[old series] Abstract Algebra Lecture 01 Part 1

First lecture in abstract algebra. Topics include facts about functions and countable sets, infinite sets of numbers commonly found as underlying sets in algebraic structures, and algebraic and transcendental numbers. This lecture is in three parts.

[crAAzyskr]

Wow, I'm glad I found this. I needed to learn this but didn't have the books! Thanks.

[lshuppp]

Extremely helpful! I am very glad I came across these lectures!

[AaronNHorvitz]

The only thing I learned in math was not to drink and derive at the same time. Other than that, great lecture! -Aaron :)

[ashleyrobinson]

This is awesome! Thank you, this makes everything I've been learning more clear. I would love the notes in pdf format if you're still willing to do that. However, I don't know how to send a personal message.

[gammaphoenix]

Hello sir. I think there might be some mistake in the second argument you gave at around 2:00. Suppose g maps from [0, 5] to[0, 10] and f maps from [0, 11] to [0, 11], and we define their codomains to be their images (ie they are surjective).
f=x, g=2x
Then fog is not surjective since fog=2x, and it maps from [0, , 5] to [0, 10] and not [0, 11].

[fawzyhegab]

I have two questions, 1) What is the difference between, "Countable unions of countable sets " and " the unions of countable unions" ? what is the definition of countable unions ?
2) What do you mean be finite products ?

[melfairebon]

very nice lecture! really need this in my comprehensive exam in abstract algebra. Pls add me to your distribution list coz i really need to study for my exam. thank you.

[geekoist]

Do you model your lectures on some textbook's chapters?

[gammaphoenix]

I see. Thank you sir. May I know the university/institute in which you teach? I am an undergraduate student in IISc and was considering where to do my summer project in the year of 2014.I am highly interested in number theory and I think you would make a great professor to do a project under.

[geekoist]

Hello, are you going to do lie algebras later?

[jason]

When you prove that the set of integers is countable, is it necessary to mention the case when m>0, n<0 or m<0, n>0, even if it is obvious to see f(m) cannot be equal to f(n)? ^_^

[PsychonautAtom]

I prefer the natural numbers to include 0 since we already have a symbol for the positive integers. However there's no universally agreed upon definition for the natural numbers.

[mariorpg]

are there problem sets going with the lecture?

[jeremymiller]

People don't forget 0 isn't part of the natural numbers. Set theorists, logicians, and computer scientists purposely include it all the time.