-1+11161 
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. batmanizzle
930. blu1
931. teh27
932. nmbhat
933. 158510
934. Merohar
935. 70five
936. cheef_resident
937. apidome
938. krunt
939. L2BSmart
940. foo
941. Therealian
942. kirang
943. junkman416
944. igbistro
945. nunofilipemargarido
946. Bennymoonbase
947. jd95
948. pinguhash
949. FuckOffGetFree
950. thesaxby
951. bishman
952. djhk12
953. Gzzkarina
954. psychedelicate
955. khichi
956. Debb2254
957. pepe454
958. theprofessor01
959. lausveneris
960. leafie3000
961. JokerFrown
962. ttift1991
963. Skidie
964. mantexx12
965. fr0zen
966. korvil
967. scoronatus
968. conspiracyofqueens
969. ivanka-a
970. anax
971. Richo1337
972. ljghome
973. hobnailedboots
974. Janette
975. kkellerz
976. module
977. yippohappo
978. braindamage
979. chicoveio
980. wwalid2050
981. R1pp3r
982. drumchaps
983. qwing
984. nawalster
985. mnmx
986. l0serdude
987. iamsurbhi
988. bbmacarthur
989. doubtme
990. zeroms
991. crichm03
992. XiewRikl
993. solstyce
994. shamwow19
995. jessncollins
996. RicoSpartan
997. eridamus
998. sotacan
999. Anayansi-Iris
1000. DAYANIDHI
1001. CaitlinJ42
1002. buguoruci
1003. frobnox
1004. allydillydally
1005. scampagna01
1006. RichardActually
1007. guneyd
1008. cryptguy
1009. JimSunkes
1010. cyberuser42
1011. jessexo
1012. Bnealis
1013. gaveen22
1014. HexMerck
1015. futrchamp
1016. da.amaya483
1017. mbarton1107
1018. kaneda
1019. heeraaa
1020. saramerlini
1021. shamano
1022. benshats
1023. Threscher
1024. borsaric
1025. martyg
1026. chairmanMeow
1027. caliphae
1028. kcuratolo
1029. xbecca3
1030. Lucifer98
1031. bacantu
1032. presidentdonkey
1033. LeVarBurton
1034. Snejana
1035. Pete
1036. palcu
1037. PEPZsquad
1038. HarleyJean
1039. levy_mCgarden
1040. spunkpike
1041. DrOfRecreation
1042. Cassiev
1043. sintrastes
1044. benknowlton
1045. imabanananut
1046. sleeplessspells
1047. Better_Angels
1048. relevant_thing
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1050. kingosraigi
1051. Ichikoa
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1053. ryanpoliver
1054. Theguybehindthescreen
1055. lurma
1056. BEG515
1057. haraf_ijhal
1058. cms
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1061. dooleynotedd
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1063. dullchuck
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1067. fauxhemian5
1068. Aleroniponi
1069. namesare4tombstones
1070. saladbar_
1071. Divyanshu
1072. JRB_2000
1073. Screwdrivers
1074. dulekt
1075. Dink2311
1076. Ozziemedes
1077. 5tefan0
1078. eKro
1079. gavhanna
1080. jmrkumar
1081. JayMendez
1082. Ishwari
1083. halfbakedbertie
1084. CypheriusRex
1085. CypheriusRex
1086. Aw35om3n355
1087. dreadman86
1088. ishani1319
1089. theoriginalmick
1090. snv_tshd
1091. just_ron
1092. bob786bob786
1093. ayman-mahgoub
1094. theslyfox064
1095. theguywithacomputer
1096. juyeon_jang
1097. garmu
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1099. bonedlime
1100. xdcx
1101. cherukurinagarjun
1102. vishachar
1103. sutton_nightmare
