Basic abstract algebra, pt.1

[nmacgre]

I've started this video over 4 times to learn abstract algebra. I bust into a trance/rave dance 4 seconds in, and forget about the math.

[DominicJakeo0o0o0o]

fuk u

[FantasyVesperia]

This is very interesting. Never thought math could be like this

[musiclearner9222]

You have no idea how grateful I am to you for these video tutorials on Groups. I would even pay you for these if you were charging money for it. I Love you!!! :) :)

[pancitSharon]

good introduction

[moorsalin3]

straightforward and clarifying, i love it

[SoutheGarden]

mind = blown

[fsaleh2011]

Fuck everyone who doesn't appreciate this. If they were actually taking abstract algebra, then they would appreciate the simplicity and straightforwardness of this video. Also, to the bitch who's complaining about the definitions of unordered and different ( @RurouniDizeru )... axioms bro. Axioms.

[VeritySeeker]

@fsaleh2011 Simplicity and straightforwardness were my goals in this series. Thanks!

[dkamka]

@VeritySeeker You are exactly right. This is very simple and to the point. The music is helful and it's done in a clever way. Forget those people who don't like this. This is a one of a kind site for abstract algebra. They should be grateful! It's so well done and there are tons of videos. I wanted to thank you again, a big THANK YOU :)

[dmathconfused]

I like it... in just under five minutes you took away all the pain of breaking into abstract algebra.... good work.... keep it coming

[thatzilla]

Not sure what people are complaining about. I am a senior Mathematics major in FL and having taken Abstract, I can say that this video is about as good a lecture as you're going to get online. To truly understand Abstract, you have to approach it in a very rigorous manor with a comprehensive knowledge of definitions and theorems, set theory, function theory, and proof methods. All of which are far beyond the scope of this video. This is a great practical overview of group theory.

[Knauzis]

Thank you. Super!

[JackTheGrower]

Hello and Thank You for your video series.

I haven't had a math class since the 1990s and I have a need now to understand sets and cycles since I wrote a transform that results in cycles.

Thanks and I look forward to watching the series from start to finish.

I look forward to being able to write down what I know so far.

[Ezzyman17]

Thank you very much for this video series, really helped me a lot.

[303750828]

Where can I find more videos for future study of abstract algebra？ Thank you！

[naqiharoon]

awesome vedio to understand fundamental of mathematics andadstrec algebra

[jbeyersphd]

This is basically irrelevant...

[eatmewithaspoon]

Gee,this is awesome. A video about math that is nothing but text and terrible music. This is way better than reading my textbook in a mediocre strip club in a tuesday night.

Sorry,but the reason I looked up a video on abstract algebra is because hearing a real person explain and rephrase concepts is more useful then reading it.  Just point a webcam at your face, and use your voice to explain this stuff without bad music. Thanks

[thunderdan7000]

@eatmewithaspoon You know, some people actually prefer text and music? Have you ever heard of the phrase "different learning styles"? and while I agree that the music sucks, it might be better than silence for some people, and the ones who don't like it can always mute it.

[erniebondy123]

I found that having no voice to go along with an example is not my learning style, but I can see how many people will benefit from this. Keep up the good work, but it's not for me.

[RurouniDizeru]

the definition of a set is tricky to do.at 2:59 you used the words "unordered, different and collection", none of which you defined. you have to define those asince many mathemtical terms can have a different meaning in a non- mathematical area.actually i have an issue with the words different and unordered being used in the first place. they could be misleading. could you please clarify what you meant when you used them

[VeritySeeker]

@RurouniDizeru Yes, but to go through set theory would be completely overkill and confusing at this stage.

[RurouniDizeru]

@VeritySeeker ok. then don't use unordered and different. say a collection of well- defined objects then

[VeritySeeker]

@RurouniDizeru I could maybe have "defined" a set better. Actually, I thought a lot about it, and I do that also in class. I try to give an intuitive understanding of what a set is, but it is actually one of the most difficult things to define in a low-level class. collection of objects could be good. With unordered I just meant that the order is not relevant, i.e. the set {1,2,3} is the same set as {3,1,2}. Of course, I could show that with an example instead.

[RurouniDizeru]

@VeritySeeker i think that would help prevent people from misconstruing.i thought that's what you meant.

[Icosohedron]

Then what is a "collection" ?

