Criteria for Divisibility
by N. N. Vorobyov
University of Chicago Press, 1980
Paper: 978-0-226-86516-4
Library of Congress Classification QA242.V6713
Dewey Decimal Classification 513.2

ABOUT THIS BOOK | AUTHOR BIOGRAPHY | TOC
ABOUT THIS BOOK
N. N. Vorob'ev's Criteria for Divisibility introduces the high school or early college student to a specific number-theoretic topic and explains the general mathematical structures which underlie the particular concepts discussed. Vorob'ev discusses the ideas of well-ordered sets, partial and linear orderings, equivalence relations, equivalence classes, algorithms, and the relationship between the determinability of algorithms defined on the integers and the well-ordering principle.

All this is done comprehensively with the help of a unique plan for study which encourages the student to skip large sections of the book on first reading and return to them later. The more general and conceptually challenging material appears in small print, so that the student must have a good grasp of the number-theoretic concepts on which the generalizations are based before making the step to generalization. The booklet provides both specific knowledge in a particular field of mathematical investigation and a fine basis on which to continue studies in mathematics.

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