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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Analysis Elementary Theory of Metric Spaces
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Elementary Theory of Metric Spaces
Robert B. Reisel (Broschiert, Englisch)
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Beschreibung
Science students have to spend much of their time learning how to do laboratory work, even if they intend to become theoretical, rather than experimental, scientists. It is important that they understand how experiments are performed and what the results mean. In science the validity of ideas is checked by experiments. If a new idea does not work in the laboratory, it must be discarded. If it does… work, it is accepted, at least tentatively. In science, therefore, laboratory experiments are the touchstones for the acceptance or rejection of results. Mathematics is different. This is not to say that experiments are not part of the subject. Numerical calculations and the examina tion of special and simplified cases are important in leading mathematicians to make conjectures, but the acceptance of a conjecture as a theorem only comes when a proof has been constructed. In other words, proofs are to mathematics as laboratory experiments are to science. Mathematics students must, therefore, learn to know what constitute valid proofs and how to construct them. How is this done? Like everything else, by doing. Mathematics students must try to prove results and then have their work criticized by experienced mathematicians. They must critically examine proofs, both correct and incorrect ones, and develop an appreciation of good style. They must, of course, start with easy proofs and build to more complicated ones. 80,24 €
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Technische Daten
Erscheinungsdatum
09.06.1998
Sprache
Englisch
EAN
9780387907062
Herausgeber
Springer US
Serien- oder Bandtitel
Universitext
Sonderedition
Nein
Autor
Robert B. Reisel
Seitenanzahl
120
Einbandart
Broschiert
Buch Untertitel
A Course in Constructing Mathematical Proofs
Schlagwörter
Beweis /Aufgabensammlung, Calc, Compact space, Connected space, Metrischer Raum, Spaces, cluster, compactness, learning, logic, mathematical induction, mathematics, metric space, theorem, time
Thema-Inhalt
PBK - Mathematische Analysis, allgemein
Höhe
235 mm
Breite
15.5 cm
Transparenz & Sicherheit
Hersteller: Springer, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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