Skip to content

Commit 4e6bdf2

Browse files
oscarlevinoscarlevin
committed
start section on recurrence relations
1 parent 1d17870 commit 4e6bdf2

13 files changed

+668
-23
lines changed

‎generated-assets/.html_assets.pkl

74 Bytes
Binary file not shown.

‎generated-assets/latex-image/dir-multigraph-relation.svg

Lines changed: 82 additions & 0 deletions
Loading

‎generated-assets/webwork/webwork-representations.xml

Lines changed: 16 additions & 16 deletions
Original file line numberDiff line numberDiff line change
@@ -2376,7 +2376,7 @@ For each of the 16 pairs of these numbers, <m>P(x,y)</m> is either true or false
23762376
<pg><![CDATA[
23772377
#############################################
23782378
### Generated from PreTeXt source
2379-
### on 2024-02-09T12:59:14-07:00
2379+
### on 2024-02-22T12:14:50-07:00
23802380
### A recent stable commit (2022-07-01):
23812381
### 6c761d3dba23af92cba35001c852aac04ae99a5f
23822382
###
@@ -2623,7 +2623,7 @@ What is the largest <m>n</m> such that <m>C_n</m> is an <em>induced</em> subgrap
26232623
<pg><![CDATA[
26242624
#############################################
26252625
### Generated from PreTeXt source
2626-
### on 2024-02-09T12:59:14-07:00
2626+
### on 2024-02-22T12:14:50-07:00
26272627
### A recent stable commit (2022-07-01):
26282628
### 6c761d3dba23af92cba35001c852aac04ae99a5f
26292629
###
@@ -2639,7 +2639,7 @@ What is the largest <m>n</m> such that <m>C_n</m> is an <em>induced</em> subgrap
26392639
## EditionText1()
26402640
## AuthorText1()
26412641
## Section1(not reported)
2642-
## Problem1(2)
2642+
## Problem1(2.2.4.2)
26432643
## Author()
26442644
## Institution()
26452645
## Language(en-US)
@@ -2836,7 +2836,7 @@ Since the number of edges is one less than the number of vertices, which is <m>x
28362836
<pg><![CDATA[
28372837
#############################################
28382838
### Generated from PreTeXt source
2839-
### on 2024-02-09T12:59:14-07:00
2839+
### on 2024-02-22T12:14:50-07:00
28402840
### A recent stable commit (2022-07-01):
28412841
### 6c761d3dba23af92cba35001c852aac04ae99a5f
28422842
###
@@ -2852,7 +2852,7 @@ Since the number of edges is one less than the number of vertices, which is <m>x
28522852
## EditionText1()
28532853
## AuthorText1()
28542854
## Section1(not reported)
2855-
## Problem1(2)
2855+
## Problem1(2.3.4.2)
28562856
## Author()
28572857
## Institution()
28582858
## Language(en-US)
@@ -2930,7 +2930,7 @@ ENDDOCUMENT();
29302930
<pg><![CDATA[
29312931
#############################################
29322932
### Generated from PreTeXt source
2933-
### on 2024-02-09T12:59:14-07:00
2933+
### on 2024-02-22T12:14:50-07:00
29342934
### A recent stable commit (2022-07-01):
29352935
### 6c761d3dba23af92cba35001c852aac04ae99a5f
29362936
###
@@ -2946,7 +2946,7 @@ ENDDOCUMENT();
29462946
## EditionText1()
29472947
## AuthorText1()
29482948
## Section1(not reported)
2949-
## Problem1(3)
2949+
## Problem1(2.3.4.3)
29502950
## Author()
29512951
## Institution()
29522952
## Language(en-US)
@@ -3047,7 +3047,7 @@ ENDDOCUMENT();
30473047
<pg><![CDATA[
30483048
#############################################
30493049
### Generated from PreTeXt source
3050-
### on 2024-02-09T12:59:14-07:00
3050+
### on 2024-02-22T12:14:51-07:00
30513051
### A recent stable commit (2022-07-01):
30523052
### 6c761d3dba23af92cba35001c852aac04ae99a5f
30533053
###
@@ -3063,7 +3063,7 @@ ENDDOCUMENT();
30633063
## EditionText1()
30643064
## AuthorText1()
30653065
## Section1(not reported)
3066-
## Problem1(4)
3066+
## Problem1(2.3.4.4)
30673067
## Author()
30683068
## Institution()
30693069
## Language(en-US)
@@ -3140,7 +3140,7 @@ ENDDOCUMENT();
31403140
<pg><![CDATA[
31413141
#############################################
31423142
### Generated from PreTeXt source
3143-
### on 2024-02-09T12:59:14-07:00
3143+
### on 2024-02-22T12:14:51-07:00
31443144
### A recent stable commit (2022-07-01):
31453145
### 6c761d3dba23af92cba35001c852aac04ae99a5f
31463146
###
@@ -3156,7 +3156,7 @@ ENDDOCUMENT();
31563156
## EditionText1()
31573157
## AuthorText1()
31583158
## Section1(not reported)
3159-
## Problem1(5)
3159+
## Problem1(2.3.4.5)
31603160
## Author()
31613161
## Institution()
31623162
## Language(en-US)
@@ -5183,7 +5183,7 @@ a. <m>{16 \choose 5} - \left[{6 \choose 1}{13 \choose 5} - {6 \choose 2}{10 \cho
51835183
<pg><![CDATA[
51845184
#############################################
51855185
### Generated from PreTeXt source
5186-
### on 2024-02-09T12:59:14-07:00
5186+
### on 2024-02-22T12:14:51-07:00
51875187
### A recent stable commit (2022-07-01):
51885188
### 6c761d3dba23af92cba35001c852aac04ae99a5f
51895189
###
@@ -5199,7 +5199,7 @@ a. <m>{16 \choose 5} - \left[{6 \choose 1}{13 \choose 5} - {6 \choose 2}{10 \cho
51995199
## EditionText1()
52005200
## AuthorText1()
52015201
## Section1(not reported)
5202-
## Problem1(3)
5202+
## Problem1(3.6.3.3)
52035203
## Author()
52045204
## Institution()
52055205
## Language(en-US)
@@ -6891,7 +6891,7 @@ and
68916891
<pg><![CDATA[
68926892
#############################################
68936893
### Generated from PreTeXt source
6894-
### on 2024-02-09T12:59:14-07:00
6894+
### on 2024-02-22T12:14:51-07:00
68956895
### A recent stable commit (2022-07-01):
68966896
### 6c761d3dba23af92cba35001c852aac04ae99a5f
68976897
###
@@ -7422,7 +7422,7 @@ and then 5 that include 3 and not 1 or 2, and so on. So you can find 28 by summ
74227422
<pg><![CDATA[
74237423
#############################################
74247424
### Generated from PreTeXt source
7425-
### on 2024-02-09T12:59:14-07:00
7425+
### on 2024-02-22T12:14:51-07:00
74267426
### A recent stable commit (2022-07-01):
74277427
### 6c761d3dba23af92cba35001c852aac04ae99a5f
74287428
###
@@ -7438,7 +7438,7 @@ and then 5 that include 3 and not 1 or 2, and so on. So you can find 28 by summ
74387438
## EditionText1()
74397439
## AuthorText1()
74407440
## Section1(not reported)
7441-
## Problem1(23)
7441+
## Problem1(5.1.5.23)
74427442
## Author()
74437443
## Institution()
74447444
## Language(en-US)

