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The Number System (Dover Books on Mathematics), by H. A. Thurston
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The teaching of mathematics has undergone extensive changes in approach, with a shift in emphasis from rote memorization to acquiring an understanding of the logical foundations and methodology of problem solving. This book offers guidance in that direction, exploring arithmetic's underlying concepts and their logical development.
This volume's great merit lies in its wealth of explanatory material, designed to promote an informal and intuitive understanding of the rigorous logical approach to the number system. The first part explains and comments on axioms and definitions, making their subsequent treatment more coherent. The second part presents a detailed, systematic construction of the number systems of rational, real, and complex numbers. It covers whole numbers, hemigroups and groups, integers, ordered fields, the order relation for rationals, exponentiation, and real and complex numbers. Every step is justified by a reference to the appropriate theorem or lemma. Exercises following each chapter in Part II help readers test their progress and provide practice in using the relevant concepts.
- Sales Rank: #1488418 in Books
- Published on: 2007-04-19
- Released on: 2007-04-19
- Original language: English
- Number of items: 1
- Dimensions: 8.51" h x .28" w x 5.46" l, .35 pounds
- Binding: Paperback
- 144 pages
Most helpful customer reviews
13 of 13 people found the following review helpful.
Necessary and sufficient
By Jeremy Roach
This is a better book than E. Landau's classic Foundations of Analysis in many ways. It has several insightful expository chapters that precede the rigorous systematic part. The integers are actually formalized (Landau only introduces negative numbers with the reals). And Cauchy sequences are used to model the irrational numbers instead of Dedekind cuts. Abstract algebraic structures (hemigroup, commutative group, field, ordered field) are defined and used to avoid duplicating theorems and proofs for the different types of numbers. Also Landau only defines integral powers whereas Thurston defines both rational and real powers.
Thanks to Dover for publishing great books like this at such a low price.
0 of 1 people found the following review helpful.
Five Stars
By Massimo Coletti
Everything as expected, thanks.
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