クレレ誌：
https://ja.wikipedia.org/wiki/%E3%82%AF%E3%83%AC%E3%83%AC%E8%AA%8C
クレレ誌はアカデミーの紀要ではない最初の主要な数学学術誌の一つである（Neuenschwander 1994, p. 1533）。ニールス・アーベル、ゲオルク・カントール、ゴットホルト・アイゼンシュタインらの研究を含む著名な論文を掲載してきた。
(引用終り)
そこで
現代の純粋・応用数学（含むガロア理論）を目指して
新スレを立てる（＾＾；
＜関連過去スレ（含むガロア理論）＞
・現代数学の系譜 工学物理雑談 古典ガロア理論も読む84
https://rio2016.5ch.net/test/read.cgi/math/1582200067/
・現代数学の系譜 工学物理雑談 古典ガロア理論も読む83
https://rio2016.5ch.net/test/read.cgi/math/1581243504/
＜前スレ＞
純粋・応用数学
https://rio2016.5ch.net/test/read.cgi/math/1582599485/1-
純粋・応用数学（含むガロア理論）2
■ このスレッドは過去ログ倉庫に格納されています
2020/06/19(金) 23:54:58.88ID:imq2ACd0
712現代数学の系譜 雑談 ◆yH25M02vWFhP
2020/07/12(日) 10:03:39.76ID:/6i4k5qr >>689
WILLIAM P. THURSTON ｗｗｗ（＾＾
（参考）
https://arxiv.org/pdf/math/9404236.pdf
APPEARED IN BULLETIN OF THE
AMERICAN MATHEMATICAL SOCIETY
Volume 30, Number 2, April 1994, Pages 161-177
ON PROOF AND PROGRESS IN MATHEMATICS
WILLIAM P. THURSTON
(抜粋)
2. How do people understand mathematics?
This is a very hard question. Understanding is an individual and internal matter
that is hard to be fully aware of, hard to understand and often hard to communicate.
We can only touch on it lightly here.
People have very different ways of understanding particular pieces of mathematics. To illustrate this, it is best to take an example that practicing mathematicians
understand in multiple ways, but that we see our students struggling with. The
derivative of a function fits well. The derivative can be thought of as:
(1) Infinitesimal: the ratio of the infinitesimal change in the value of a function
to the infinitesimal change in a function.
(2) Symbolic: the derivative of x^n is nx^(n-1), the derivative of sin(x) is cos(x),
the derivative of f ・ g is f′ ・ g * g′, etc.
(3) Logical: f′(x) = d if and only if for every ε there is a δ such that when
0 < |Δx| < δ,
|{(f(x + Δx) - f(x))/Δx}- d |< δ.
(4) Geometric: the derivative is the slope of a line tangent to the graph of the
function, if the graph has a tangent.
(5) Rate: the instantaneous speed of f(t), when t is time.
(6) Approximation: The derivative of a function is the best linear approximation to the function near a point.
(7) Microscopic: The derivative of a function is the limit of what you get by looking at it under a microscope of higher and higher power.
つづく
WILLIAM P. THURSTON ｗｗｗ（＾＾
（参考）
https://arxiv.org/pdf/math/9404236.pdf
APPEARED IN BULLETIN OF THE
AMERICAN MATHEMATICAL SOCIETY
Volume 30, Number 2, April 1994, Pages 161-177
ON PROOF AND PROGRESS IN MATHEMATICS
WILLIAM P. THURSTON
(抜粋)
2. How do people understand mathematics?
This is a very hard question. Understanding is an individual and internal matter
that is hard to be fully aware of, hard to understand and often hard to communicate.
We can only touch on it lightly here.
People have very different ways of understanding particular pieces of mathematics. To illustrate this, it is best to take an example that practicing mathematicians
understand in multiple ways, but that we see our students struggling with. The
derivative of a function fits well. The derivative can be thought of as:
(1) Infinitesimal: the ratio of the infinitesimal change in the value of a function
to the infinitesimal change in a function.
(2) Symbolic: the derivative of x^n is nx^(n-1), the derivative of sin(x) is cos(x),
the derivative of f ・ g is f′ ・ g * g′, etc.
(3) Logical: f′(x) = d if and only if for every ε there is a δ such that when
0 < |Δx| < δ,
|{(f(x + Δx) - f(x))/Δx}- d |< δ.
(4) Geometric: the derivative is the slope of a line tangent to the graph of the
function, if the graph has a tangent.
(5) Rate: the instantaneous speed of f(t), when t is time.
(6) Approximation: The derivative of a function is the best linear approximation to the function near a point.
(7) Microscopic: The derivative of a function is the limit of what you get by looking at it under a microscope of higher and higher power.
つづく
713現代数学の系譜 雑談 ◆yH25M02vWFhP
2020/07/12(日) 10:04:12.99ID:/6i4k5qr >>712
つづき
This is a list of different ways of thinking about or conceiving of the derivative,
rather than a list of different logical definitions. Unless great efforts are made to
maintain the tone and flavor of the original human insights, the differences start
to evaporate as soon as the mental concepts are translated into precise, formal and
explicit definitions.
I can remember absorbing each of these concepts as something new and interesting, and spending a good deal of mental time and effort digesting and practicing
with each, reconciling it with the others. I also remember coming back to revisit
these different concepts later with added meaning and understanding.
(引用終り)
つづき
This is a list of different ways of thinking about or conceiving of the derivative,
rather than a list of different logical definitions. Unless great efforts are made to
maintain the tone and flavor of the original human insights, the differences start
to evaporate as soon as the mental concepts are translated into precise, formal and
explicit definitions.
I can remember absorbing each of these concepts as something new and interesting, and spending a good deal of mental time and effort digesting and practicing
with each, reconciling it with the others. I also remember coming back to revisit
these different concepts later with added meaning and understanding.
(引用終り)
714現代数学の系譜 雑談 ◆yH25M02vWFhP
2020/07/12(日) 10:08:29.29ID:/6i4k5qr■ このスレッドは過去ログ倉庫に格納されています
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