‎source/assets/class-relation.tex

Lines changed: 15 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,15 @@
1+
\begin{tikzpicture}[scale=1.5]
2+
\node[circle,draw] (a) at (0,2) {\tiny Al};
3+
\node[circle,draw] (b) at (1,2) {\tiny Bob};
4+
\node[circle,draw] (c) at (2,2) {\tiny Cat};
5+
\node[circle,draw] (d) at (3,2) {\tiny Dirk};
6+
\node[circle,draw] (e) at (4,2) {\tiny Eva};
7+
\node[circle,draw] (C) at (.5,0) {\tiny Calc};
8+
\node[circle,draw] (D) at (2,0) {\tiny Disc};
9+
\node[circle,draw] (S) at (3.5,0) {\tiny Stat};
10+
\draw (a) edge (C) (a) edge (S);
11+
\draw (b) edge (C) (b) edge (D);
12+
\draw (c) edge (C) (c) edge (S);
13+
\draw (d) edge (S);
14+
\draw (e) edge (C) (e) edge (D);
15+
\end{tikzpicture}

‎source/assets/dir-class-inv-relation.tex

Lines changed: 18 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,18 @@
1+
\begin{tikzpicture}[scale=1.5]
2+
\node[circle, draw] (a1) at (72:1) {\tiny Al};
3+
\node[circle, draw] (a2) at (0:1) {\tiny Bob};
4+
\node[circle, draw] (a3) at (-72:1) {\tiny Cat};
5+
\node[circle, draw] (a4) at (-144:1) {\tiny Dirk};
6+
\node[circle, draw] (a5) at (144:1) {\tiny Eva};
7+
\foreach \i in {1,...,5}
8+
\draw[<->] (a\i) edge [in=164-\i*72, out=124-\i*72,looseness=10] (a\i);
9+
10+
\draw[<->] (a2) edge (a1);
11+
\draw[<->] (a3) edge (a1);
12+
\draw[<->] (a4) edge (a1);
13+
\draw[<->] (a5) edge (a1);
14+
\draw[<->] (a3) edge (a2);
15+
\draw[<->] (a5) edge (a2);
16+
\draw[<->] (a4) edge (a3);
17+
\draw[<->] (a5) edge (a3);
18+
\end{tikzpicture}

‎source/assets/dir-multigraph-relation.tex

Lines changed: 14 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,14 @@
1+
\begin{tikzpicture}[scale=1.5]
2+
\foreach \i in {1,...,6} {
3+
\node[circle, draw] (a\i) at (120-\i*60:1) {\tiny \i};
4+
\draw[->] (a\i) edge [in=100-\i*60, out=140-\i*60,looseness=12] (a\i);
5+
}
6+
\draw[->] (a2) edge (a1);
7+
\draw[->] (a3) edge (a1);
8+
\draw[->] (a4) edge (a1);
9+
\draw[->] (a4) edge (a2);
10+
\draw[->] (a5) edge (a1);
11+
\draw[->] (a6) edge (a1);
12+
\draw[->] (a6) edge (a2);
13+
\draw[->] (a6) edge (a3);
14+
\end{tikzpicture}

‎source/ch_graphtheory.ptx

Lines changed: 1 addition & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -205,6 +205,7 @@
205205
<xi:include href="sec_gt-planar.ptx"/>
206206
<xi:include href="sec_gt-paths.ptx"/>
207207
<xi:include href="sec_gt-coloring.ptx"/>
208+
<xi:include href="sec_gt-relations.ptx" />
208209
<xi:include href="sec_gt-matchings.ptx"/>
209210
<xi:include href="sec_gt-conc.ptx"/>
210211
</chapter>

‎source/ch_structures.ptx

Lines changed: 1 addition & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -11,6 +11,7 @@
1111

1212
<xi:include href="sec_structures-sets.ptx" />
1313
<xi:include href="sec_structures-functions.ptx" />
14+
<!-- <xi:include href="sec_structures-relations.ptx" /> -->
1415

1516

1617

0 commit comments

Comments
 (0)