Group theory 3: Homomorphisms

This is lecture 3 of an online mathematics course on group theory.
It gives a review of homomorphisms and isomorphisms and gives
some examples of these.

[tejasrao]

Your lectures are very good -- deserve more views

[Yadoozz]

Some great gems along the way:
4:40: "Or ln if you want to use this dreadful notation"
10:10: "In fact, writing up the multiplication tables of a group is nearly always a really stupid thing to do".
Really enjoying these presentations. I did a course on abstract algebra in the Fall. Learned to do the operations, but didn't really understand the meaning of it all, or the application. Got renewed interest in group theory after studying the history of mathematics over Winter, and Lagrange's work on solving the fifth order polynomial equation.
Your presentations focus on the symmetries, making much more sense to me, a phycisist, than the abstract course I followed.
Thanks for these videos!

[yenanwang]

It's indeed a great lecture. Thank you Professor Borcherds.

[PunmasterSTP]

Homomorphisms? More like "Heroically good lectures with great information!" 🙏

[f-th]

Shouldn't the first example of a homomorphism be the distributive property of multiplication? E.g. doubling is a homomorphism for Z.

[ericvosselmans]

isn't z/4z a group of 4 equivalence classes, instead of a group of 4 numbers? Or did I learn it the wrong way ?

[satyajit]

Did prof mean automorphism around 4.00 ?

[stavrosklaoudatos]

Thanks for the amazing lecture. It's sad how such an amazing video has gotten only 6k views while some people get millions and millions of views for dancing for 30 seconds! Wish you the best!

[tomasmanriquezvalenzuela]

And what's the Chern-Weil homemorphism?