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The * Encyclopedia of Mathematics* (also

The 2002 version contains more than 8,000 entries covering most areas of mathematics at a graduate level, and the presentation is technical in nature. The encyclopedia is edited by Michiel Hazewinkel and was published by Kluwer Academic Publishers until 2003, when Kluwer became part of Springer. The CD-ROM contains animations and three-dimensional objects.

The encyclopedia has been translated from the Soviet *Matematicheskaya entsiklopediya* (1977) originally edited by Ivan Matveevich Vinogradov and extended with comments and three supplements adding several thousand articles.

Until November 29, 2011, a static version of the encyclopedia could be browsed online free of charge online. This URL now redirects to the new wiki incarnation of the EOM.

A new dynamic version of the encyclopedia is now available as a public wiki online. This new wiki is a collaboration between Springer and the European Mathematical Society. This new version of the encyclopedia includes the entire contents of the previous online version, but all entries can now be publicly updated to include the newest advancements in mathematics. All entries will be monitored for content accuracy by members of an editorial board^{ [1] } selected by the European Mathematical Society.

- Vinogradov, I. M. (Ed.),
*Matematicheskaya entsiklopediya*, Moscow, Sov. Entsiklopediya, 1977. - Hazewinkel, M. (Ed.),
*Encyclopaedia of Mathematics*(set), Kluwer, 1994 ( ISBN 1-55608-010-7).- Hazewinkel, M. (Ed.),
*Encyclopaedia of Mathematics*, Vol. 1 (A–B), Kluwer, 1987 ( ISBN 1-55608-000-X). - Hazewinkel, M. (Ed.),
*Encyclopaedia of Mathematics*, Vol. 2 (C), Kluwer, 1988 ( ISBN 1-55608-001-8). - Hazewinkel, M. (Ed.),
*Encyclopaedia of Mathematics*, Vol. 3 (D–Fey), Kluwer, 1989 ( ISBN 1-55608-002-6). - Hazewinkel, M. (Ed.),
*Encyclopaedia of Mathematics*, Vol. 4 (Fib–H), Kluwer, 1989 ( ISBN 1-55608-003-4). - Hazewinkel, M. (Ed.),
*Encyclopaedia of Mathematics*, Vol. 5 (I–Lit), Kluwer, 1990 ( ISBN 1-55608-004-2). - Hazewinkel, M. (Ed.),
*Encyclopaedia of Mathematics*, Vol. 6 (Lob–Opt), Kluwer, 1990 ( ISBN 1-55608-005-0). - Hazewinkel, M. (Ed.),
*Encyclopaedia of Mathematics*, Vol. 7 (Orb–Ray), Kluwer, 1991 ( ISBN 1-55608-006-9). - Hazewinkel, M. (Ed.),
*Encyclopaedia of Mathematics*, Vol. 8 (Rea–Sti), Kluwer, 1992 ( ISBN 1-55608-007-7). - Hazewinkel, M. (Ed.),
*Encyclopaedia of Mathematics*, Vol. 9 (Sto–Zyg), Kluwer, 1993 ( ISBN 1-55608-008-5). - Hazewinkel, M. (Ed.),
*Encyclopaedia of Mathematics*, Vol. 10 (Index), Kluwer, 1994 ( ISBN 1-55608-009-3). - Hazewinkel, M. (Ed.),
*Encyclopaedia of Mathematics*, Supplement I, Kluwer, 1997 ( ISBN 0-7923-4709-9). - Hazewinkel, M. (Ed.),
*Encyclopaedia of Mathematics*, Supplement II, Kluwer, 2000 ( ISBN 0-7923-6114-8). - Hazewinkel, M. (Ed.),
*Encyclopaedia of Mathematics*, Supplement III, Kluwer, 2002 ( ISBN 1-4020-0198-3).

- Hazewinkel, M. (Ed.),
- Hazewinkel, M. (Ed.),
*Encyclopaedia of Mathematics on CD-ROM*, Kluwer, 1998 ( ISBN 0-7923-4805-2). *Encyclopedia of Mathematics*, public wiki monitored by an editorial board under the management of the European Mathematical Society.^{ [1] }

In mathematics, the **ascending chain condition** (**ACC**) and **descending chain condition** (**DCC**) are finiteness properties satisfied by some algebraic structures, most importantly ideals in certain commutative rings. These conditions played an important role in the development of the structure theory of commutative rings in the works of David Hilbert, Emmy Noether, and Emil Artin. The conditions themselves can be stated in an abstract form, so that they make sense for any partially ordered set. This point of view is useful in abstract algebraic dimension theory due to Gabriel and Rentschler.

