-1+1984 
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. tpkalman
930. sergeybok
931. lol_dongs
932. batmanizzle
933. blu1
934. teh27
935. nmbhat
936. 158510
937. Merohar
938. 70five
939. cheef_resident
940. apidome
941. krunt
942. L2BSmart
943. foo
944. Therealian
945. kirang
946. junkman416
947. igbistro
948. nunofilipemargarido
949. Bennymoonbase
950. jd95
951. pinguhash
952. FuckOffGetFree
953. thesaxby
954. bishman
955. djhk12
956. Gzzkarina
957. psychedelicate
958. khichi
959. Debb2254
960. pepe454
961. theprofessor01
962. lausveneris
963. leafie3000
964. JokerFrown
965. ttift1991
966. Skidie
967. mantexx12
968. fr0zen
969. korvil
970. scoronatus
971. conspiracyofqueens
972. ivanka-a
973. anax
974. Richo1337
975. ljghome
976. hobnailedboots
977. Janette
978. kkellerz
979. module
980. yippohappo
981. braindamage
982. chicoveio
983. wwalid2050
984. R1pp3r
985. drumchaps
986. qwing
987. nawalster
988. mnmx
989. l0serdude
990. iamsurbhi
991. bbmacarthur
992. doubtme
993. zeroms
994. crichm03
995. XiewRikl
996. solstyce
997. shamwow19
998. jessncollins
999. RicoSpartan
1000. eridamus
1001. sotacan
1002. Anayansi-Iris
1003. DAYANIDHI
1004. CaitlinJ42
1005. buguoruci
1006. frobnox
1007. allydillydally
1008. scampagna01
1009. RichardActually
1010. guneyd
1011. cryptguy
1012. JimSunkes
1013. cyberuser42
1014. jessexo
1015. Bnealis
1016. gaveen22
1017. HexMerck
1018. futrchamp
1019. da.amaya483
1020. mbarton1107
1021. kaneda
1022. heeraaa
1023. saramerlini
1024. shamano
1025. benshats
1026. Threscher
1027. borsaric
1028. martyg
1029. chairmanMeow
1030. caliphae
1031. kcuratolo
1032. xbecca3
1033. Lucifer98
1034. bacantu
1035. presidentdonkey
1036. LeVarBurton
1037. Snejana
1038. Pete
1039. palcu
1040. PEPZsquad
1041. HarleyJean
1042. levy_mCgarden
1043. spunkpike
1044. DrOfRecreation
1045. Cassiev
1046. sintrastes
1047. benknowlton
1048. imabanananut
1049. sleeplessspells
1050. Better_Angels
1051. relevant_thing
1052. shitzfez
1053. kingosraigi
1054. Ichikoa
1055. TheSn4ke
1056. ryanpoliver
1057. Theguybehindthescreen
1058. lurma
1059. BEG515
1060. haraf_ijhal
1061. cms
1062. cms
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1064. dooleynotedd
1065. 10saumiljoshi24
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1068. yannipang
1069. fauxhemian5
1070. fauxhemian5
1071. Aleroniponi
1072. namesare4tombstones
1073. saladbar_
1074. Divyanshu
1075. JRB_2000
1076. Screwdrivers
1077. dulekt
1078. Dink2311
1079. Ozziemedes
1080. 5tefan0
1081. eKro
1082. gavhanna