60才からの数学への理解
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0218132人目の素数さん
2011/02/05(土) 10:09:48I sometimes joke that "mathematical maturity" is the ability to understand poor exposition.
Lang's proofs are often too terse, and even experienced readers will sometimes have to work hard
to fill in all the gaps.
For this reason this book is not the best choice for most beginning graduate students.
Nevertheless, time and time again in my study of algebraic number theory and algebraic geometry,
when there has been some nugget of algebra that I had forgotten or never learned,
I have found it in Lang and not in other standard texts.
So for me, this book is an indispensable reference.
Lang also has a knack for giving insightful summaries of advanced topics.
Most other authors will at most mention an advanced topic without
really telling you anything about it, but Lang actually gives useful introductions
to a large number of topics of current research interest.
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