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Taddeüs Kroes
trs
Commits
a19046f3
Commit
a19046f3
authored
13 years ago
by
Sander Mathijs van Veen
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Applied Krzysztof's suggestions.
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docs/proposal.tex
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a19046f3
...
...
@@ -8,7 +8,7 @@
\setlength
{
\parindent
}{
0pt
}
\setlength
{
\parskip
}{
1ex plus 0.5ex minus 0.2ex
}
\title
{
Mathematical Term Rewrit
ing
S
ystem
}
\title
{
An interactive math tutor
ing
s
ystem
for secondary schools
}
\author
{
Taddeus Kroes (taddeuskroes@hotmail.com)
\and
Sander Mathijs van Veen (smvv@kompiler.org)
}
...
...
@@ -24,21 +24,23 @@ reductions. The basic idea is that the student can work on an assignment using
an online text editor. The text entered in the editor is converted to a
mathematical notation and displayed on the screen in real-time. If the student
gets stuck while rewriting a mathematical formula, he or she can request a
'
hint' from the system. The system should recognize
the
best reduction to
apply
at that time, and
push
the student in the right direction by displaying
a
textual hint that tells the user what sort of reduction can be applied.
T
he
system should a
lso be able to apply th
at reduction itself.
`
hint' from the system. The system should recognize
a
best reduction to
apply
at that time, and
guide
the student in the right direction by displaying
a
textual hint that tells the user what sort of reduction can be applied.
W
he
n
asked the
system should a
pply an appropri
at
e
reduction
step
itself.
This document lists the different sections in which the project can be
divided,
along with their expected gradations.
This document lists the different sections in which the project can be
divided,
along with their expected gradations.
\section
{
Purpose
}
\begin{itemize}
\item
A user can simplify / reduce a mathematical expression.
\item
Program can verify the user's reduction step.
\item
Program can verify the user's reduction step
s
.
\item
A user should be able to ask for zero, one or more hints (with a
maximum of one hint per reduction step).
maximum of one hint per reduction step). In case the hint does not help,
the system should output the outcome of an appropriate single reduction
step.
\item
Program can generate exercises using predefined templates.
\end{itemize}
...
...
@@ -50,54 +52,53 @@ divided, along with their expected gradations.
\item
Parse expressions and interpret functions (
\texttt
{
integrate()
}
,
\texttt
{
expand()
}
,
\texttt
{
diff()
}
, etc.). This will include building a
parser generator using
\emph
{
bison
}
and
\emph
{
flex
}
.
\item
Canonicalize an expression:
$
4
+
x
^
2
+
x
\rightarrow
x
^
2
+
x
+
4
$
.
\item
Bring an expression to a normal form:
$
4
+
x
^
2
+
x
\rightarrow
x
^
2
+
x
+
4
$
.
\end{itemize}
\subsection
{
Validation and tutoring
}
\begin{itemize}
\item
Validate e
xpressions with the expression of given exercise
.
\item
Validate e
acg reduction step and the final input
.
\item
If requested, select the best hint (based on the chosen strategy).
\item
Generate exercise using predefined templates.
\item
Generate exercise
s
using predefined templates.
\end{itemize}
\subsubsection
{
Modules
}
Each module will require design of an appropriate set of term
rewriting rules and selection of an appropriate reduction strategy
that allows for nondeterminism, both in the choice of the rewriting
rule and in the choice of the subterm to which the rule will be
applied. Nondeterminism is needed for validating every user's input
(outcome of a single reduction step) against the previous term.
\begin{itemize}
\item
Expressions without variables.
$
(
3
+
4
)
\times
(
5
+
7
)
$
\item
Expressions without variables.
$
(
3
+
4
)
\times
(
5
+
7
)
$
,
$
\frac
{
3
}{
4
}
+
\frac
{
4
}{
5
}$
\item
Linear expressions.
$
(
3
+
2
p
)
\times
7
$
\item
Linear expressions with absolute values.
$
|x
-
1
|
=
2
$
\item
Systems of linear equations (two variables).
\item
Equations of the second degree.
$
(
x
+
1
)(
x
-
2
)
+
2
x
+
7
$
,
$$
\
\begin
{
array
}{
|rcr|
}
3
x
+
2
y
&
=
&
5
\\
2
x
-
3
y
&
=
&
6
\end
{
array
}
\
\rightarrow
\
\begin
{
array
}{
|rcr|
}
x
+
\frac
{
2
}{
3
}
y
&
=
&
\frac
{
5
}{
3
}
\\
x
-
\frac
{
3
}{
2
}
y
&
=
&
3
\end
{
array
}
\
\rightarrow
\
\frac
{
5
}{
3
}
-
\frac
{
2
}{
3
}
y
=
3
+
\frac
{
3
}{
2
}
y
\
\rightarrow
\dots
\
\begin
{
array
}{
|rcr|
}
x
&
=
&
2
\frac
{
1
}{
13
}
\\
y
&
=
&
-
\frac
{
8
}{
13
}
\end
{
array
}
$$
\item
Trigonometric functions.
\item
Derivatives.
\item
Trigonometric functions, as considered in VWO.
\item
Derivatives, as considered in VWO.
\item
Integrals (computing antiderivates).
\end{itemize}
\subsection
{
Graphical user interface
}
\subsection
{
Graphical user interface
and evaluation
}
\begin{itemize}
\item
Mathematical notation viewer:
...
...
@@ -105,8 +106,8 @@ divided, along with their expected gradations.
\item
Rewrite shell expressions to
\LaTeX
.
\item
\LaTeX
$
$
to HTML/CSS/JS using
\emph
{
MathJax
}
.
\end{itemize}
\item
Vie
w hints (if requested by the user) in the notation viewer.
\item
Evaluate the GUI with some early adopters (
few
pupils and a teacher).
\item
Sho
w hints (if requested by the user) in the notation viewer.
\item
Evaluate the GUI with some early adopters (
some
pupils and a teacher).
\end{itemize}
\subsection
{
Screencast, tutorial and final report
}
...
...
@@ -115,6 +116,8 @@ divided, along with their expected gradations.
\item
Create a screencast to demonstrate the project.
\item
Write a few short-length tutorials (how to use the system).
\item
Write the final report (e.g. evaluation of the project).
\item
Clarify for which chapters of the VWO mathematic books the system can
be used.
\end{itemize}
\section
{
European Credits
}
...
...
@@ -124,7 +127,7 @@ divided, along with their expected gradations.
EC
&
Component
\\
\midrule
3
&
Input parsing and canonical form
\\
9
&
Validation
and
tutoring
\\
9
&
Validation
,
tutoring
and evaluation
\\
3
&
Graphical user interface
\\
3
&
Screencast, tutorial and final report
\\
\bottomrule
...
...
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