The striking theorems showcased in this book are among the most
profound results of twentieth-century analysis. The authors'
original approach combines rigorous mathematical proofs with
commentary on the underlying ideas to provide a rich insight into
these landmarks in mathematics. Results ranging from the proof of
Littlewood's conjecture to the Banach-Tarski paradox have been
selected for their mathematical beauty as well as educative value
and historical role. Placing each theorem in historical
perspective, the authors paint a coherent picture of modern
analysis and its development, whilst maintaining mathematical
rigour with the provision of complete proofs, alternative proofs,
worked examples, and more than 150 exercises and solution hints.
This edition extends the original French edition of 2009 with a new
chapter on partitions, including the Hardy-Ramanujan theorem, and a
significant expansion of the existing chapter on the Corona
problem.
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