672:. Ideally, the image should be self-explanatory without the caption. I fear that, by using a concrete application, like an image of a Rubik's cube or a circle with arrows in it, we give the reader a false impression even if we correctly explain it in the caption. Apologies for dismissing your different lead image ideas. I agree with you that the current abstract algebra image is not ideal either. Maybe the best option would be to remove it and only have the elementary algebra image.
472:. This could be done but I think it is not the easiest way to introduce abstract algebra. Most introductions to abstract algebra start with more familiar examples of algebraic structures, like the ring of integers. Its true that there is an overlap here with elementary algebra. The main difference is that elementary algebra studies how equations formulated within these algebraic structures can be solved while abstract algebra studies and compares the algebraic structures themselves.
537:
516:
154:
1168:
articles on very general topics like this one, especially when there are good technical encyclopedias are available. For wide-scope articles, it's not so much about particular in-depth details but about getting the overview right. A while back, there was a similar discussion about the FA nomination of the article
1167:
I added a secondary source for this claim in the history section. For articles on narrow topics, I would agree with you that it is often preferable to minimize the use of general encyclopedias because of the importance of getting specific details right. But I feel that the situation is different for
298:
If you or someone else would be willing to read through the article and provide some feedback, this would be helpful to consider potential problems that I may have overlooked. The peer review can be done casually without precisely following the FA criteria and your background in mathematics would be
642:
Permutation groups could work if the article was written for mathematicians. But since it is written for a general audience, we would probably have to explain to them first what a permutation is before they can understand that a permutation group is an example of an algebraic structure.
788:
Thanks for pointing this out. I adjusted the two sentence to make them more general while also mentioning exponentiation, roots, and logarithms. We have to find a middle way here since they should be mentioned but at the same time shouldn't be at the center of the discussion.
1145:. It looks to me like most of the "analytic, evaluative, interpretive, or synthetic claim" made in this article have citations to a non-encyclopedic source even if there is also an encyclopedic source, but there are a few exceptions, for example this sentence:
283:
To be honest, I'm not actually an expert in FAC, and I don't even have one. You can try to find someone interested in this topic, or ask non-mathematics users to review your article, from which they may find something that will be added or should be removed.
732:
This article is well-written in a clear style and it is masterfully balanced. I especially appreciate the large number of pictures and the fact that it doesn't focus on only one meaning of the word "algebra". However, there are some
387:
862:
After looking into this, I think "verbal descriptions" just means that they wrote down equations using words and abbreviations instead of symbols. I think this is not how most people would interpret this sentence.
736:(I) When I read the descriptions of elementary algebra in this article, as a reader, I am left with the impression that elementary algebra is about solving single polynomial equations. Two examples:
1028:
996:
920:
Unfortunately, I'm not sure how to explain it better. I moved the paragraph to a footnote. This way, it's still there for the curious but is less likely to confuse the average reader.
650:
as the second image? Perhaps a circle with a curved arrow. I believed that it is simple enough for a layman to understand and that it is not normally covered in elementary algebra. --
1173:
586:
470:
416:
1072:
1048:
620:
952:
The description of subalgebras reads backwards in the sense that instead of telling us what a subalgebra is, it just apparently lists a few facts about them:
336:
76:
694:), so I think it would be better to include it somewhere else in the article, maybe a short paragraph in the section "Applications". I'll look into it.
785:
I think we should mention that exponentiation, roots, logs, and simultaneous equations can come up in problems under the scope of elementary algebra.
856:
They relied on verbal descriptions of problems and solutions until the 16th and 17th centuries, when a rigorous mathematical formalism was developed.
226:
917:
Surely at least one of these two statements is true: (a) quasi-identities can be explained better or (b) they don't belong in this article.
1177:
756:
Arithmetic is the study of numerical operations and investigates how numbers are combined and transformed using arithmetic operations like
1148:
Mathematicians soon realized the relevance of group theory to other fields and applied it to disciplines like geometry and number theory.
204:
This has been posted for over a month without comment. Are you still looking for comments, or can this be closed and nominated to FAC?