An **encyclopedia** or **encyclopædia** is a reference work or compendium providing summaries of knowledge either general or special to a particular field or discipline. Encyclopedias are divided into articles or entries that are arranged alphabetically by article name or by thematic categories, or else are hyperlinked and searchable. Encyclopedia entries are longer and more detailed than those in most dictionaries. Generally speaking, encyclopedia articles focus on *factual information* concerning the subject named in the article's title; this is unlike dictionary entries, which focus on linguistic information about words, such as their etymology, meaning, pronunciation, use, and grammatical forms.

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**Ajima Naonobu**, also known as **Ajima Manzō Chokuyen**, was a Japanese mathematician of the Edo period.

**Paraconsistent mathematics**, sometimes called **inconsistent mathematics**, represents an attempt to develop the classical infrastructure of mathematics based on a foundation of paraconsistent logic instead of classical logic. A number of reformulations of analysis can be developed, for example functions which both do and do not have a given value simultaneously.

**Aida Yasuaki** also known as **Aida Ammei**, was a Japanese mathematician in the Edo period.

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* Die Musik in Geschichte und Gegenwart: Allgemeine Enzyklopädie der Musik (MGG)* is one of the world's most comprehensive encyclopedias of music history and musicology, on account of its scope, content, wealth of research areas, and reference to related subjects. It has appeared in two self-contained printed editions and a continuously updated and expanding digital edition, titled

In mathematics, a **character sum** is a sum of values of a Dirichlet character χ *modulo**N*, taken over a given range of values of *n*. Such sums are basic in a number of questions, for example in the distribution of quadratic residues, and in particular in the classical question of finding an upper bound for the least quadratic non-residue *modulo**N*. Character sums are often closely linked to exponential sums by the Gauss sums.

In mathematical logic, **abstract algebraic logic** is the study of the algebraization of deductive systems arising as an abstraction of the well-known Lindenbaum–Tarski algebra, and how the resulting algebras are related to logical systems.

* Den Store Danske Encyklopædi* is the most comprehensive contemporary Danish language encyclopedia. The 20 volumes of the encyclopedia were published successively between 1994 and 2001; a one-volume supplement was published in 2002 and two index volumes in 2003. The work comprises 115,000 articles, ranging in size from single-line cross references to the 130-page entry on Denmark. The articles were written by a staff of about 4,000 academic experts led by editor-in-chief Jørn Lund. Articles longer than a few dozen lines are signed by their authors. Many articles are illustrated.

In mathematics, **symmetrization** is a process that converts any function in variables to a symmetric function in variables. Similarly, **antisymmetrization** converts any function in variables into an antisymmetric function.

In mathematics, a **matrix coefficient** is a function on a group of a special form, which depends on a linear representation of the group and additional data. Precisely, it is a function on a compact topological group *G* obtained by composing a representation of *G* on a vector space *V* with a linear map from the endomorphisms of *V* into *V* 's underlying field. It is also called a **representative function**. They arise naturally from finite-dimensional representations of *G* as the matrix-entry functions of the corresponding matrix representations. The Peter–Weyl theorem says that the matrix coefficients on *G* are dense in the Hilbert space of square-integrable functions on *G*.

In the mathematical theory of partial differential equations, a **Monge equation**, named after Gaspard Monge, is a first-order partial differential equation for an unknown function *u* in the independent variables *x*_{1},...,*x*_{n}

**Al-Hassar** or **Abu Bakr Muhammad ibn Abdallah ibn Ayyash al-Hassar** was a 12th-century Moroccan mathematician. He is the author of two books *Kitab al-bayan wat-tadhkar*, a manual of calculation and *Kitab al-kamil fi sinaat al-adad*, on the breakdown of numbers. The first book is lost and only a part of the second book remains.

**Helaine Selin** is an American librarian, historian of science, author and the editor of several bestselling books.

**Michiel Hazewinkel** is a Dutch mathematician, and Emeritus Professor of Mathematics at the Centre for Mathematics and Computer Science and the University of Amsterdam, particularly known for his 1978 book *Formal groups and applications* and as editor of the *Encyclopedia of Mathematics*.

In the mathematical field of topology, there are various notions of a ** P-space** and of a

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