-1+11214 
Modern Algebra (Abstract Algebra) Made Easy

I really enjoyed Modern Algebra, so much so that I decided to make a lecture series explaining all the different topics via examples, proofs, and fun pieces of insight.

Lectures
  1. the Binary Operation

    In this video, I introduce the binary operation, and give some examples, T/F questions, and a proof using the idea of the binary operation. Hope you like it, Comments/Questions/Criticism welcome!

  2. Groups

    In this video, I explain a simple concept in Modern (abstract) Algebra, groups. A also give 3 examples of problems dealing with groups. I hope you like it. Let me know what you thought!

  3. Subgroups

    In this video I explain the basics of what it means to be a subgroup, and show some fun problems working with subgroups.

  4. Cyclic Groups & Generators

    This time I talk about what a Cyclic Group/Subgroup is and give examples, theory, and proofs rounding off this topic. I hope you enjoy it, was really fun to make.

  5. Permutations

    In this video, I introduce permutations, show examples and T/F questions. Hope you like it, let me know if you have any questions, comments, criticisms!

  6. Orbits & Cycles

    In this video, I contrast, compare, and further define permutations, cycles, and orbits. I also show examples of each, and there's one proof at the end. Hope you like it!

  7. Cosets & Lagrange's Theorem

    In this video, I give definitions, examples, T/F qustions, and proofs talking about cosets and Lagrange's Thm. Hope you like it. Feel free to give me some constructive feedback!

  8. Direct Products and Finitely Generated Abelian Groups

    In this lecture, I define and explain in detail what Finitely Generated Abelian Groups are. I give examples, proofs, and some interesting tidbits that are hard to come by. Hope you like it!

  9. Group Homomorphisms

    In this video, I give definitions, examples, and proofs talking about group homomorphisms. Hope you like it. Feel free to give me some constructive feedback!

    Works Cited: The only significant source for these videos is 'A First Course in Abstract Algebra', 2nd ed. by John Fraleigh. Though most of the problems and definitions come from this book, I explain the all the material & solutions in my own words.

  10. Factor (Quotient) Groups

    In this video, I give definitions, examples, and proofs talking about factor groups. Hope you like it. Feel free to give me some constructive feedback!

    Works Cited: The only significant source for these videos is 'A First Course in Abstract Algebra', 2nd ed. by John Fraleigh. Though most of the problems and definitions come from this book, I explain the all the material & solutions in my own words.

Prerequisites

For the first few lectures, you really don't need any fancy math. I try to break it down to where anyone can understand. That being said, you should probably have taken at least through High School Algebra.

For the later parts, it does help to have taken a Discrete Math/Intro to Advanced Math class.

Syllabus

0 - Binary Operation 1 - Groups 2 - Subgroups 3 - Cyclic Groups and Generators 4 - Permutations 5 - Orbits and Cycles 6 - Cosets and Lagrange's Theorem 7 - Direct Products and Finitely Generated Abelian Groups 8 - Group Homomorphisms

Additional information

I've been a full-time math tutor for over 5 years. After the first 2 or 3 of those years, I began to take a serious interest in math. It really is a beautiful subject, and Modern Algebra is, to me, the best example of why math can be so simple, but so beautiful.

Teacher qualifications

BS-Mathematics. I hope to continue studying Math for my Master's in the Spring/Fall 2013.