126:
1227:
69:
772:. For example, the operation of addition combines two numbers, called the addends, into a third number, called the sum, as in
122:
433:
107:
690:
I like the idea of using Rubik's cube as an example. It's not particularly representative of
Algebra in general (see
62:
1074:. A subalgebra has to use the same operations as the algebraic structure and they have to follow the same axioms.
50:
1202:
1158:
1116:
939:
885:
99:
251:
Maybe we can start from the sources, images, and other FAC criterias to be checked before heading to the FAC?
1001:
969:
327:
780:
There is no mention of exponentiation, roots, or logs in the context of elementary algebra in this article.
776:. Elementary algebra relies on the same operations while allowing variables in addition to regular numbers.
823:...it is possible to express a general law that applies to any possible combinations of numbers, like the
809:...it is possible to express a general law that applies to any possible combinations of numbers, like the
769:
589:
17:
175:. I was hoping to get feedback on its current status and what improvements are required to fulfill the
824:
810:
744:
525:
421:
289:
256:
229:
to attract more reviewers. I was hoping to keep it open a little longer to see if someone responds.
1198:
1197:
Thanks for all your work improving this article, and good luck again on getting this to FA status!
1174:
Wikipedia_talk:Featured_article_candidates/archive90#Usage_of_tertiary_sources_in_the_article_Logic
1154:
1142:
1112:
935:
881:
554:
550:
546:
536:
515:
505:
44:
1105:
740:
622:
corresponds to a cube move, which is the effect of any sequence of rotations of the cube's faces.
521:
1206:
1192:
1162:
1120:
1087:
943:
929:
903:
889:
875:
845:
798:
717:
703:
681:
659:
637:
499:
481:
308:
293:
278:
260:
238:
213:
191:
559:
1188:
1083:
925:
899:
871:
841:
794:
713:
699:
677:
600:
596:
487:
477:
304:
274:
234:
187:
708:
I found a way to mention Rubik's cube together with the image in the section "Applications".
1126:
748:
655:
633:
542:
495:
441:
429:
285:
266:
252:
209:
446:
392:
852:(III) I am a bit worried about this sentence in the lead, which seems worded strangely:
176:
880:
I like your edit, but I added the word "symbolic" to it and now I like it even better.
765:
1057:
1033:
605:
524:
studies which values solve equations formed using arithmetical operations, especially
382:{\displaystyle \mathbb {C} ,\ \mathbb {N} ,\ \mathbb {Q} \ {\text{and}}\ \mathbb {Z} }
1221:
691:
593:
172:
1125:
One GA reviewer brought up the encyclopedia articles in the references and notes at
1184:
1079:
921:
895:
867:
837:
790:
709:
695:
673:
473:
300:
270:
244:
230:
199:
183:
161:
115:
1104:
of encyclopedia articles in the references and notes, which would seem to violate
962:
Another tool of comparison is the relation between an algebraic structure and its
761:
651:
629:
491:
425:
1129:, but they didn't seem to mind. To be specific, the policy that worries me is:
963:
248:
220:
205:
1132:
Articles may make an analytic, evaluative, interpretive, or synthetic claim
1078:
I reformulated the passage to have the explanation in a more natural order.
757:
92:
1051:
914:(IV) Maybe the section on universal algebra can be written better?
1169:
647:
148:
171:
I've listed this article for peer review to prepare it for a
299:
particularly valuable in identifying possible improvements.
670:
visual confirmation that they've arrived at the right page
440:
Thanks for the input! I assume you are referring to the
866:
I reformulated the sentence, I hope it is clearer now.
141:
134:
103:
1136:
it has been published by a reliable secondary source.
1060:
1036:
1004:
972:
608:
562:
449:
395:
339:
668:for abstract algebra that gives the average reader
389:are covered in elementary algebra classes. Perhaps
1066:
1042:
1022:
990:
614:
580:
464:
410:
381:
934:Seems like the best solution at this time to me.
1153:It shouldn't be super bad to fill in the gaps.
