Kundenrezensionen


1 Rezension
5 Sterne:
 (1)
4 Sterne:    (0)
3 Sterne:    (0)
2 Sterne:    (0)
1 Sterne:    (0)
 
 
 
 
 
Durchschnittliche Kundenbewertung
Sagen Sie Ihre Meinung zu diesem Artikel
Eigene Rezension erstellen
 
 
Hilfreichste Bewertungen zuerst | Neueste Bewertungen zuerst

11 von 11 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen Test the limits !, 5. Oktober 2004
Von 
Palle E T Jorgensen "Palle Jorgensen" (Iowa City, Iowa United States) - Alle meine Rezensionen ansehen
(REAL NAME)   
Rezension bezieht sich auf: Counterexamples in Analysis (Dover Books on Mathematics) (Taschenbuch)
In my teaching of the basic tools of mathematical analysis; and even going back to my student days, I noticed the hurdle that separates the beautiful definitions from the `messy' examples. Often students tell me that the theory looks so easy, `but how do we construct an example to illustrate the limits of the theory?' -----A counter example?
Part of the difficulty is that the definitions involve quantifiers; and how do you check the quantifier `for all' ? And on top of that, there are the axioms of set theory: the axiom of choice, or one of its equivalent variants.
The lovely little book by Gelbaum-Olmsted was a savior to many of us when we started out in math, and it appeared first in 1961. But I had almost forgotten about it until by accident (while browsing in the bookstore) I stumbled over a new edition of it about a year ago, a lovely Dover reprinted edition. And so affordable !
In all the other books you learn about the wonderful things that are true about convergence, sets on the line or in the plane, modern variants of the so called Fundamental Theorem of Calculus, and in Gelbaum-Olmstead you learn the things that aren't true. And then there are all the lovely Cantor constructions, The Devil's Staircase, space filling curves, and much more; beautiful, but little known constructions going back to Lebesgue, and some to Riemann.
But more importantly the book gives students an edge when they have to do the assigned exercises in your analysis course. Many told me that the book is a 'secret weapon'.
Palle Jorgensen, October 2004.
Helfen Sie anderen Kunden bei der Suche nach den hilfreichsten Rezensionen 
War diese Rezension für Sie hilfreich? Ja Nein


Hilfreichste Bewertungen zuerst | Neueste Bewertungen zuerst

Dieses Produkt

Counterexamples in Analysis (Dover Books on Mathematics)
Counterexamples in Analysis (Dover Books on Mathematics) von John M. H. Olmsted (Taschenbuch - 12. Mai 2003)
EUR 16,66
Auf Lager.
In den Einkaufswagen Auf meinen Wunschzettel
Nur in den Rezensionen zu diesem Produkt suchen