Analysis II (Texts and Readings in Mathematics, Band 38) - Hardcover

Tao, Terence

Hardcover

ISBN 10: 9380250657 ISBN 13: 9789380250656

Verlag: Hindustan Book Agency, 2014

Inhaltsangabe

Thisis part two of a two-volume book on real analysis and is intended for seniorundergraduate students of mathematics who have already been exposed tocalculus. The emphasis is on rigour and foundations of analysis. Beginning withthe construction of the number systems and set theory, the book discusses thebasics of analysis (limits, series, continuity, differentiation, Riemannintegration), through to power series, several variable calculus and Fourieranalysis, and then finally the Lebesgue integral. These are almost entirely setin the concrete setting of the real line and Euclidean spaces, although thereis some material on abstract metric and topological spaces. The book also has appendiceson mathematical logic and the decimal system. The entire text (omitting someless central topics) can be taught in two quarters of 25–30 lectures each. Thecourse material is deeply intertwined with the exercises, as it is intendedthat the student actively learn the material (and practice thinking and writingrigorously) by proving several of the key results in the theory. 

Über diesen Titel

Über die Autorin bzw. den Autor

Terence "Terry" Chi-Shen Tao, FAA FRS, is an Australian mathematician. His areas of interests are in harmonic analysis, partial differential equations, algebraic combinatorics, arithmetic combinatorics, geometric combinatorics, compressed sensing and analytic number theory. As of 2015, he holds the James and Carol Collins chair in mathematics at the University of California, Los Angeles. Professor Tao is a co-recipient of the 2006 Fields Medal and the 2014 Breakthrough Prize in Mathematics. He maintains a personal mathematics blog, which has been described by Timothy Gowers as “the undisputed king of all mathematics blogs”.

Von der hinteren Coverseite

Thisis part two of a two-volume book on real analysis and is intended for seniorundergraduate students of mathematics who have already been exposed tocalculus. The emphasis is on rigour and foundations of analysis. Beginning withthe construction of the number systems and set theory, the book discusses thebasics of analysis (limits, series, continuity, differentiation, Riemannintegration), through to power series, several variable calculus and Fourieranalysis, and then finally the Lebesgue integral. These are almost entirely setin the concrete setting of the real line and Euclidean spaces, although thereis some material on abstract metric and topological spaces. The book also has appendiceson mathematical logic and the decimal system. The entire text (omitting someless central topics) can be taught in two quarters of 25 30 lectures each. Thecourse material is deeply intertwined with the exercises, as it is intendedthat the student actively learn the material (and practice thinking and writingrigorously) by proving several of the key results in the theory.

Details zur Ausgabe

• Verlag: Hindustan Book Agency
• Erscheinungsdatum: 2014
• Sprache: Englisch
• ISBN 10: 9380250657
• ISBN 13: 9789380250656
• Einband: Gebundene Ausgabe
• Auflage: 3
• Anzahl der Seiten: 218
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: Nicht verfügbar