Titlebook: A Concrete Introduction to Higher Algebra; Lindsay N. Childs Textbook 19952nd edition Springer Science+Business Media New York 1995 algebr

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Kristóf Fenyvesi,Tuuli LähdesmäkiMathematics grows through the development and study of new concepts. The history of numbers illustrates this growth.

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Marcílio Franca,Alessandra Macedo FrancaThis chapter describes the method of proof by induction, in several versions, and includes some useful examples, notably the division theorem. The division theorem, in turn, is used to develop representations of numbers in various bases.

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Rhetoric, Economics, and NatureThis chapter is devoted to defining and studying Gauss’s useful notion of congruence for integers.

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Text and Context: , (A Preface),With the notion of congruence we can define many new sets of “numbers.” The process is analogous to the idea behind the definition of the rational numbers, as discussed in Chapter 1. You may wish to review Chapter 1 while reading this chapter.

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Mapping Dark Matter and the Venice ParadoxIn this chapter we describe a few of the many uses of congruences—to tournaments, to generating “random” numbers, to finding prime numbers and factoring, and to cryptography. Numerous other applications will arise in later chapters.

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