[Icosohedron]

Then what is a "collection" ?

[Icosohedron]

@RurouniDizeru  Then what is a collecton ?

[VeritySeeker]

@Icosohedron Then what is the word "then"?

[Icosohedron]

@VeritySeeker "Then" is part of an implication ( p -> q ). Defining a "set" as a "collection" is not helpful. But for what you are doing here, as you say, you don't want to worry about the definition of set, and just leave as undefined term.

[crowbat]

thanks for the vid awesome reviewwwwwwwwwwwwwwwwwww

[MegaAtheistman]

@truckdawg911 Wow are you ever a fucking creatard!

[truckdawg911]

@MegaAtheistman

LOL go outside troll the sun won't kill you. Man just imagining how funny looking you must be makes me bust a gut........

[MegaAtheistman]

@truckdawg911 You have allot of assumptions for a dumb ass creatard! Go back to your looser life. May god be less and nothing fails like prayer.

[mushroomxxxzzz]

@truckdawg911 Ignorant fuck 

[VeritySeeker]

@truckdawg911 And what if I did? The problem is?

[praetorian0000]

thanks for the video...i'm halfway through my abstract class its going well and i have a great prof but its cool to have an extra resource...great idea!!!

[Monkeyradar]

OK, just saw the first. I'm going to continue with them all

[signinname41]

Not only do i think the choice to have music in the background was unique and creative idea for a math video, but you also made a good song choice.

[VeritySeeker]

@signinname41 Thanks, mate.

[LuisRC91]

at first i expected Michael Jackson

[drunkencop]

This is good. It lays out the basics nicely and in an unthreatening way. And I like the format you've chosen. (Sal Khan does his thing, and I have no idea why other commenters are insisting that you should imitate him. You're doing fine.)

[Starstruckinpr26]

This sucks! I did not understand a thing! :-P

[VeritySeeker]

@Starstruckinpr26 Awww ...

[PicNiK]

Wtf is this video? It's just same text with background music. This is a slow and painful way to read a book...

Useless to me.

Thanks for the effort.... You should make a video like Sal's from Khan Academy.

[VeritySeeker]

@PicNiK Then read a book. I prefer books too.

[gredangeo]

I find the music strangely fitting to the video somehow.

[swimmingdrummerboy]

math = <3. And yes, by =, I mean are equal.

[TheFlanker35]

Thanks, I like these videos. They helped me learn something new.

[J0EH3AD]

The music is terrible... And you should use speaking and drawing as KhanAcademy does.

[LadislauFernandes]

These videos are the most original I have ever seen on youtube... congrats

[MrDogbert2]

I love this series, by the way.

[DeathZeroTolerance]

* binary operation?

[VeritySeeker]

@DeathZeroTolerance Sure, why not?

[VladimirVichfret]

nice video series :3

[TheLiberalSoup]

sweating wheabs out of my eyeballs... subscribed

[njra123]

I understand that abstract algebra is modern algebra, like linear algebra

[wlwak]

your language is not accurate. If a is in A and b in B and f(a)=b then the function f maps the element a in the domain set A to an element b in the codomain set B.

What you wrote at 4:17 is not correct. Frankly it's anti-correct. The function is what does the ''assigning'' so only elements of the domain can be ''assigned'' by the function. The domain is mapped to the codomain by means of the function not the other way round.

[VeritySeeker]

Hmm, I think it is correct. My native is not english, so I might be wrong, but this is what I meant: I did not mean that b is sent to a, or that b maps to a. But the function f is a relation, and to every element in A it assigns an element in B, and in this example b is the element assigned to a.

[ScammerSlayer]

From what I take of it, you are notation is fine in the video. You clarified that the set A was the domain and B was the range (codomain.) You mentioned that functions were one to one but what you left out, which could clear your case, is that functions are also "onto". That means every element in B is mapped from an element in A. This being the case, your choice of a and b where arbitrary so you could say "there exists an a such that f(a)=b for a an element in A and B an element in B.

[pbkielyo]

@ScammerSlayer yeah people asume khan as a sort of standard... which is sad. i am sometimes upset with it. Khan is great in what he is doing, it´s only really practical. This video is about abstract algebra which isn´t fucking disney land. verityseekers videos are for big boys i guess. if you understand all his videos in just 5 minutes with out watching it again i assume you study math and win the fucking fields medal. mathematics is the biggest challenge. It´s not like khan let it look like.

