Kernel (mathematics) - Kernel (mathematics) The term kernel has several meanings in mathematics, some related to each other, some unrelated. In analysis, one consider an integral operator T which transforms a function f into a function Tf given by the integral formula The function K that appears in this formula is called the kernel of the operator T. This usage applies also to convolution operators such as the Dirichlet kernel. Unrelated to this, if f is any function in any context, then the kernel of f is a certain equivalence relation on the domain of f which is defined in terms of f. For more on this in general, see Kernel (function). This notion is used heavily in abstract algebra. But in the case of Mal'cev algebras, it can be.
Identity (mathematics) - Identity (mathematics) In mathematics, an identity is an equality that remains true regardless of the values of any variables that appear within it. Identities for classes of functions Logarithmic identities Exponential identities Trigonometric identities Hyperbolic function identities Hypergeometric function identities Combinatorial identities Named identities Bézout's identity Euler's identity.
Illinois Mathematics and Science Academy - Illinois Mathematics and Science Academy The Illinois Mathematics and Science Academy, or IMSA, is a public high school of approximately six hundred students, with a focus on mathematics and science, although other subjects are studied as well. It was founded by Leon Lederman. It is a boarding school, and also considered a magnet school; that is, it draws the best students from across the state. As such, IMSA has a strong academic reputation. This article is a stub. You can help Wikipedia by fixing it..
Interval (mathematics) - Interval (mathematics) In elementary algebra, an interval is a set that contains every real number between two indicated numbers, and possibly the two numbers themselves. For example, the interval "(10,20)" stands for all real numbers between 10 and 20, not including 10 or 20. On the other hand, the interval "[10,20]" includes every number between 10 and 20 along with the numbers 10 and 20. Other possibilities are listed below. In higher mathematics, a formal definition is the following: An interval is a subset S of a totally ordered set T with the property that whenever x and y are in S and x < z < y then z is in S. As mentioned above, a particularly important case is when T = R, the set.
International Mathematics Olympiad - International Mathematics Olympiad The International Mathematics Olympiad (IMO, also called the International Mathematical Olympiad) is an annual contest for high school students. It is the oldest of the science olympiads. The first IMO was held in Romania in 1969. Since then it has been held every year except 1980. About 80 countries send teams of (at most) 6 students each (plus one team leader and one observer). Teams are not officially recognized - all scores are given only to individual contestants. Constestants must be under the age of 20 and must not have any post-secondary school education. Subject to these conditions, an individual may participate any number of times in the IMO. The paper consists of 6 problems, with each problem being worth 7 points. The total.
Karl Wilhelm Feuerbach - doctorate at age 22, he became a professor of mathematics at the Gymnasium at Erlangen. In 1822 he wrote a small book on mathematics noted mainly for a theorem at the bottom of one of the pages on the nine point circle. Shortly before his death he introduced homogeneous coordinates, independent of Möbius..
Karl Pearson - Publications 5 Other Useful Sites 6 Further Reading Biography Karl Pearson was born in London on the 27th March 1857. He was educated privately at University College School, after which he went to King's College, Cambridge to study mathematics. He then spent part of 1879 and 1880 studying medieval and 16th-century German literature at the universities of Berlin and Heidelberg - in fact, he became sufficiently knowledgeable in this field that he was offered a post in the German department at Cambridge University. His next career move was to Lincoln's Inn, where he read law until 1881 (although he never practised). After this, he returned to mathematics, deputising for the mathematics professor at King's College London in 1881 and for the professor at University College London in 1883. In 1884, he.
Karsten Niebuhr - small farmer. He had little education, and for several years of his youth had to do the work of a peasant. His bent was towards mathematics, and he managed to obtain some lessons in surveying. It was while he was working at this subject that one of his teachers, in 1760, proposed to him to join the expedition which was being sent out by Frederick V of Denmark for the scientific exploration of Egypt, Arabia and Syria. To qualify himself for the work of surveyor and geographer, he studied hard at mathematics for a year and a half before the expedition set out, and also managed to acquire some knowledge of Arabic. The expedition sailed in January 1761, and, landing at Alexandria, ascended the Nile. Proceeding to Suez, Niebuhr made a.
