Advanced Calculus
by Lynn H. Loomis, Shlomo Sternberg · first published 2014
2mentions
1recommended by
2HN commenters
2011–2014first – last mentioned
50% recommend50% neutral
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…solving, contests, and inequalities, say by Polya or Andreescu. ... a higher-level view of day-to-day mathematical practice. There probably isn't one book for this, but I'd recommend Loomis and Sternberg's Advanced Calculus as a summation of linear algebra and calculus on manifolds; you'd also need to read on complex and functional analysis, algebra (Lang and the unofficial companion volume?), topology ... ... a broad but…
on “Ask HN: Math books like SICP?” ↗…Company, Inc., Princeton, New Jersey. Walter Rudin, 'Principles of Mathematical Analysis, Third Edition', McGraw-Hill. Michael Spivak, 'Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus', W. A. Benjamin, New York. Working successfully through those three is quite sufficient to understand proof-based college math! Those three are all old; in particular Halmos wrote the first edition…
on “Teachers write their own online textbook, save district $175,000” ↗