Analysis I - Rilegato

Tao, Terence

Rilegato

ISBN 10: 9380250649 ISBN 13: 9789380250649

Casa editrice: Amer Mathematical Society, 2014

Riassunto

Thisis part one 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.

Su questo libro

Informazioni sull?autore

Terence "Terry" Chi-ShenTao, FAA FRS, is an Australian mathematician.His areas of interests are in harmonic analysis, partial differential equations, algebraiccombinatorics, arithmetic combinatorics, geometriccombinatorics, compressedsensing and analyticnumber theory. As of 2015, he holds the James and Carol Collins chair inmathematics at the University of California, Los Angeles.Professor Tao is a co-recipient of the 2006 Fields Medal andthe 2014 Breakthrough Prize in Mathematics.He maintains a personal mathematics blog, which has been describedby TimothyGowers as “the undisputed king of all mathematics blogs”.

Dalla quarta di copertina

Thisis part one 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.

Dettagli dell?edizione

• Editore: Amer Mathematical Society
• Data di pubblicazione: 2014
• ISBN 10: 9380250649
• ISBN 13: 9789380250649
• Rilegatura: Copertina rigida
• Lingua: Inglese
• Numero edizione: 3
• Numero di pagine: 347
• Contatto del produttore: non disponibile