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!

   • the Binary Operation
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!

   • Groups
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.

   • 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.

   • Cyclic Groups & Generators
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!

   • Permutations
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!

   • Orbits & Cycles
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!

   • Cosets & Lagrange's Theorem
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!

   • Direct Products and Finitely Generated Abelian Groups
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.

   • Group Homomorphisms
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.

    • Factor (Quotient) Groups

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.

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

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.

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