Vector calculus - Vector calculus Vector calculus is a field of mathematics concerned with multivariate real analysis of vectorss in 2 or more dimensions. It consists of a suite of formulas and problem solving techniques very useful for engineering and physics. We consider vector fields, which associate a vector to every point in space, and scalar fields, which associate a scalar to every point in space. For example, the temperature of a swimming pool is a scalar field: to each point we associate a scalar value of temperature. The water flow in the same pool is a vector field: to each point we associate a velocity vector. Three operations are important in vector calculus: gradient: measures the rate and direction of change in a scalar field; the gradient of a scalar field is a.
Karlheinz Brandenburg - 3, more commonly known as MP3. 1980 Master of Science in Electrical engineering 1982 Master of Science in Mathematics 1989 Doctor of Philosophy in Electrical engineering 1989 - 1990 worked at AT&T Bell Labs, USA 1990 returned to Erlangen to research on audio coding techniques 1993 appointed head at the Fraunhofer Institute für Integrierte Schaltungen (Fraunhofer IIS-A) He also authored a book called Applications of Digital Signal Processing to Audio and Acoustics. He currently holds 24 different patents on audio coding techniques, with several more pending..
Kähler manifold - Kähler manifold In mathematics, a hermitian metric on a complex vector bundle E, on a smooth manifold M, is a positive-definite hermitian form on each vector space EP, that varies smoothly with the point P of M. This is the hermitian analogue, when M is a complex manifold and E its tangent bundle, of a Riemannian metric. The case that is most important in practice satisfies some further conditions. A Kähler metric on a complex manifold M is a hermitian metric as just defined, satisfying a condition that has several equivalent one characterisations (the most geometric being that parallel transport gives rise to complex-linear mappings on the tangent spaces). In terms of local coordinates it is specified in this way: if is the metric, then the associated Kähler.
Kernel - a shell, husk, or integument. The term kernel can also mean a single seed or grain, as "a kernel of corn". The kernel of an operating system is its essential component, such as the Linux kernel. In mathematics, kernel has several different, somewhat unrelated meanings; see Kernel (mathematics), or go directly to Kernel (function), Kernel (algebra), or Kernel (category theory). This is a disambiguation page; that is, one that points to various pages that might otherwise have the same name..
Kernel (algebra) - Kernel (algebra) In the various branches of mathematics that fall under the heading of abstract algebra, the kernel of a homomorphism measures the degree to which the homomorphism fails to be injective. The definition of kernel takes various forms in various contexts. But in all of them, the kernel of a homomorphism is trivial (in a sense relevant to that context) if and only if the homomorphism is injective. The fundamental theorem on homomorphisms (or first isomorphism theorem) is a theorem, again taking various forms, that applies to the quotient algebra defined by the kernel. In this article, we first survey kernels for some important types of algebraic structures; then we give general definitions from universal algebra for generic algebraic structures. Table of contents showTocToggle("show","hide") 1 Survey of examples 1.1.
Kernel (category theory) - category theory and its applications to other branches of mathematics, kernels are a generalization of the kernels of group homomorphisms and the kernels of module homomorphisms and certain other kernels from algebra. Intuitively, the kernel of the morphism f : A → B is the "most general" morphism k : K → A which, when composed with f, yields zero. Note that kernel pairs and difference kernels (aka binary equalisers) sometimes go by the name "kernel"; while related, these aren't quite the same thing and are not discussed in this article. Table of contents showTocToggle("show","hide") 1 Definition 2 First properties 3 Examples 4 Relation to other categorical concepts 5 Relationship to algebraic kernels Definition Let C be a category. In order to define a kernel in the general category-theoretical sense, C.
