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...
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
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".
@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?
@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.
@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.
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?
@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.
@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
@behnamasid Yes, Galois was killed in a duel. Probably about a woman. What a waste of genius. He was in fact the first to coin the word "group" for this mathematical object.
That was AMAZING! I am currently taking Abstract and we had to write a paper on when we would use concepts from it in our future mathematical career. Honestly, I could not make a connection with it being useful to me later. You helped me to make that connection in four minutes! Thank you.
Well, it is an interesting question. But in this case I am talking about a definition, and there is nothing to prove about a definition, and so we invented it, not discovered it. The results following the definition are discovered. In my opinion, though. It is a question not easy to answer.
he really hit the nail on the head. My heart skips a beat when I think about isomorphisms-- they're so beautiful. It's so beautiful that you can generalize such natural systems and make new systems, it's like a whole new universe--gah I sound nuts
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...
bdew7777 1 week ago
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
Emperorlawson 2 months ago
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".
alquiora 6 months ago
@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?
omgz0rtbh 5 months ago
@omgz0rtbh like I said invention is merely a discovery... Without maths this universe wouldn't exist
alquiora 5 months ago
This has been flagged as spam show
@omgz0rtbh like I said invention is merely a discovery... Without maths this universe wouldn't exist
alquiora 5 months ago
@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 5 months ago
@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.
VeritySeeker 5 months ago
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
DMAshura 9 months ago
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?
jaeger42 1 year ago
@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.
VeritySeeker 1 year ago
@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
MrAsiansunite 1 year ago
Comment removed
jaeger42 1 year ago
Did the guy at 3:06 die in a duel?
behnamasid 1 year ago
@behnamasid Yes, Galois was killed in a duel. Probably about a woman. What a waste of genius. He was in fact the first to coin the word "group" for this mathematical object.
VeritySeeker 1 year ago
That was AMAZING! I am currently taking Abstract and we had to write a paper on when we would use concepts from it in our future mathematical career. Honestly, I could not make a connection with it being useful to me later. You helped me to make that connection in four minutes! Thank you.
Iam80b 1 year ago
good videos. However, you changed to fade in and fade out for the writing in this seventh video, and it makes it harder to read!!!!!
fergalegallagher 1 year ago
1:58 - or did we discover it?
jacksonwalters 1 year ago
@jacksonwalters
Well, it is an interesting question. But in this case I am talking about a definition, and there is nothing to prove about a definition, and so we invented it, not discovered it. The results following the definition are discovered. In my opinion, though. It is a question not easy to answer.
VeritySeeker 1 year ago
BGM is really amazing!!! wonderful video!
bookding 1 year ago
I would like to know what background music is playing here...
CathySander 1 year ago
Thanks for reminding me. I have updated the description with this info.
VeritySeeker 1 year ago
I recognized Galois and I think Euler. Who are the others?
Drregaleagle 2 years ago
@Drregaleagle:
Euler, Gauss, Abel, Galois, Cayley, Lie, Noether and Lagrange.
VeritySeeker 2 years ago
These videos are great. Keep making them!
magestaff567 2 years ago
can you include the names of those mathematicians? i have to say that I don't know all of them.
xinliw 2 years ago
hahaha exactly what noker1989 said. part 7 was a trailer for the rest of the parts =]
skinnylee 2 years ago
Amazing again.
seijurouhiko 2 years ago
is part 7 a movie trailor? very dramatic. But really clear and alot easier to understand this way!
noker1989 2 years ago 2
he really hit the nail on the head. My heart skips a beat when I think about isomorphisms-- they're so beautiful. It's so beautiful that you can generalize such natural systems and make new systems, it's like a whole new universe--gah I sound nuts
pyrofreakingmaniac 3 years ago 2
Math is beautiful.
signinname41 3 years ago 3
great series. i want to see more. why i go to universitiy, here i learn the same =)
libuntux 3 years ago 4
haha., still you gotta go to university to learn deeply
claslow 3 years ago 3
Your work is very appreciated. The entire series is nicely done and I'm looking forward to more.
rsati 3 years ago 2
Is that Enya? I friggin love Enya!!!!
Nanumir 3 years ago
It is indeed.
VeritySeeker 3 years ago
This is awesome, I really appreciate the effort gone into these videos. Thank you. :)
mishy88 3 years ago 6
great thank you keep making more they are really helping me
MathMikie 3 years ago