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iMMT
papers
Commits
bf5a27ad
Commit
bf5a27ad
authored
Apr 25, 2015
by
Michael Kohlhase
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adoptions/phenomena.tex
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bf5a27ad
...
@@ -177,37 +177,6 @@ which allows arbitrary time structures.
...
@@ -177,37 +177,6 @@ which allows arbitrary time structures.
% \ednote{MK@MK: more, e.g. about the distinction of notations and
% \ednote{MK@MK: more, e.g. about the distinction of notations and
% differing concepts.}
% differing concepts.}
\begin{newpart}
{
MK: re-read
}
\subsection
{
Common Ground and Recaps in Mathematical Textbooks
}
The situation in mathematical textbooks is similar in structure to that in research papers
--perhaps more pronounced. Consider the following passage from Rudin's classical
introductory textbook to Functional Analysis~
\cite
[p. 6f]
{
Rudin:fa73
}
.
\begin{labeledquote}
\sf
\textbf
{
1.5 Topological spaces
}
A
\emph
{
topological space
}
is a set
$
S
$
in which a
collection
$
\tau
$
of subsets (called
\emph
{
open sets
}
) has been specified, with the
following properties:
$
S
$
is open,
$
\emptyset
$
is open, [
\ldots
] Such a collection is
called a
\emph
{
topology
}
on
$
S
$
. [
\ldots
]
\end{labeledquote}
and later -- vector spaces have been recapped earlier in section 1.4:
\begin{labeledquote}
\sf
\textbf
{
1.6 Topological vector spaces
}
Suppose
$
\tau
$
is a topology on a vector space
$
X
$
such that
\begin{compactenum}
[(a)]
\item
\emph
{
every point of
$
X
$
is a closed set, and
}
\item
\emph
{
the vector space operations are continuous with respect to
$
\tau
$}
\end{compactenum}
Under these conditions,
$
\tau
$
is said to be a
\emph
{
vector topology
}
on
$
X
$
, and
$
X
$
is a
\emph
{
topological vector space
}
.
\end{labeledquote}
Note that Rudin does not directly cite the literature in these quotes, but in the preface
he mentions the vast literature on function analysis and in Appendix B he cites the
original literature for each chapter. The situation in textbooks is also different from
research articles in that textbooks -- like survey articles, and by their very nature --
do not add new knowledge or new results, but aggregate and organize the already published
ones, possibly reformulating them for a more uniform exposition. But still, one can
distinguish
\end{newpart}
\subsection
{
Secondary Literature: Education/Survey
}
\subsection
{
Secondary Literature: Education/Survey
}
...
@@ -215,8 +184,8 @@ A similar effect can be observed with educational materials or survey articles,
...
@@ -215,8 +184,8 @@ A similar effect can be observed with educational materials or survey articles,
concern is not to make an original contribution to the knowledge commons, but to prepare a
concern is not to make an original contribution to the knowledge commons, but to prepare a
document that helps an individual or group study or better understand a body of already
document that helps an individual or group study or better understand a body of already
established knowledge. Consider for instance, slides and background materials (lecture
established knowledge. Consider for instance, slides and background materials (lecture
notes, books, encyclopaedias), where the slides often have telegraphic versions of
the real
notes,
text
books, encyclopaedias), where the slides often have telegraphic versions of
statements, which verbalize more rigorous definition.
the real
statements, which verbalize more rigorous definition.
This is illustrated in Example
\ref
{
ex:course
}
which is inspired from the notes of a first
This is illustrated in Example
\ref
{
ex:course
}
which is inspired from the notes of a first
year computer science course taught by the first author. The example is a simplified and
year computer science course taught by the first author. The example is a simplified and
...
@@ -242,6 +211,39 @@ the courses become insular; how are students going to communicate with mathemati
...
@@ -242,6 +211,39 @@ the courses become insular; how are students going to communicate with mathemati
have learned their maths from other courses? This is where alluding to the literature
have learned their maths from other courses? This is where alluding to the literature
comes in, by connecting the course notes with it.
comes in, by connecting the course notes with it.
\begin{newpart}
{
MK: re-read
}
The situation in mathematical textbooks is similar in structure to that in research
papers --perhaps more pronounced. Consider the following passage from Rudin's classical
introductory textbook to Functional Analysis~
\cite
[p. 6f]
{
Rudin:fa73
}
.
\begin{labeledquote}
\sf
\textbf
{
1.5 Topological spaces
}
A
\emph
{
topological space
}
is a set
$
S
$
in which a
collection
$
\tau
$
of subsets (called
\emph
{
open sets
}
) has been specified, with the
following properties:
$
S
$
is open,
$
\emptyset
$
is open, [
\ldots
] Such a collection is
called a
\emph
{
topology
}
on
$
S
$
. [
\ldots
]
\end{labeledquote}
and later -- vector spaces have been recapped earlier in section 1.4:
\begin{labeledquote}
\sf
\textbf
{
1.6 Topological vector spaces
}
Suppose
$
\tau
$
is a topology on a vector space
$
X
$
such that
\begin{compactenum}
[(a)]
\item
\emph
{
every point of
$
X
$
is a closed set, and
}
\item
\emph
{
the vector space operations are continuous with respect to
$
\tau
$}
\end{compactenum}
Under these conditions,
$
\tau
$
is said to be a
\emph
{
vector topology
}
on
$
X
$
, and
$
X
$
is a
\emph
{
topological vector space
}
.
\end{labeledquote}
Note that Rudin does not directly cite the literature in these quotes, but in the preface
he mentions the vast literature on function analysis and in Appendix B he cites the
original literature for each chapter. The situation in textbooks is also different from
research articles in that textbooks -- like survey articles, and by their very nature --
do not add new knowledge or new results, but aggregate and organize the already published
ones, possibly reformulating them for a more uniform exposition. But still, one can
distinguish recap parts -- as the ones above -- which are much more telegraphic in nature
from the primary material presented in the textbook.
\end{newpart}
\subsection
{
Common Ground in Formal Mathematics
}
\subsection
{
Common Ground in Formal Mathematics
}
Where applicable, common ground in formal mathematics is typical established via direct
Where applicable, common ground in formal mathematics is typical established via direct
imports of symbols, theorems, notations, etc. Formal documents emphasize correctness and
imports of symbols, theorems, notations, etc. Formal documents emphasize correctness and
...
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