000			02031nam a22002535i 4500
001			978-981-10-1789-6
003			DE-He213
005			20210812160325.0
008			160829s2016 si | s |||| 0|eng d
020			_a9789811017896 _9978-981-10-1789-6
024	7		_a10.1007/978-981-10-1789-6 _2doi
082	0	4	_a515 _223
100	1		_aTao, Terence. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut
245	1	0	_aAnalysis I _h[electronic resource] : _bThird Edition / _cby Terence Tao.
250			_a1st ed. 2016.
264		1	_aSingapore : _bSpringer Singapore : _bImprint: Springer, _c2016.
300			_aXIX, 350 p. _bonline resource.
520			_aThis is part one of a two-volume book on real analysis and is intended for senior undergraduate students of mathematics who have already been exposed to calculus. The emphasis is on rigour and foundations of analysis. Beginning with the construction of the number systems and set theory, the book discusses the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and then finally the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. The book also has appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of 25-30 lectures each. The course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory. .
650		0	_aMathematical analysis.
650		0	_aAnalysis (Mathematics).
650	1	4	_aAnalysis. _0https://scigraph.springernature.com/ontologies/product-market-codes/M12007
710	2		_aSpringerLink (Online service)
773	0		_tSpringer Nature eBook
856	4	0	_uhttps://doi.org/10.1007/978-981-10-1789-6
999			_c1474 _d1474