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Elementary Theory of Metric Spaces. A Course in Constructing Mathematical. Universitext
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Bester Preis: € 4,56 (vom 03.11.2016)Elementary Theory of Metric Spaces
ISBN: 9780387907062 bzw. 0387907068, in Englisch, Springer, Deutschland, Taschenbuch, neu.
Publisher/Verlag: Springer, Berlin | A Course in Constructing Mathematical Proofs | 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. | 0. Some Ideas of Logic.- I. Sets and Mappings.- 1. Some Concepts of Set Theory.- 2. Some Further Operations on Sets.- 3. Mappings.- 4. Surjective and Injective Mappings.- 5. Bijective Mappings and Inverses.- II. Metric Spaces.- 1. Definition of Metric Space and Some Examples.- 2. Closed and Open Balls; Spheres.- 3. Open Sets.- 4. Closed Sets.- 5. Closure of a Set.- 6. Diameter of a Set; Bounded Sets.- 7. Subspaces of a Metric Space.- 8. Interior of a Set.- 9. Boundary of a Set.- 10. Dense Sets.- 11. Afterword.- III. Mappings of Metric Spaces.- 1. Continuous Mappings.- 2. Continuous Mappings and Subspaces.- 3. Uniform Continuity.- IV. Sequences in Metric Spaces.- 1. Sequences.- 2. Sequences in Metric Spaces.- 3. Cluster Points of a Sequence.- 4. Cauchy Sequences.- 5. Complete Metric Spaces.- V. Connectedness.- 1. Connected Spaces and Sets.- 2. Connected Sets in R.- 3. Mappings of Connected Spaces and Sets.- VI. Compactness.- 1. Compact Spaces and Sets.- 2. Mappings of Compact Spaces.- 3. Sequential Compactness.- 4. Compact Subsets of R.- Afterword.- Appendix M. Mathematical Induction.- Appendix S. Solutions. | Format: Paperback | Language/Sprache: english | 205 gr | 120 pp.
Elementary Theory of Metric Spaces (1998)
ISBN: 9780387907062 bzw. 0387907068, in Englisch, Springer Jun 1998, Taschenbuch, neu, Nachdruck.
This item is printed on demand - Print on Demand Neuware - 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. 120 pp. Englisch.
Elementary Theory of Metric Spaces (1998)
ISBN: 9780387907062 bzw. 0387907068, in Englisch, Springer Jun 1998, Taschenbuch, neu.
Neuware - 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. 136 pp. Englisch.
Elementary Theory of Metric Spaces: A Course in Constructing Mathematical Proofs (Universitext)
ISBN: 9780387907062 bzw. 0387907068, in Englisch, Springer, gebraucht.
Von Händler/Antiquariat, Better World Books Ltd.
Springer. Used - Good. Ships from the UK. Former Library book. Shows some signs of wear, and may have some markings on the inside. 100% Money Back Guarantee. Your purchase also supports literacy charities.
Elementary Theory of Metric Spaces. A Course in Constructing Mathematical. Universitext (1982)
ISBN: 9783540907060 bzw. 3540907068, in Deutsch, New York , Heidelberg , Berlin : Springer, Taschenbuch, gebraucht.
118 S. : graph. Darst. , 24 cm Versand erfolgt am folgenden Werktag / stempel innen, bib.exempl, *** UNBENUTZT *** Sprache: Deutsch.
Elementary Theory of Metric Spaces: A Course in Constructing Mathematical Proofs (1982)
ISBN: 9783540907060 bzw. 3540907068, in Deutsch, 120 Seiten, Springer-Verlag GmbH, Taschenbuch, gebraucht.
Von Händler/Antiquariat, fachbuecher-weltversand.
Die Beschreibung dieses Angebotes ist von geringer Qualität oder in einer Fremdsprache. Trotzdem anzeigen
Elementary Theory of Metric Spaces: A Course in Constructing Mathematical Proofs (Universitext) (1998)
ISBN: 9780387907062 bzw. 0387907068, in Englisch, Springer, Taschenbuch.
Von Händler/Antiquariat, Ergodebooks.
Springer, 1998-06-09. Paperback. Used:Good. Ships Fast. Expedite Shipping Available.
Elementary Theory of Metric Spaces
ISBN: 9781461381884 bzw. 1461381886, in Englisch, Springer Nature, neu, E-Book.
Die Beschreibung dieses Angebotes ist von geringer Qualität oder in einer Fremdsprache. Trotzdem anzeigen
ELEMENTARY THEORY OF METRIC SPACES A Course in Constructing Mathematical Proofs (1982)
ISBN: 9783540907060 bzw. 3540907068, in Deutsch, Springer Verlag, New York, Taschenbuch, gebraucht.
Die Beschreibung dieses Angebotes ist von geringer Qualität oder in einer Fremdsprache. Trotzdem anzeigen