894:I agree, the word helps sharpen the contrast.
269:, that sounds good, thanks for taking a look!
225:Thanks for the reminder! I now posted to the
1108:. I wonder if this came up in the GA reviews?
70:
8:
1017:
1005:
985:
973:
419:
323:My first take is that the second image in
77:
63:
32:
1059:
1035:
1003:
971:
607:
561:
448:
394:
375:
374:
367:
361:
360:
351:
350:
341:
340:
338:
1023:{\displaystyle \langle B,\circ \rangle }
991:{\displaystyle \langle A,\circ \rangle }
652:Shmuel (Seymour J.) Metz Username:Chatul
630:Shmuel (Seymour J.) Metz Username:Chatul
492:Shmuel (Seymour J.) Metz Username:Chatul
827:, which is expressed in the equation...
35:
1183:Thanks for all the improvement ideas!
1127:Talk:Algebra/GA1#Referencing_and_other
825:commutative property of multiplication
7:
1178:Knowledge:Peer_review/Logic/archive3
747:and seeks to discover which values
508:as an example of abstract algebra?
486:Yes, Orthogonal group. How about a
24:
535:
514:
152:
1141:Which is actually listed under
575:
563:
459:
453:
405:
399:
1:
813:expressed in the equation...
664:It's very difficult to find
1244:
811:principle of commutativity
805:(II) Change this excerpt:
581:{\displaystyle (G,\cdot )}
418:would be a better choice?
173:featured article candidacy
1207:11:45, 28 July 2024 (UTC)
1193:07:31, 28 July 2024 (UTC)
1163:20:57, 25 July 2024 (UTC)
1121:19:35, 25 July 2024 (UTC)
1088:16:34, 27 July 2024 (UTC)
944:17:55, 27 July 2024 (UTC)
930:16:34, 27 July 2024 (UTC)
904:16:43, 26 July 2024 (UTC)
890:16:29, 26 July 2024 (UTC)
876:16:17, 26 July 2024 (UTC)
846:11:15, 26 July 2024 (UTC)
799:11:12, 26 July 2024 (UTC)
718:07:44, 27 July 2024 (UTC)
704:16:08, 26 July 2024 (UTC)
682:15:17, 28 July 2024 (UTC)
660:10:24, 28 July 2024 (UTC)
638:13:51, 26 July 2024 (UTC)
500:17:07, 25 July 2024 (UTC)
482:16:16, 25 July 2024 (UTC)
309:11:34, 25 July 2024 (UTC)
294:10:42, 25 July 2024 (UTC)
279:10:37, 25 July 2024 (UTC)
261:09:39, 25 July 2024 (UTC)
239:07:44, 25 July 2024 (UTC)
214:15:48, 24 July 2024 (UTC)
192:17:05, 14 June 2024 (UTC)
177:featured article criteria
227:WikiProject Mathematics
1228:June 2024 peer reviews
1068:
1044:
1024:
992:
833:Or something similar.
666:a representative image
616:
599:. Each element of the
582:
466:
412:
383:
1069:
1045:
1025:
993:
617:
583:
467:
413:
384:
164:discussion is closed.
