Basic abstract algebra, pt.7

This is a video series about basic abstract algebra and group theory. We will keep it basic so that anyone can follow the videoes.

This is the seventh video in the series. Do not take anything for granted.

Music Enya - Cursum Perficio.

Category:

Education

Tags:

• basic
• abstract
• algebra
• group
• theory
• mathematics
• math
• theorem
• prove
• proof
• science
• axioms
• do
• not
• take
• anything
• for
• granted

[alquiora]

I really really hate it when people say they invent mathematics. THEY DON'T!

What they invent is the language to DESCRIBE mathematics. The properties, functions, relationships and all sorts of other features of mathematics are already exist (sort of set in stone) ...just waiting for humans to discover them by means of using the "language".

[omgz0rtbh]

@alquiora Your reasoning has an implication that you may not expect. If mathematics already exists, then surely all numbers already exist. Each piece of finite information can be described as an integer, so all information that exists or could exist is already described in the natural numbers. Now, all our inventions are described in mathematics, all of our discoveries, all of our science. So what, then, could be an invention if everything already exists?

[VeritySeeker]

@omgz0rtbh You are correct. If all mathematics already exist, before we think about it, cars existed already in 1200 because it was (in theory) possible for atoms to be arranged into a car.

[VeritySeeker]

@alquiora There are lots of constructions in mathematics that are invented. And often they later turn into something useful.

By your logic, cars already existed in 1200 because the arrangement of atoms already allowed cars to exist. There are lots of constructions in mathematics way more complex than a car. Way more complex than something we can understand. That's why we still do research in mathematics.

[jaeger42]

Could you possibly explain a little bit about the applications of abstract algebra? I think you mentioned in a comment on another video that group theory has many applications so could you elaborate a bit on those? I'm in a class now and oftentimes wonder what this stuff is useful for. What about other big topics, like rings and fields, ideals, and field extensions?

[VeritySeeker]

@jaeger42 Hi, yes group theory has many applications. Within mathematics groups are very common in all branches, and I guess we would have no idea what to do without them. Furthermore, they are fundamental in cryptography and coding theory. Your CD player and CD's rely on them. If we didn't have group theory, your CD would have a hard time playing - or not even exist at all. Without group theory, you would not be able to pay your bills through the internet. There are lots of applications.

[mishy88]

This is awesome, I really appreciate the effort gone into these videos. Thank you. :)

[libuntux]

great series. i want to see more. why i go to universitiy, here i learn the same =)

[bdew7777]

Like all the other viewers thanks for the effort of these videos! Just a question: can you recommend any good text with decent exercise regarding Abstract Algebra that also contains the answers to these questions? I am using a book by Joseph Gallian, however the book contains few elementary exercises and I feel that when I practice the subject I get a better understanding. Thanks in advance...

[Emperorlawson]

I once had a math professor (who did research in abstract algebra) tell me that there's generally a 30-or-so-year lag between mathematical theory and application. One example he gave was an encryption algorithm from RSA. The math behind it had been published for decades before RSA got ahold of it and said, "Hey, we can use this!" He said it's good for things to stay that way, because if application catches up with research it will have to wait for research to advance.. if that makes sense lol

[alquiora]

@omgz0rtbh like I said invention is merely a discovery... Without maths this universe wouldn't exist

[DMAshura]

Dude, I dunno what it is with your videos.

But they make math ... like ... dramatic.

I feel like I'm waiting for the next twist.

I love it. :D

[MrAsiansunite]

@jaeger42 Applications in CD, cryptography are good examples, but the most exiting use of group theory is in particle physics, without group theory we cannot understand our Universe and answer the question Why We Are Here