1104. theaccountant
1105. muhtar
1106. kguler
1107. analy7er
1108. d34dkn16h7
1109. AmerieHartree
1110. fezspinkguitar
1111. brettjay
1112. senpi
1113. SvetikG
1114. Truffles
1115. kevivyor
1116. EntropicalForest
1117. Rbrown
1118. JacyFace
1119. jungjalapeno
1120. Higs
1121. eddytheflow
1122. ShadowSIPS
1123. ahmadmzak
1124. acebowen
1125. aboutdabusiness
1126. 20sat92
1127. cyho
1128. spy_2380
1129. snow_drop32
1130. fml-6626
1131. orchidsage
1132. kbanks4130
1133. rick101
1134. Dhunsi
1135. mchelley
1136. _redheadredemption_
1137. tom_sorrow
1138. ish94
1139. Michaelpelotte
1140. ineedtopeepee
1141. advanced_basic
1142. hooray4alex
1143. fuckpatricksmom
1144. hderms
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1149. jimmmyboy
1150. apeters
1151. coolamebe
1152. uberstalker
1153. afiaust
1154. hannibal
1155. TheTravelingSpaceman
1156. outterspaceproduct
1157. apocrypha13142
1158. sreyes27
1159. PudBox
1160. mejia_daniel
1161. 889889771
1162. nicoekkart
1163. comfyc
1164. breexrawrx
1165. yapluss
1166. sfiltz
1167. Reddcancer96
1168. hiphop90
1169. ljxj
1170. cetahavis
1171. Megareyzor
1172. calebcardozo
1173. Canoener
1174. nomad_mind
1175. Abrusco
1176. Cody72
1177. the.actress
1178. captaindrek
1179. mpykan
1180. evilloid
1181. 1234yann
1182. jokullinn
1183. baysiderogue
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1185. fkya
1186. eldinerio
1187. lella
1188. james_9702
1189. xrysakalu
1190. Giedrius
1191. akeem.bacchus
1192. akbotik_92
1193. reganj
1194. DritJiffer
1195. Di2
1196. pranay1101
1197. msoup
1198. sdzugalo
1199. thayveline
1200. conhood6617
1201. naolermias
1202. AmandaLynnA
1203. princesspoohs
1204. salthoff
1205. Joecorgi
1206. Zackman
1207. kgwscarffe
1208. swarren9
1209. Mystery
1210. kayama
1211. WarGy_Luremus
1212. rajrahul
1213. Cmoreno723
1214. Driplone
1215. bobbi.bee
1216. Count_of_Monte_Crisco
1217. madschwenn
1218. Spider999ix
1219. SaraJamous
1220. pbdrpepperpb
1221. burubaxair
1222. Aspirina
1223. onex0907
1224. ChaceHunter
1225. darkespin
1226. UnidentifiedBlkMan
1227. EvilEgg
1228. Tallkobben
1229. Andres
1230. ayacsa
1231. afeef_afi
1232. kristanaquin545
1233. mhared
1234. Revcass
1235. remotep
1236. solrik
1237. davitik
1238. QuantumQuark5
1239. seanknight
1240. monica_a
1241. sarah-ziad
1242. Mastermind_Simpleton
1243. opaedo
1244. ilfg
1245. shlomer
1246. luccunha
1247. starskip
1248. oohso80s
1249. miagirl75
1250. thedanielchacko
1251. giovanod
1252. frontraiderz
1253. aguerrapa
1254. HighlyEvolved
1255. scantron_amazing
1256. Dhruval250
1257. juststudent_1
1258. __hsams__
1259. cioly
1260. gordomperdomper
1261. I_am_a_dumb
1262. tammuz
1263. tidalwave
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1265. zellekley
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1267. brelovely15
1268. avi6687
1269. kaito123488
1270. jayver
1271. faustwaltzer
1272. MorsMiles
1273. asrs
1274. brwesley7
1275. manzar7
1276. rggmcn
1277. Pappan125
1278. Wit_Huntybee
1279. passthegouda
1280. joe24grube