18:Knowledge:Peer review
1058:
1034:
1002:
970:
745:polynomial equations
606:
588:that represents the
560:
547:algebraic structures
526:polynomial equations
504:How about using the
465:{\displaystyle O(n)}
447:
411:{\displaystyle O(n)}
393:
337:
333:is not appropriate;
998:is a subalgebra of
1064:
1040:
1020:
988:
741:Elementary algebra
612:
578:
551:Rubik's Cube group
522:Elementary algebra
506:Rubik's Cube group
462:
408:
379:
1067:{\displaystyle B}
1043:{\displaystyle A}
743:is interested in
615:{\displaystyle G}
597:mechanical puzzle
488:permutation group
437:
424:comment added by
373:
370:
366:
359:
349:
169:
168:
142:Watch peer review
87:
86:
1235:
1100:(V) There are a
1073:
1071:
1070:
1065:
1049:
1047:
1046:
1041:
1029:
1027:
1026:
1021:
997:
995:
994:
989:
775:
671:
667:
621:
619:
618:
613:
587:
585:
584:
579:
543:Abstract algebra
539:
518:
471:
469:
468:
463:
442:Orthogonal group
417:
415:
414:
409:
388:
386:
385:
380:
378:
372:
371:
368:
365:
364:
358:
354:
348:
344:
332:
326:
224:
203:
156:
155:
149:
139:
130:
111:
79:
72:
65:
47:
33:
1243:
1242:
1238:
1237:
1236:
1234:
1233:
1232:
1218:
1217:
1056:
1055:
1032:
1031:
1000:
999:
968:
967:
773:
669:
665:
627:
626:
625:
624:
623:
604:
603:
558:
557:
540:
531:
530:
529:
519:
445:
444:
391:
390:
335:
334:
330:
324:
218:
197:
153:
145:
120:
97:
91:
83:
51:Manual of Style
43:
31:
22:
21:
20:
12:
11:
5:
1241:
1239:
1231:
1230:
1220:
1219:
1216:
1215:
1214:
1213:
1212:
1211:
1210:
1209:
1199:Mathwriter2718
1181:
1155:Mathwriter2718
1151:
1150:
1149:
1139:
1138:
1137:
1113:Mathwriter2718
1111:Best of luck!
1109:
1098:
1097:
1096:
1095:
1094:
1093:
1092:
1091:
1090:
1063:
1039:
1019:
1016:
1013:
1010:
1007:
987:
984:
981:
978:
975:
954:
953:
950:
949:
948:
947:
946:
936:Mathwriter2718
912:
911:
910:
909:
908:
907:
906:
882:Mathwriter2718
860:
859:
858:
850:
849:
848:
831:
830:
829:
817:
816:
815:
803:
802:
801:
783:
782:
781:
778:
766:multiplication
753:
734:
729:
728:
727:
726:
725:
724:
723:
722:
721:
720:
688:
687:
686:
685:
684:
611:
577:
574:
571:
568:
565:
541:
534:
533:
532:
520:
513:
512:
511:
510:
509:
502:
461:
458:
455:
452:
407:
404:
401:
398:
377:
363:
357:
353:
347:
343:
328:multiple image
321:
320:
319:
318:
317:
316:
315:
314:
313:
312:
311:
167:
166:
157:
147:
146:
144:
90:
85:
84:
82:
81:
74:
67:
59:
56:
55:
54:
53:
48:
38:
37:
30:
25:
23:
15:
14:
13:
10:
9:
6:
4:
3:
2:
1240:
1229:
1226:
1225:
1223:
1208:
1204:
1200:
1196:
1195:
1194:
1190:
1186:
1182:
1179:
1175:
1171:
1166:
1165:
1164:
1160:
1156:
1152:
1147:
1146:
1144:
1140:
1135:
1131:
1130:
1128:
1124:
1123:
1122:
1118:
1114:
1110:
1107:
1103:
1099:
1089:
1085:
1081:
1077:
1076:
1075:
1061:
1053:
1037:
1030:then the set
1014:
1011:
1008:
982:
979:
976:
965:
960:
959:
958:
957:
956:
955:
951:
945:
941:
937:
933:
932:
931:
927:
923:
919:
918:
916:
915:
913:
905:
901:
897:
893:
892:
891:
887:
883:
879:
878:
877:
873:
869:
865:
864:
861:
857:
854:
853:
851:
847:
843:
839:
835:
834:
