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Books > Science & Mathematics > Mathematics > Algebra
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Number Systems - An Introduction to Algebra and Analysis (Hardcover)
Loot Price: R2,011
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Number Systems - An Introduction to Algebra and Analysis (Hardcover)
Series: Pure and Applied Undergraduate Texts
Expected to ship within 12 - 17 working days
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This book offers a rigorous and coherent introduction to the five
basic number systems of mathematics, namely natural numbers,
integers, rational numbers, real numbers, and complex numbers. It
is a subject that many mathematicians believe should be learned by
any student of mathematics including future teachers. The book
starts with the development of Peano arithmetic in the first
chapter which includes mathematical induction and elements of
recursion theory. It proceeds to an examination of integers that
also covers rings and ordered integral domains. The presentation of
rational numbers includes material on ordered fields and
convergence of sequences in these fields. Cauchy and Dedekind
completeness properties of the field of real numbers are
established, together with some properties of real continuous
functions. An elementary proof of the Fundamental Theorem of
Algebra is the highest point of the chapter on complex numbers. The
great merit of the book lies in its extensive list of exercises
following each chapter. These exercises are designed to assist the
instructor and to enhance the learning experience of the students.
General
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