfy the other conditions. A semi-group has an associative binary operation but might not have an identity element. A monoid is a semi-group which does have an identity but might not have an inverse for every element. A quasi-group sa... |
992 | "Algebra"
The most important of these are rings and fields. A ring has two binary operations (+) and (×), with × distributive over +. Under the first operator (+) it forms an abelian group. Under the second operator (×) it is associative, but it does not need to have an identity, or inverse, so division is not required... |
993 | "Algebra"
The integers are an example of a ring. The integers have additional properties which make it an integral domain. A field is a ring with the additional property that all the elements excluding 0 form an abelian group under ×. The multiplicative (×) identity is written as 1 and the multiplicative inverse of a i... |
994 | "Applied mathematics"
Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical science and specialized knowledge. The term "applied mat... |
995 | "Applied mathematics"
Historically, applied mathematics consisted principally of applied analysis, most notably differential equations; approximation theory (broadly construed, to include representations, asymptotic methods, variational methods, and numerical analysis ); and applied probability. These areas of mathemat... |
996 | "Applied mathematics"
[1] Engineering and computer science departments have traditionally made use of applied mathematics. Today, the term "applied mathematics" is used in a broader sense. It includes the classical areas noted above as well as other areas that have become increasingly important in applications. Even fi... |
997 | "Applied mathematics"
Many mathematicians distinguish between "applied mathematics", which is concerned with mathematical methods, and the "applications of mathematics" within science and engineering. A biologist using a population model and applying known mathematics would not be doing applied mathematics, but rather ... |
998 | "Applied mathematics"
[2] The success of modern numerical mathematical methods and software has led to the emergence of computational mathematics, computational science, and computational engineering, which use high-performance computing for the simulation of phenomena and the solution of problems in the sciences and e... |
999 | "Applied mathematics"
[3] Some mathematicians emphasize the term applicable mathematics to separate or delineate the traditional applied areas from new applications arising from fields that were previously seen as pure mathematics. [4] For example, from this viewpoint, an ecologist or geographer using population models... |
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