Writing Proofs: Direct Proof

We outline the method of direct proof and give a few examples of statements that are proved using this method.

[paul]

It would appear that Michael derived inspiration for this course from Joseph Gallian's book 'Contemporary Abstract Algebra'. Whether this is true or not I highly recommend said book as a perfect companion to this YouTube course. It shares with this course the multitude of examples. It has loads of good excercises. It has online support. The similarity in the philosophy behind the book and Michaels brilliant course are obvious to me. Do with this recommendation as you see fit.

[kryptynite]

I'm a math student and have failed Abstract Algebra twice, which is a requirement for my degree. I've even taken time away from university to ensure that this is really what I want to do with my life. I'm hoping to return in the coming spring semester to finish out my degree and ace the class that depressed and frustrated me to no end. Thank you for making this playlist, and especially for including basic concepts in writing proofs. I'll be digesting these videos over the next few months as I prepare myself for what feels like Ragnarok

[hypergraphic]

Very cool. From a programming perspective, it's like you are taking source code, and transforming it into an abstract syntax tree that you can walk over and reason about. Awesome.

[albertyeung]

Your presentation is excellent to the introduction of abstract algebra

[tomholroyd]

Circling back around from your most recent videos, I must say, nice background. I've been looking for more logic content. Conjunction is left adjoint to implication, you know.

[jabunapg]

But why doesn't the proof work from continuity to differentiability? I think not every continuos function is differentiable.

[SayHelllllo]

8:00 but the limit of x-a is 0, thus we multiply both sides of the equation by 0. Why can we do that?