Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions. There is debate over whether mathematical objects such as numbers and points exist naturally or are human creations. The mathematician Benjamin Peirce called mathematics "the science that draws necessary conclusions". Albert Einstein, on the other hand, stated that "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to...

ISBN: 978-6-1333-0766-7
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Naive set theory is one of several theories of sets used in the discussion of the foundations of mathematics. The informal content of this naive set theory supports both the aspects of mathematical sets familiar in discrete mathematics (for example Venn diagrams and symbolic reasoning about their Boolean algebra), and the everyday usage of set theory concepts in most contemporary mathematics. Sets are of great importance in mathematics; in fact, in modern formal treatments, most mathematical objects (numbers, relations, functions, etc.) are defined in terms of sets. Naive set theory can be seen as a stepping-stone to more formal treatments, and suffices for many purposes. Данное...

ISBN: 978-6-1333-2895-2
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! A naive Bayes classifier is a simple probabilistic classifier based on applying Bayes' theorem (from Bayesian statistics) with strong (naive) independence assumptions. A more descriptive term for the underlying probability model would be "independent feature model". In simple terms, a naive Bayes classifier assumes that the presence (or absence) of a particular feature of a class is unrelated to the presence (or absence) of any other feature. For example, a fruit may be considered to be an apple if it is red, round, and about 4" in diameter. Even though these features depend on the existence of the other features, a naive Bayes classifier considers all of these properties to independently...

ISBN: 978-6-1303-3446-8
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Naive Set Theory is a mathematics textbook by Paul Halmos originally published in 1960. This book is an undergraduate introduction to not-very-naive set theory. It is still considered by many to be the best introduction to set theory for beginners. While the title states that it is naive, which is usually taken to mean without axioms, the book does introduce all the axioms of Zermelo-Fraenkel set theory and gives correct and rigorous definitions for basic objects. Where it differs from a "true" axiomatic set theory book is its character: there are no long-winded discussions of axiomatic minutiae, and there is next to nothing about advanced topics like large cardinals. Instead, it tries to be...

ISBN: 978-6-1312-9729-8
Издательство: Книга по требованию
Дата выхода: июль 2011

Naive set theory is one of several theories of sets used in the discussion of the foundations of mathematics. The informal content of this naive set theory supports both the aspects of mathematical sets familiar in discrete mathematics, and the everyday usage of set theory concepts in most contemporary mathematics. Sets are of great importance in mathematics; in fact, in modern formal treatments, most mathematical objects are defined in terms of sets. Naive set theory can be seen as a stepping-stone to more formal treatments, and suffices for many purposes. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после...

ISBN: 978-6-1303-1079-0
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! The Nakagami distribution or the Nakagami-m distribution is a probability distribution related to the gamma distribution. It has two parameters: a shape parameter and a second parameter controlling spread, . Its probability density function (pdf) is f(x;,mu,omega) = frac{2mu^mu {Gamma(mu)omega^mu}x^{2mu-1}expleft(-frac{mu}{omega}x^2right). Its cumulative distribution function is F(x;,mu,omega) = Pleft(mu, frac{mu}{omega}x^2right), where P is the incomplete gamma function (regularized). Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1312-9733-5
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, more specifically abstract algebra and especially commutative algebra, Nakayama's lemma also known as the Krull–Azumaya theorem governs the interaction between the Jacobson radical of a ring (typically a commutative ring) and its finitely generated modules. Informally, the lemma immediately gives a precise sense in which finitely generated modules over a commutative ring behave like vector spaces over a field. It is a significant tool in algebraic geometry, because it allows local data on algebraic varieties, in the form of modules over local rings, to be studied pointwise as vector spaces over the residue field of the ring. Данное издание не является...

ISBN: 978-6-1303-3455-0
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High Quality Content by WIKIPEDIA articles! Nalini Joshi is an Australian mathematician. Joshi is currently a Professor and the Head of School in the School of Mathematics and Statistics at the University of Sydney (she is the first woman to hold either position in the School), and President of the Australian Mathematical Society. She is a member of the School's Applied Mathematics Research Group. Joshi completed her undergraduate studies at the University of Sydney, receiving a Bachelor of Science with Honours in applied mathematics. She holds a Master of Arts and Doctor of Philosophy from Princeton University in applied mathematics. She completed her Ph.D. in 1987 under the supervision of Martin David Kruskal. Данное...

ISBN: 978-6-1334-6852-8
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, Nambu dynamics is a generalization of Hamiltonian mechanics involving multiple Hamiltonians. Recall that Hamiltonian mechanics is based upon the flows generated by a smooth Hamiltonian over a symplectic manifold. The flows are symplectomorphisms and hence obey Liouville's theorem. This was soon generalized to flows generated by a Hamiltonian over a Poisson manifold. In 1973, Yoichiro Nambu suggested a generalization involving Nambu-Poisson manifolds with more than one Hamiltonian. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения...

