The New Mathematics"This book reveals that the concepts of advanced mathematics lie hidden in the elementary mathematics we all learned in school. The author brings these concepts out of their hiding places as he traces the steps by which our number system has grown from the ordinary whole we use for counting, through integers, rational numbers, and real numbers, to the complex numbers with which the electrical engineer describes an alternating current. In this way, he shows the familiar origin of such unfamiliar concepts and terms of the new mathematics as groups, rings, fields, vector spaces, algebras, homomorphisms, isomorphisms, and homeomorphisms."-- |
Contents
Numbers for Counting | 13 |
Number Systems Without Numbers | 35 |
New Numbers From Old | 44 |
Copyright | |
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Common terms and phrases
a₁ abelian group addition and multiplication algebra answer arrow assign belongs binary operation c₁ called cardinal number Chapter commutative law complex number system components construct defined definition digits distributive law distributive with respect divide empty set equal example fact field finger finite number five laws fraction ideal identity element infinite decimal intersection isomorphic linear mappings mathematics means multiplication table natural number system negative neighborhood nest of intervals notation obey the five one-to-one correspondence open set ordered pairs pair of numbers partial sums plane point of adherence polynomials positive integers properties quotient quotient group rational number system real number system reciprocal remainder represent residue classes modulo respect to addition reverse mapping scalar multiplication sequence subset symbol system of integers tion topological space topological structure unity element vector space zero divisors zero element