[ScammerSlayer]

@pbkielyo Mathematics can be a challenging field of study, especially higher order classes like Abstract Algebra, Number Theory, Topology, Non-Euclidean Geometry, ect...but its also a foundational topic as well. In order to do Calculus, one must know their Trigonometry and Algebra. To do Algebra, a strong background in basic mathematics is needed.

[VeritySeeker]

@ScammerSlayer Absolutely.

[VeritySeeker]

@ScammerSlayer Yes, the mathematics is correct. I might have used bad English language, but b is the element assigned to a in this video. Me writing the letter b before a doesn't mean f(b)=a. It means f(a)=b. I am used to people making logic going the wrong way. You seemed to get it, though ;).

[wintroller]

What the hell is this shit? This is like Algebra on crack and shrooooooms. The music said so. aahahhaouaiherwuohwefgiwheahbs­;odjg;lkbsjaeogh bae; jwlkjh what the bloody hell is this moo-zik?

[analyitic1]

i like it, but i dont like the music, its annoying.

[luayabd]

thank you verey much, it was super

[Vandius24]

sad to say its still to hard for me but ill watch all your vids and see what i can learn

[69erthx1138]

Can the fact that Rationals being expressed as fractions represent a kind of closure under multiplication (actually inverse multiplication)?, and conversely Irrationals don't have an exact or closed form under this same operation.

[VeritySeeker]

Indeed yes.

[69erthx1138]

Well, I guess having my nose in the books did payoff after all, at least until the book got slammed shut anyhow...

[MasterKanaar]

That is understandable because a rational number can not equal and irrational number in any set. Therefore, both have separate rules under closed multiplication.

[pkkda]

I had trouble getting started with the basics when self studying abstract algebra from various books. But after watching your videos that has changed. Thanks!

[stylefighterdks]

thanks a lot!!! it was a pleasure to view your teaching...

[mohd5588]

nice job man, looking forward to the next vid

[shobia99]

first natural number is zero isnt it?

[VeritySeeker]

Depends on the definition that we use. Some consider 0 to be a part of the natural numbers, while some don't. I didn't make up my mind about that, and so use the two different definitions freely, but as long as it is clear, that's ok.

[wintroller]

@shobia99

You asking that is like me asking "the first natural number is -infinity, right?" We all know that's a load of crap up the ceiling.

[Zetapoo]

I am trying to refresh my knowledge of this subject, thank you for doing this.

[ortega24024]

The only "poo" thing about the zeta function is that we don't know where its zeros are!

[orcodrilo]

Good job I am taking this class and your explanation is straight fun and simple.

[basicfruit]

I think this is a really good video, but I hate the music--not to insult your tastes, friend, but individual preferences aside, if the goal is to teach people algebra, why don't you just read your text aloud and have the audio played along to it? That would be really useful and not just have a decorative function, unlike the music.

[VeritySeeker]

I do not own a mic or cam at the moment, unfortunately.

[UndeadTheta]

thanks that was really helpful!

[vegapunk00]

nice work man!

[renijohn012270]

Sorry, Tecno Music and learning Algebra just don't mix!

You= FAIL!

[VeritySeeker]

You = CLICHÈ

[AlanCFA]

PJ O'Rourke once wrote that he knew that he was getting old because every time he turned on the radio, it sounded like the china cabinet being tipped over.

Cool way to teach abstract algebra. I got through Calc I-III, Diff Eq, and Linear Algebra, but never got to the abstract stuff. I have Allan Clark's book, but it is hard to stay motivate outside of a classroom.

If anyone here likes Real Analysis, there is a free download of a good textbook - search for Bruckner, Bruckner, and Thompson.

[xxbeyonce97xx]

Well I say that It was Intresting but I just wanted to see!!!!!!!!!!

[tharock220]

Ugh, I just finished into to algebra structures on Thursday, and I've never been so happy. Truthfully, I did not like it. The concrete stuff like sets, equivelence, induction was easy, but once we got to groups, rings, homomorphisms, and kernels I started to hate life. I got through it though. Possibly with an A.

[Phanu9000]

Wow that was an amazing intro that literally anyone can follow! Great job!!!