ISBN: 978-6-1312-9741-0
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, Nambu dynamics is a generalization of Hamiltonian mechanics involving multiple Hamiltonians. Recall that Hamiltonian mechanics is based upon the flows generated by a smooth Hamiltonian over a symplectic manifold. The flows are symplectomorphisms and hence obey Liouville's theorem. This was soon generalized to flows generated by a Hamiltonian over a Poisson manifold. In 1973, Yoichiro Nambu suggested a generalization involving Nambu-Poisson manifolds with more than one Hamiltonian. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения...

ISBN: 978-6-1335-3788-0
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Name Taken was an indie rock/punk rock band from Orange, California originally known as All Thats Left until they discovered that the name was already taken; thus the name "Name Taken". The band originally started in the eighth grade when the band would play shows in the amphitheatre at lunch and later expanded to such compilations as Atticus I and Warped Tour 2002. The band split up in 2005 after two years of touring to pursue their college education. Chad and Blake attended Cal State Fullerton and Ryan Edwards attending Berkley. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд...

ISBN: 978-6-1335-6878-5
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! This article lists and discusses the usage and derivation of names of large numbers, together with their possible extensions. The following table lists those names of large numbers which are found in many English dictionaries and thus have a special claim to being "real words". The "Traditional British" values shown are unused in American English and are obsolete in British English, but are dominant in many non-English-speaking areas, including continental Europe and Spanish-speaking countries in Latin America. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после...

ISBN: 978-6-1303-3467-3
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Napoleon's problem is a famous compass construction problem. In it, a circle and its center are given. The challenge is to divide the circle into four equal arcs using only a compass. Napoleon Bonaparte was known to be an amateur mathematician but it is not known if he either created or solved the problem. Napoleon's friend the Italian mathematician Lorenzo Mascheroni introduced the limitation of using only a compass (no straight edge) into geometric constructions. But actually, the challenge above is child's play compared to the real Napoleon's problem, consisting in finding the center of a given circle with compass alone. Данное издание не является...

ISBN: 978-6-1312-9791-5
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In combinatorics, the Narayana numbers N(n, k), n = 1, 2, 3 ..., 1 ? k ? n, form a triangle of natural numbers, called Narayana triangle, that occur in various counting problems. They are named for T.V. Narayana, a mathematician from India. Natural numbers have two main purposes: counting ("there are 6 coins on the table") and ordering ("this is the 3rd largest city in the country"). These purposes are related to the linguistic notions of cardinal and ordinal numbers, respectively. A more recent notion is that of a nominal number, which is used only for naming. Properties of the natural numbers related to divisibility, such as the distribution of prime numbers, are studied in number theory....

ISBN: 978-6-1303-3267-9
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In combinatorics, the Narayana numbers N, form a triangle of natural numbers, called Narayana triangle, that occur in various counting problems. They are named for Narayana, a mathematician from India. The Narayana numbers can be expressed in terms of binomial coefficients. An example of a counting problem whose solution can be given in terms of the Narayana numbers N, is the number of expressions containing n pairs of parentheses which are correctly matched and which contain k distinct nestings. For instance, with four pairs of parentheses six sequences can be created which each contain two times the sub-pattern. Данное издание не является оригинальным....

ISBN: 978-6-1303-3336-2
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In algebraic number theory, the narrow class group of a number field K is a refinement of the class group of K that takes into account some information about embeddings of K into the field of real numbers. Suppose that K is a finite extension of Q. Recall that the ordinary class group of K is defined to be C_K = I_K / P_K,,! where IK is the group of fractional ideals of K, and PK is the group of principal fractional ideals of K, that is, ideals of the form aOK where a is a unit of K. The narrow class group is defined to be the quotient C_K^+ = I_K / P_K^+. Данное издание не является оригинальным. Книга печатается по технологии...

ISBN: 978-6-1312-9799-1
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In algebraic geometry, a Nash blowing-up is a process in which, roughly speaking, each singular point is replaced by all the limiting positions of the tangent spaces at the non-singular points. Strictly speaking, if X is an algebraic variety of pure codimension r embedded in a smooth variety of dimension n, Sing(X) denotes the set of its singular points and X_text{reg}:=Xsetminus text{Sing}(X) it is possible to define a map tau:X_text{reg}rightarrow Xtimes G_r^n, where G_{r}^{n} is the Grassmanian of r-planes in n-space, by (a): = (a,TX,a), where TX,a is the tangent space of X at a. Now, the closure of the image of this map together with the projection to X is called the Nash blowing-up of X....