Latest Update

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929. nmbhat
930. 158510
931. Merohar
932. 70five
933. cheef_resident
934. apidome
935. krunt
936. L2BSmart
937. foo
938. Therealian
939. kirang
940. junkman416
941. igbistro
942. nunofilipemargarido
943. Bennymoonbase
944. jd95
945. pinguhash
946. FuckOffGetFree
947. thesaxby
948. bishman
949. djhk12
950. Gzzkarina
951. psychedelicate
952. khichi
953. Debb2254
954. pepe454
955. theprofessor01
956. lausveneris
957. leafie3000
958. JokerFrown
959. ttift1991
960. Skidie
961. mantexx12
962. fr0zen
963. korvil
964. scoronatus
965. conspiracyofqueens
966. ivanka-a
967. anax
968. Richo1337
969. ljghome
970. hobnailedboots
971. Janette
972. kkellerz
973. module
974. yippohappo
975. braindamage
976. chicoveio
977. wwalid2050
978. R1pp3r
979. drumchaps
980. qwing
981. nawalster
982. mnmx
983. l0serdude
984. iamsurbhi
985. bbmacarthur
986. doubtme
987. zeroms
988. crichm03
989. XiewRikl
990. solstyce
991. shamwow19
992. jessncollins
993. RicoSpartan
994. eridamus
995. sotacan
996. Anayansi-Iris
997. DAYANIDHI
998. CaitlinJ42
999. buguoruci
1000. frobnox
1001. allydillydally
1002. scampagna01
1003. RichardActually
1004. guneyd
1005. cryptguy
1006. JimSunkes
1007. cyberuser42
1008. jessexo
1009. Bnealis
1010. gaveen22
1011. HexMerck
1012. futrchamp
1013. da.amaya483
1014. mbarton1107
1015. kaneda
1016. heeraaa
1017. saramerlini
1018. shamano
1019. benshats
1020. Threscher
1021. borsaric
1022. martyg
1023. chairmanMeow
1024. caliphae
1025. kcuratolo
1026. xbecca3
1027. Lucifer98
1028. bacantu
1029. presidentdonkey
1030. LeVarBurton
1031. Snejana
1032. Pete
1033. palcu
1034. PEPZsquad
1035. HarleyJean
1036. levy_mCgarden
1037. spunkpike
1038. DrOfRecreation
1039. Cassiev
1040. sintrastes
1041. benknowlton
1042. imabanananut
1043. sleeplessspells
1044. Better_Angels
1045. relevant_thing
1046. shitzfez
1047. kingosraigi
1048. Ichikoa
1049. TheSn4ke
1050. ryanpoliver
1051. Theguybehindthescreen
1052. lurma
1053. BEG515
1054. haraf_ijhal
1055. cms
1056. cms
1057. imnotsosureyou
1058. dooleynotedd
1059. 10saumiljoshi24
1060. dullchuck
1061. lazypakman
1062. yannipang
1063. fauxhemian5
1064. fauxhemian5
1065. Aleroniponi
1066. namesare4tombstones
1067. saladbar_
1068. Divyanshu
1069. JRB_2000
1070. Screwdrivers
1071. dulekt
1072. Dink2311
1073. Ozziemedes
1074. 5tefan0
1075. eKro
1076. gavhanna
1077. jmrkumar
1078. JayMendez
1079. Ishwari
1080. halfbakedbertie
1081. CypheriusRex
1082. CypheriusRex
1083. Aw35om3n355
1084. dreadman86
1085. ishani1319
1086. theoriginalmick
1087. snv_tshd
1088. just_ron
1089. bob786bob786
1090. ayman-mahgoub
1091. theslyfox064
1092. theguywithacomputer
1093. juyeon_jang
1094. garmu
1095. churro777
1096. bonedlime
1097. xdcx
1098. cherukurinagarjun
1099. vishachar
1100. sutton_nightmare
1101. theaccountant
1102. muhtar
1103. kguler
1104. analy7er
1105. d34dkn16h7
1106. AmerieHartree
1107. fezspinkguitar
1108. brettjay
1109. senpi
1110. SvetikG
1111. Truffles
1112. kevivyor
1113. EntropicalForest
1114. Rbrown
1115. JacyFace
1116. jungjalapeno
1117. Higs
1118. eddytheflow
1119. ShadowSIPS
1120. ahmadmzak
1121. acebowen
1122. aboutdabusiness
1123. 20sat92
1124. cyho
1125. spy_2380
1126. snow_drop32
1127. fml-6626
1128. orchidsage
1129. kbanks4130
1130. rick101
1131. Dhunsi
1132. mchelley
1133. _redheadredemption_
1134. tom_sorrow
1135. ish94
1136. Michaelpelotte
1137. ineedtopeepee
