Language:EnglishPublisher:Cambridge University PressISBN-13:9781009538671ISBN-10:1009538675UPC:9781009538671Book Category:MathematicsBook Subcategory:Mathematical AnalysisSize:9.00 x 6.00 x 0.49 inchesWeight:0.7011Product ID:SC833N2DK5
Understanding the natural numbers, which we use to count things, comes naturally. Meanwhile, the real numbers, which include a wide range of numbers from whole numbers to fractions to exotic ones like π, are, frankly, really difficult to describe rigorously. Instead of waiting to take a theorem-proof graduate course to appreciate the real numbers, readers new to university-level mathematics can explore the core ideas behind the construction of the real numbers in this friendly introduction. Beginning with the intuitive notion of counting, the book progresses step-by-step to the real numbers. Each sort of number is defined in terms of a simpler kind by developing an equivalence relation on a previous idea. We find the finite sets' equivalence classes are the natural numbers. Integers are equivalence classes of pairs of natural numbers. Modular numbers are equivalence classes of integers. And so forth. Exercises and their solutions are included.
Language:EnglishPublisher:Cambridge University PressISBN-13:9781009538671ISBN-10:1009538675UPC:9781009538671Book Category:MathematicsBook Subcategory:Mathematical AnalysisSize:9.00 x 6.00 x 0.49 inchesWeight:0.7011Product ID:SC833N2DK5
Scheinerman, Edward: - Edward Scheinerman is Professor of Applied Mathematics and Statistics at Johns Hopkins University. He is the author of various books including textbooks, a research monograph, and a volume for general readership, The Mathematics Lover's Companion (2017). He has twice been awarded the Mathematical Association of America's Lester R. Ford Award for outstanding mathematical exposition and has received numerous teaching awards at Johns Hopkins. His research publications are in discrete mathematics.
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Understanding the natural numbers, which we use to count things, comes naturally. Meanwhile, the real numbers, which include a wide range of numbers from whole numbers to fractions to exotic ones like π, are, frankly, really difficult to describe rigorously. Instead of waiting to take a theorem-proof graduate course to appreciate the real numbers, readers new to university-level mathematics can explore the core ideas behind the construction of the real numbers in this friendly introduction. Beginning with the intuitive notion of counting, the book progresses step-by-step to the real numbers. Each sort of number is defined in terms of a simpler kind by developing an equivalence relation on a previous idea. We find the finite sets' equivalence classes are the natural numbers. Integers are equivalence classes of pairs of natural numbers. Modular numbers are equivalence classes of integers. And so forth. Exercises and their solutions are included.
Scheinerman, Edward: - Edward Scheinerman is Professor of Applied Mathematics and Statistics at Johns Hopkins University. He is the author of various books including textbooks, a research monograph, and a volume for general readership, The Mathematics Lover's Companion (2017). He has twice been awarded the Mathematical Association of America's Lester R. Ford Award for outstanding mathematical exposition and has received numerous teaching awards at Johns Hopkins. His research publications are in discrete mathematics.