Kerrison Predictor - such a version of the Predictor as the M5. To produce the M5 the Singer Corporation was brought in in in December 1940 to produce 1,500 a month to equip their existing 37mm guns. However in February 1941 the US Navy decided to use the Bofors gun as well, and the Army then agreed to in order to simplify production. Singer required massive changes in the company, including building new factories and the switching of a foundry from steel to aluminum, that production didn't start until January 1943. Nevertheless the production line proved to be sound, and the order was filled for their Director, Antiaircraft, M5 by the middle of 1944. With aircraft speeds increasing dramatically during the war, even the speed of the Kerrison Predictor proved lacking by the end..
Kettering University - used to be the main manufactuing location for General Motors. Students at Kettering University may specialize in engineering, computer science, applied mathematics, and other disciplines. Attending Kettering involves not only traditional classroom studies but also organized employment with any of hundreds of co-op employers worldwide. Stuents follow a unique schecule, broken up into A-Section and B-Section. A-Section attends classes from July to September and from Janurary to March, while B-Section attends classes from October to December and April to June. During the 3 month periods between class terms, studens are supposed to be working and gaining work experience. By about the sophomore year, most studens are working for one of the many co-op employers that hire Kettering students. Because of this schedule, it often takes students five years—rather than the traditional.
Kenneth E. Iverson - Award in 1979 for his contributions to mathematical notation and programming language theory. He received his Bachelor's degree in Mathematics and Physics in 1951 from Queen's University, Kingston in Canada. At Harvard University, he received his Master's degree in 1951 in Mathematics and his Ph.D in Applied Mathematics in 1954. As an assistant professor at Harvard, Iverson developed a mathematical notation for manipulating arrays that he taught to his students. In 1962, he began work for IBM and working with Adin Falkoff, created APL based on the notation he had developed. He was named an IBM Fellow in 1970. He later developed the J programming language, Books A Programming Language (1962).
Kenneth Appel - Wolfgang Haken at the University of Illinois in Urbana, solved one of the most famous problems in mathematics, the four-color theorem. They proved that any two-dimensional map, with certain limitations, can be filled in with four colors without any adjacent "countries" sharing the same color. The proof is one of the most controversial of modern mathematics because of its heavy dependence on computer "number-crunching" to sort through possibilities. Even Appel has agreed, in numerous interviews, that it lacks elegance and provided no new insight that has guided future mathematical research. Others, however, have pointed to this work as the start of a sea-change in mathematicians' attitudes toward computers - which they had largely disdained as a tool for engineers rather than for theoreticians - leading to the creation of what is.
Kernel (function) - Kernel (function) In mathematics, the kernel of a function f is an equivalence relation on the function's domain that roughly expresses the idea of "equivalent as far as the function f can tell". Note that there are several other meanings of the word "kernel" in mathematics; see Kernel (mathematics) for these. For the formal definition, let X and Y be sets and let f be a function from X to Y. If x and x' are elements of X, then x and x' are equivalent if f(x) and f(x') are equal as elements of Y. The kernel of f is the equivalence relation thus defined. The kernel may be denoted "=f" (or a variation) and may be defined symbolically as Like any equivalence relation, the kernel can be.
Kepler conjecture - Kepler conjecture In mathematics, the Kepler conjecture is a conjecture about sphere packing in three dimensional Euclidean space. It says that no arrangement of equal spheres filling space has a greater average density than that of the cubic close packing (face centred cubic) and hexagonal close packing arrangements. The density of these arrangements is a little over 74%. In 1998 Thomas Hales, presently Andrew Mellon Professor at the University of Pittsburgh, announced that he had a proof of the Kepler conjecture. Hales' proof is a proof by exhaustion involving checking of many individual cases using complex computer calculations. Referees have said that they are "99% certain" of the correctness of Hales' proof. So the Kepler conjecture is now very close to becoming a theorem. Table of contents showTocToggle("show","hide").