[tsliyan]

Excellent work who ever you are.

I started going through your videos. Anything on Measure Theory? Lebesgue Measure.

[lolspleenage]

yeahhhhhhh I'm going to get down with abstract algebra

[MetaIhead89]

I heard abstract math is very hard. I'm thinking about majoring in math, but will I do ok in this class? So far I've taken multivariable cal and linear algebra and I got A in both.

[VeritySeeker]

Of course abstract algebra can be hard at times, but you will certainly be able to take a first course. And if you like it and are motivated, then keep on working and you will manage. Linear algebra is probably the first time you saw some abstract concepts like vector spaces (depending on if you defined vector spaces in general or not). Good luck!

[DanielCriticalMX]

this uses similar symbolism to Truth Functional Logic. I am currently taking a course in TFL and I am learning calculus this year, which is very exciting!

[EdurarTe]

damn i didnt get it :S

[pickitupp]

When I first saw your series on ab. alg. I was thrilled to have found them....then I took a course in abstract algebra and it wasn't fun. Discrete math just isn't my thing I suppose. Nothing you can do about it though. Your videos are still awesome. Weiter so!

[kricknguyen]

this is great, thank you so much! =]

[o2thezone]

These videos are great! Would you consider doing some on Intro to Analysis? Metric spaces, continuity and limits... :)

[GR1o6180339887498948]

This is a nice video, but do you know any good textbooks for abstract algebra?

[VeritySeeker]

Absolutely. I recommend Basic Abstract Algebra by Bhattacharya, Jain and Nagpaul. It covers a lot of topics.

[GR1o6180339887498948]

Hey thanks I will look it up.

[titusjewell]

The music detracts from the text. I have to read with the sound off.

[88ale]

We define: A set is an unordered collection of different objects. But "set" and "collection" are synonyms so it doesn't seem a good definition.

[VeritySeeker]

Set and collection aren't really synonymous, since I am defining the mathematical use of "set" (not the english word). Furthermore, I should not use the word "set" when defining the mathematical notion of a set. I do not want to go into set theory here.

[RoGuEclaud]

lol --> * WTF? :P

[RoGuEclaud]

PS. awesome videos! thanks a whole lot

[gulomb]

Great videos, but please stop the horrible banging noises.

[richardpfeynman]

cool

[notoriousvcm]

Also, I know these videos are suposed to be "Basic," but, could you please make some where you explain "Congruent Modulus M," and Proofs.

Believe it or not, my University offers no Proof courses, and all my High School teachers were freaking coaches, so, I never, EVER, covered proofs in High School.

I won't leave without saying: THANK YOU!!!

THANK YOU!!! You're my hero today. I was this close to dropping that class. Now, you've given me hope.

[VeritySeeker]

Hi and thanks for your encouraging comments. Congruences will be a topic in the next video. I am still working on it. Thanks for commenting. Stay in there! You can do it.

[VeritySeeker]

I will try to make a video about how mathematics is built up and how to attempt doing a proof.

[Kinghercules]

yeah an intro to higher math would be good.

[PortapottyKarate]

a = b mod m iff m | (a - b)

[fourty2]

Hi, will you be doing anything with permutation groups?

[VeritySeeker]

That will be natural to do yes.

[fourty2]

It would actually be very helpful if you can explain the similarity between permutation groups and modulo's, my teacher today was referring to that, thanks for any help my friend

[VeritySeeker]

I am not sure what connection/similarity your teacher was referring to.

But amazingly, every group G is isomorphic to a permutation group (a subgroup of the group consisting of all permutations of G (which is the group of all bijections from G to G)). What is so nice about this, is that we can prove theorems about permutation groups and they will also hold for groups in general.

He might have been talking about Cayley's theorem?

[fourty2]

oh, he might have been saying something about how if we can prove something within a permutation group then we can apply it to different groups, like Zn, ahhh i see now, thank you sir, but could you please explain in some more detail why it's true that if you prove something about a permutation group then it hold for all groups

[VeritySeeker]

I will look at permutation groups very soon in the videos. But before that I want to look at number theory (I am making that video now as we speak) and factor groups (modulo).

I can try to explain a little here:

A permutation group H on G is a subgroup of the group consisting of ALL permutations of G. That means that H consists of permutations of G (but not necessarily all permutations).

