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  • Eisenstein's criterion — In mathematics, Eisenstein s criterion gives sufficient conditions for a polynomial to be irreducible over the rational numbers (or equivalently, over the integers; see Gauss s lemma). Suppose we have the following polynomial with integer… …   Wikipedia

  • Algebraic number field — In mathematics, an algebraic number field (or simply number field) F is a finite (and hence algebraic) field extension of the field of rational numbers Q. Thus F is a field that contains Q and has finite dimension when considered as a vector… …   Wikipedia

  • Europe, history of — Introduction       history of European peoples and cultures from prehistoric times to the present. Europe is a more ambiguous term than most geographic expressions. Its etymology is doubtful, as is the physical extent of the area it designates.… …   Universalium

  • Discriminant of an algebraic number field — A fundamental domain of the ring of integers of the field K obtained from Q by adjoining a root of x3 − x2 − 2x + 1. This fundamental domain sits inside K ⊗QR. The discriminant of K is 49 = 72.… …   Wikipedia

  • logic, history of — Introduction       the history of the discipline from its origins among the ancient Greeks to the present time. Origins of logic in the West Precursors of ancient logic       There was a medieval tradition according to which the Greek philosopher …   Universalium

  • ECONOMIC HISTORY — This article is arranged according to the following outline: first temple period exile and restoration second temple period talmudic era muslim middle ages medieval christendom economic doctrines early modern period sephardim and ashkenazim… …   Encyclopedia of Judaism

  • ZIONISM — This article is arranged according to the following outline: the word and its meaning forerunners ḤIBBAT ZION ROOTS OF ḤIBBAT ZION background to the emergence of the movement the beginnings of the movement PINSKER S AUTOEMANCIPATION settlement… …   Encyclopedia of Judaism

  • HISTORICAL SURVEY: THE STATE AND ITS ANTECEDENTS (1880–2006) — Introduction It took the new Jewish nation about 70 years to emerge as the State of Israel. The immediate stimulus that initiated the modern return to Zion was the disappointment, in the last quarter of the 19th century, of the expectation that… …   Encyclopedia of Judaism

  • TALMUD, BABYLONIAN — (Heb. תַּלְמוּד בַּבְלִי), a literary work of monumental proportions (5,894 folio pages in the standard printed editions), which draws upon the totality of the spiritual, intellectual, ethical, historical, and legal traditions produced in… …   Encyclopedia of Judaism

  • Islāmic world — Introduction  prehistory and history of the Islamic community.       Adherence to Islām is a global phenomenon: Muslims predominate in some 30 to 40 countries, from the Atlantic to the Pacific and along a belt that stretches across northern… …   Universalium

  • EDUCATION, JEWISH — This entry is arranged according to the following outline. Bibliography at the end of a section is indicated by (†). in the biblical period the nature of the sources historical survey the patriarchal period and the settlement the kingdom the… …   Encyclopedia of Judaism

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