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Foundations of Analysis: Third Edition
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AMS Chelsea Publishing
1966; 136 pp; hardcover
Volume: 79
Reprint/Revision History:
first AMS printing 2001
ISBN-10: 0-8218-2693-X
ISBN-13: 978-0-8218-2693-5
List Price: US$30 Member Price: US$27
Order Code: CHEL/79.H

Grundlagen der Analysis: Fourth Edition - Edmund Landau

Why does $$2 \times 2 = 4$$? What are fractions? Imaginary numbers? Why do the laws of algebra hold? And how do we prove these laws? What are the properties of the numbers on which the Differential and Integral Calculus is based? In other words, What are numbers? And why do they have the properties we attribute to them? Thanks to the genius of Dedekind, Cantor, Peano, Frege and Russell, such questions can now be given a satisfactory answer. This English translation of Landau's famous Grundlagen der Analysis-also available from the AMS-answers these important questions.

Reviews

"Certainly no clearer treatment of the foundations of the number system can be offered ... one can only be thankful to the author for this fundamental piece of exposition, which is alive with his vitality and genius."

-- American Mathematical Monthly

• Natural Numbers: 1.1 Axioms; 1.2 Addition; 1.3 Ordering; 1.4 Multiplication
• Fractions: 2.1 Definition and equivalence; 2.2 Ordering; 2.3 Addition; 2.4 Multiplication; 2.5 Rational numbers and integers
• Cuts: 3.1 Definition; 3.2 Ordering; 3.3 Addition; 3.4 Multiplication; 3.5 Rational cuts and integral cuts
• Real Numbers: 4.1 Definition; 4.2 Ordering; 4.3 Addition; 4.4 Multiplication; 4.5 Dedekind's fundamental theorem
• Complex Numbers: 5.1 Definition; 5.2 Addition; 5.3 Multiplication; 5.4 Subtraction; 5.5 Division; 5.6 Complex conjugates; 5.7 Absolute value; 5.8 Sums and products; 5.9 Powers; 5.10 Incorporation of the real numbers into the system of complex numbers