Remaining character count is out, so I continue below...

[VeritySeeker]

... continues here:

The logic is as follows: If F is ANY group, then Cayley tells us that F is actually isomorphic (algebraically the same) as some permutation group!

If we can prove a theorem about permutation groups in general, it follows that F also will satisfy this theorem, since it is a permutation group too (by Cayley). So hence since F was ANY group we want it to be, then any group will satisfy the theorem.

All groups are permutation groups - up to isomorphism.

[notoriousvcm]

Abstract Algebra, and Number Theory, and I understand none of them. NONE... N...O... N... E. The professor tries to aid this, but she only ends up confusing me more. YOU, on the other hand, are not confusing me... at all.

I have been able to get through most of my Math courses trouble-free. Heck, I even got through Digital Logic, and Computer Architecture (Which is hard) trouble free!

And I can't understand Abstract Algebra?

Please, please, please... please don't stop. Keep them coming.

...

[notoriousvcm]

I have to ask you, politely... actually, I am BEGGING you here, please DO NOT stop these videos. PLEASE. They are so easy to follow, you wouldn't even understand.

I am a Mathematics and Computer Science (Double Major) that is trying to get through college, so that I can get to Graduate School and earn my Masters.

Any ways, I don't want to bore you with my life... but this is the thing... I don't freaking understand my Abstract Algebra professor. I have, not kidding, 5 DIFFERENT books on...

[69erthx1138]

Is perhaps one of your course books required text and the others optional? I know many professors will give recommended texts with the required ones (and sometimes a reading list).

[claslow]

fantastic beginning., i will watch all of the rest. regards, from iowa

[kikuchiyo77]

Favretto - Yes U R (feat. Naan)

VS, you are pretty damn hip for somebody into abstract algebra! Nice!

[kikuchiyo77]

Great great presentation...but damn, what song is this? I love it, but can't make out enough lyrics to google it.

Please credit your sources in the future.

[uj8r48u584548j]

That was an excellent motivating section and introduction to rigorous mathematics!

[lajungesombre]

here is what i like about this video 1. it assumes nothing 2. it explains whatever is written 3. the humour and the pictures/presentation is engaging 4. the music (which i usually mute, but listen to when i feel like) 5. the time given to understand the concepts short, sweet, simple i love it i love you you rock keep up the good work -H

[terencezdy]

may be more about rings module and field....

[VeritySeeker]

Sure, I could say something about that, but this is supposed to be very basic, and these things need to be well-known before one can start with rings, modules and fields.

[britcruise]

Really excellent work. I don't know why this stuff isn't taught earlier in schools

[Nanumir]

awesome please post more more more

[bxs0099]

exhiliarating. great choicen of music.

[bxs0099]

Wow. My spelling really sucks at 7:00 am. That should read,

"Exhilarating. Great choice of music."

Cheers.

[zugimon21]

i want to have your babies, i love you so much keep it up!

[elephantman2222]

i just like the music

[rustintable]

Could you please say the words so I can just listen.

I have many good books on the topic. I would just like something more visual audio for when I am not in the mood to read.

Great idea though....

[RenmazuoX2]

EXTREMELY Useful. The explanation is actually in English!! Awesome video. Thanks a lot!

[VeritySeeker]

Thanks a lot, RenmazuoX2. Nothing makes me happier about these videos than if they are understandable ;).

[0musing]

good for a very quick review. Thanks!

[VeritySeeker]

Thanks, 0musing. It is not easy to do a deep dive into the subject, but hopefully it is good for an introduction and repetition.

[pickitupp]

I'll be taking absract algebra next semester so I'm thrilled to have found this! I'm taking linear algebra II, which I am told is good preparation. thank you thank you!

[VeritySeeker]

Linear algebra is a good preparation to take abstract algebra. In linear algebra one is introduced to some abstract concepts like vector spaces. Thanks for watching.

[trystanlea]

Thanks, very helpful

[peterpan795]

helpful stuff, keep up

[VeritySeeker]

Thanks, peterpan795. I hope the videos can help a little those who just picked up a book on abstract algebra.

[pollardrho06]

Continue with the videos... I feel Abstract Algebra is a fascinating branch of mathematics... worthy of your time... keep up the good work

[VeritySeeker]

Thank you, pollardrho06. I will be checking out your videos too.