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Its authors have divided Elementary Number Theory, Group Theory and Ramanujan Graphs into four chapters. The first of these provides background in graph theory, including material on the girth of graphs (the length of the shortest cycle), on graph coloring, and on the use of the probabilistic method to prove the existence of graphs for which both the girth and the number of colors needed are ...
Mathematics. Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics." [1]
1938. Publisher. Clarendon Press. OCLC. 879664. An Introduction to the Theory of Numbers is a classic textbook in the field of number theory, by G. H. Hardy and E. M. Wright. The book grew out of a series of lectures by Hardy and Wright and was first published in 1938. The third edition added an elementary proof of the prime number theorem, and ...
The books cover plane and solid Euclidean geometry, elementary number theory, and incommensurable lines. Elements is the oldest extant large-scale deductive treatment of mathematics. It has proven instrumental in the development of logic and modern science , and its logical rigor was not surpassed until the 19th century.
Elementary number. An elementary number is one formalization of the concept of a closed-form number. The elementary numbers form an algebraically closed field containing the roots of arbitrary expressions using field operations, exponentiation, and logarithms. The set of the elementary numbers is subdivided into the explicit elementary numbers ...
Disquisitiones Arithmeticae (Latin for Arithmetical Investigations) is a textbook on number theory written in Latin by Carl Friedrich Gauss in 1798, when Gauss was 21, and published in 1801, when he was 24. It had a revolutionary impact on number theory by making the field truly rigorous and systematic and paved the path for modern number ...