832:
828:
826:
821:
820:
818:
814:
812:
807:
806:
804:
800:
796:
792:
787:
786:
784:
779:
777:
771:
767:
763:
759:
754:
752:
750:
746:
742:
738:
737:
735:
731:
730:
719:
715:
711:
707:
706:
705:
701:
697:
693:
692:MOS:LEADIMAGE
689:
683:
679:
675:
663:
662:
661:
657:
653:
649:
645:
644:
641:
640:
639:
635:
631:
609:
602:
598:
595:
591:
572:
569:
566:
556:
552:
548:
544:
538:
527:
523:
517:
507:
503:
501:
497:
493:
489:
485:
484:
483:
479:
475:
456:
450:
443:
439:
438:
435:
431:
427:
423:
402:
396:
355:
345:
329:
322:
310:
306:
302:
297:
296:
295:
291:
287:
282:
281:
280:
276:
272:
268:
264:
263:
262:
258:
254:
250:
246:
242:
241:
240:
236:
232:
228:
222:
217:
216:
215:
211:
207:
201:
196:
195:
194:
193:
189:
185:
180:
178:
174:
165:
163:
158:
151:
150:
143:
138:
137:
133:
128:
124:
119:
118:
114:
109:
105:
101:
96:
95:
89:
88:
80:
75:
73:
68:
66:
61:
60:
58:
57:
52:
49:
46:
45:Copying check
42:
41:
40:
39:
34:
29:
26:
19:
1143:WP:SECONDARY
1133:
1101:
961:
855:
822:
808:
755:
739:
594:Rubik's Cube
420:— Preceding
181:
170:
159:
135:
131:
117:Article talk
116:
112:
93:
27:
1106:WP:TERTIARY
762:subtraction
549:, like the
162:peer review
104:visual edit
964:subalgebra
749:solve them
646:How about
286:Dedhert.Jr
267:Dedhert.Jr
253:Dedhert.Jr
836:Changed.
819:To this:
774:2 + 5 = 7
590:structure
1222:Category
770:division
758:addition
545:studies
434:contribs
422:unsigned
182:Thanks,
1185:Phlsph7
1134:only if
1080:Phlsph7
922:Phlsph7
896:Phlsph7
868:Phlsph7
838:Phlsph7
791:Phlsph7
733:issues.
710:Phlsph7
696:Phlsph7
674:Phlsph7
592:of the
474:Phlsph7
301:Phlsph7
271:Phlsph7
245:Phlsph7
231:Phlsph7
200:Phlsph7
184:Phlsph7
127:history
108:history
94:Article
36:Toolbox
28:Algebra
1172:, see
1052:subset
768:, and
426:Chatul
265:Hello
1170:Logic
1050:is a
966:. If
648:SO(2)
555:group
490:? --
249:Z1720
221:Z1720
206:Z1720
160:This
136:Watch
16:<
1203:talk
1189:talk
1176:and
1159:talk
1117:talk
1084:talk
940:talk
926:talk
900:talk
886:talk
872:talk
842:talk
795:talk
714:talk
700:talk
678:talk
656:talk
634:talk
553:, a
496:talk
478:talk
430:talk
305:talk
290:talk
275:talk
257:talk
235:talk
210:talk
188:talk
123:edit
100:edit
1102:lot
1054:of
628:--
601:set
369:and
247:, @
179:.
1224::
1205:)
1191:)
1161:)
1119:)
1086:)
1018:⟩
1015:∘
1006:⟨
986:⟩
983:∘
974:⟨
942:)
928:)
902:)
888:)
874:)
844:)
797:)
764:,
760:,
716:)
702:)
680:)
658:)
636:)
573:⋅
498:)
480:)
436:)
432:•
331:}}
325:{{
307:)
292:)
277:)
259:)
237:)
212:)
190:)
140:•
125:|
106:|
102:|
1201:(
1187:(
1180:.
1157:(
1115:(
1082:(
1062:B
1038:A
1012:,
1009:B
980:,
977:A
938:(
924:(
898:(
884:(
870:(
840:(
793:(
751:.
712:(
698:(
676:(
654:(
632:(
610:G
576:)
570:,
567:G
564:(
528:.
494:(
476:(
460:)
457:n
454:(
451:O
428:(
406:)
403:n
400:(
397:O
376:Z
362:Q
356:,
352:N
346:,
342:C
303:(
288:(
273:(
255:(
243:@
233:(
223::
219:@
208:(
202::
198:@
186:(
132:·
129:)
121:(
113:·
110:)
98:(
78:e
71:t
64:v
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.