ISBN: 978-6-1312-9808-0
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High Quality Content by WIKIPEDIA articles! The Nash embedding theorems (or imbedding theorems), named after John Forbes Nash, state that every Riemannian manifold can be isometrically embedded into some Euclidean space. Isometric means preserving the length of every path. For instance, bending without stretching or tearing a page of paper gives an isometric embedding of the page into Euclidean space because curves drawn on the page retain the same arclength however the page is bent. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1312-9817-2
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High Quality Content by WIKIPEDIA articles! In real algebraic geometry, a Nash function on an open semialgebraic subset U of Rn is an analytic function f: U -> R satisfying a non trivial polynomial equation P(x,f(x)) = 0 for all x in U. (A semialgebraic subset of Rn is a subset obtained from subsets of the form {x in Rn : P(x)=0} or {x in Rn : P(x) > 0}, where P is a polynomial, by taking finite unions, finite intersections and complements.) Polynomial and regular rational functions are Nash functions; the function xmapsto sqrt{1+x^2} is Nash on R; the function which associates to a real symmetric matrix its i-th eigenvalue (in increasing order) is Nash on the open subset of symmetric matrices with no multiple eigenvalue. Actually,...

ISBN: 978-6-1312-9833-2
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High Quality Content by WIKIPEDIA articles! A Nasik magic hypercube is a magic hypercube with the added restriction that all possible lines through each cell sum correctly to S = frac{m(m^n+1)}{2} where S = the magic constant, m = the order and n = the dimension, of the hypercube. Or, to put it more concisely, all pan-r-agonals sum correctly for r = 1...n. The above definition is the same as the Hendricks definition of perfect, but different than the Boyer/Trump definition. See Perfect magic cube Because of the confusion over the term perfect when used with reference to magic squares, magic cubes, and in general magic hypercubes, I am proposing the above as an unambiguous term. Following is an attempt to use the magic cube as a specific...

ISBN: 978-6-1312-9856-1
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! A Nasik magic hypercube is a magic hypercube with the added restriction that all possible lines through each cell sum correctly to S = frac{m(m^n+1)}{2} where S = the magic constant, m = the order and n = the dimension, of the hypercube. Or, to put it more concisely, all pan-r-agonals sum correctly for r = 1...n. The above definition is the same as the Hendricks definition of perfect, but different than the Boyer/Trump definition. See Perfect magic cube Because of the confusion over the term perfect when used with reference to magic squares, magic cubes, and in general magic hypercubes, I am proposing the above as an unambiguous term. Following is an attempt to use the magic cube as a specific...

ISBN: 978-6-1303-3087-3
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Nathan Joseph Divinsky (born October 29, 1925) is a Canadian mathematician, chess master, and chess writer, who is also known for being the former husband of the 19th Prime Minister of Canada, Kim Campbell. Divinsky and Campbell were married from 1972 to 1983. Born in Cornwall, Ontario, he moved to Winnipeg a few years later. He received a Bachelor of Science from the University of Winnipeg in 1946. He received a Master of Science in 1947 and Ph.D. in Mathematics in 1950 from the University of Chicago. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения...

ISBN: 978-6-1311-8229-7
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High Quality Content by WIKIPEDIA articles! The National Council of Teachers of Mathematics (NCTM) was founded in 1920. It has grown to be the world's largest organization concerned with mathematics education, having close to 100,000 members across the USA and Canada, and internationally. NCTM holds annual national and regional conferences for American teachers and publishes four print journals and one on-line journal. Its published standards have been highly influential in the direction of mathematics education in the United States and Canada. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения...

ISBN: 978-6-1303-9589-6
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In India, the National Highways are the primary long-distance roadways. Most are maintained by the Government of India, others are operated under a public-private partnership by the private sector. Most are two-lane (one in each direction). They span about 67,000 km (42,000 mi), of which about 200 km (120 mi) are designated expressways and 10,000 km (6,200 mi) have four lanes or more. Indian highways constitute approximately 2% of the total road network of India, but carry nearly 40% of the total traffic. The National Highways Development Project, currently being implemented, seeks to massively expand India's highway network. Данное издание не является оригинальным. Книга печатается по...

ISBN: 978-6-1313-0426-2
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High Quality Content by WIKIPEDIA articles! National Conference on Mathematical and Computational Models (NCMCM) is a national level applied mathematics conference organized by Department of Mathematics and Computer Applications, PSG College of Technology, Coimbatore, India every other year. It is a national level technical conference sponsored by the Defence Research and Development Organisation, Ministry of HRD and PSG Institutions. The conference attracts large number of original technical papers from all over India and the world. The conference is open to academia as well as to industry. The next conference is due to take place on December 2009. Данное издание не является оригинальным. Книга...

ISBN: 978-6-1312-9904-9
Издательство: Книга по требованию
Дата выхода: июль 2011