1138. advanced_basic
1139. hooray4alex
1140. fuckpatricksmom
1141. hderms
1142. justanr
1143. bendaizer
1144. ivanureddit00
1145. throwawaymathy
1146. jimmmyboy
1147. apeters
1148. coolamebe
1149. uberstalker
1150. afiaust
1151. hannibal
1152. TheTravelingSpaceman
1153. outterspaceproduct
1154. apocrypha13142
1155. sreyes27
1156. PudBox
1157. mejia_daniel
1158. 889889771
1159. nicoekkart
1160. comfyc
1161. breexrawrx
1162. yapluss
1163. sfiltz
1164. Reddcancer96
1165. hiphop90
1166. ljxj
1167. cetahavis
1168. Megareyzor
1169. calebcardozo
1170. Canoener
1171. nomad_mind
1172. Abrusco
1173. Cody72
1174. the.actress
1175. captaindrek
1176. mpykan
1177. evilloid
1178. 1234yann
1179. jokullinn
1180. baysiderogue
1181. 742617
1182. fkya
1183. eldinerio
1184. lella
1185. james_9702
1186. xrysakalu
1187. Giedrius
1188. akeem.bacchus
1189. akbotik_92
1190. reganj
1191. DritJiffer
1192. Di2
1193. pranay1101
1194. msoup
1195. sdzugalo
1196. thayveline
1197. conhood6617
1198. naolermias
1199. AmandaLynnA
1200. princesspoohs
1201. salthoff
1202. Joecorgi
1203. Zackman
1204. kgwscarffe
1205. swarren9
1206. Mystery
1207. kayama
1208. WarGy_Luremus
1209. rajrahul
1210. Cmoreno723
1211. Driplone
1212. bobbi.bee
1213. Count_of_Monte_Crisco
1214. madschwenn
1215. Spider999ix
1216. SaraJamous
1217. pbdrpepperpb
1218. burubaxair
1219. Aspirina
1220. onex0907
1221. ChaceHunter
1222. darkespin
1223. UnidentifiedBlkMan
1224. EvilEgg
1225. Tallkobben
1226. Andres
1227. ayacsa
1228. afeef_afi
1229. kristanaquin545
1230. mhared
1231. Revcass
1232. remotep
1233. solrik
1234. davitik
1235. QuantumQuark5
1236. seanknight
1237. monica_a
1238. sarah-ziad
1239. Mastermind_Simpleton
1240. opaedo
1241. ilfg
1242. shlomer
1243. luccunha
1244. starskip
1245. oohso80s
1246. miagirl75
1247. thedanielchacko
1248. giovanod
1249. aguerrapa
1250. HighlyEvolved
1251. scantron_amazing
1252. Dhruval250
1253. juststudent_1
1254. __hsams__
1255. cioly
1256. gordomperdomper
1257. I_am_a_dumb
1258. tammuz
1259. tidalwave
1260. patrick.g
1261. zellekley
1262. alexantherethegreat
1263. brelovely15
1264. avi6687
1265. kaito123488
1266. jayver
1267. faustwaltzer
1268. MorsMiles
1269. asrs
1270. brwesley7
1271. manzar7
1272. rggmcn
1273. Pappan125
1274. Wit_Huntybee
1275. passthegouda
1276. joe24grube
1277. Mohammed_salih
1278. Maheshkarthik
1279. hardy1234
1280. DuesExMachina96
1281. Mete0r1t3
1282. savantsavage
1283. soueuls
1284. messi
1285. sam12.1
1286. vinicius97
1287. sevenstarsofstef
1288. mrdanielgriffith
1289. VonFoerster
1290. rrjlhj
1291. bobbiburrows2
1292. AdrianaNistor
1293. curioussagittarius
1294. frontraiderz
1295. Thorhey
1296. dpdocs21
1297. keenlearner
1298. CampCarthage
1299. nowellahhh
1300. Sithsaber
1301. JakubTetek
1302. nicolasblackburn
1303. nishai
1304. seanxedge
1305. spencair
1306. Zero21
1307. blakjak02
1308. alexthepandaman
1309. Monica101
1310. Mel8
1311. sarah_ren
1312. theEMPTYlife
1313. redditmucation
1314. heisenbergss
1315. sharpr1987
1316. Slz00
1317. ICanSniffOutTheVegan
1318. JoshuaWeinberger
1319. Gargantuon
1320. H.Felix
1321. bymythroat
1322. nelgar31
1323. tanamayfield
1324. vanillaCocaCola
1325. kd73
1326. schmiter
1327. nodari
1328. villarealca
1329. causa77
1330. asm
1331. Halkilt
1332. taartun
1333. Chiyo
1334. MooseRuse
1335. hallocaffeine
1336. JaiEzikeil
1337. pinkaleph
1338. ddorksey
1339. R3vis1on
1340. Ajrosario
1341. rmpvieira
1342. RRodrigues
1343. nitsud
1344. StarchiId