Extremely clear and covers all the basics. The best gentle introduction to algebraic structures I've been able to find!
@arify7344
7 жыл бұрын
Good luck in your Algebra exams, fellow students
@ArifYunando
5 жыл бұрын
Hello Arif
@its_roggy
3 жыл бұрын
Thanks, we have one tomorrow
@imcloudy1909
3 жыл бұрын
Y am I doing this in year 9...?
@daytonrowen4515
3 жыл бұрын
i know it is quite off topic but does anyone know a good site to stream newly released movies online?
@supongmenwalling5318
2 жыл бұрын
I failed...ooooooo😭🤣
@nadaabdulla7556
3 жыл бұрын
I finished the course 2 years ago, I didn't understand it then, but now I'm interested and regret that I didn't do my best :(
@johntryl8009
Жыл бұрын
The example of Z mod n (when n=prime) being a field and not a ring is the coolest thing ever. Furthermore, your explanation of why complex numbers are a vector space made things finally click ... it has scalar multiplication and it has addition, but it just has even more properties. This was so helpful. Thank you for being super approachable and clear!
@lamalamalex
10 ай бұрын
I do agree with you that you built up according to complexity of the structures. With vector spaces appropriately at the end. So that’s why I find it very strange that that’s where we start students at. Linear algebra being such an early class students takes. It can even be taken before a multi variable calculus course.
@plaustrarius
6 жыл бұрын
cannot thank you enough for this video!!
@mcmoodoo
6 ай бұрын
Absolute Gold! Thank you, sir!
@leylaalkan6630
6 жыл бұрын
Thanks for these amazing clarifications.
@rithikseth1404
6 жыл бұрын
Thanks very helpful for my engineering studies ....
@funnyman4744
8 ай бұрын
this is a great crash course!
@Ivane.h
Жыл бұрын
Single-handedly getting me trough ADM mit Gittenberger...
@AkamiChannel
Жыл бұрын
This was great. I just wish you had gone into what an algebra is. I'm on a mission to understand that, but google and youtube search results are completely worthless to me because they're full of content explaining ordinary algebra.
@HamblinMath
Жыл бұрын
An "algebra" is a vector space over a field that has multiplication of vectors. Complex numbers are an example of an algebra.
@AkamiChannel
Жыл бұрын
@@HamblinMath Yes, I had realized as much. Was thinking of a more formal explanation like one often sees for vector spaces. I did find one on youtube yesterday. It seemed to me, though, that the formal definition of an algebra is so general that just having a vague idea of it is enough.
@aritraroygosthipaty3662
5 жыл бұрын
A very helpful lecture.
@jasminefitzsimons896
Жыл бұрын
ok I literally love you
@eset3649
6 жыл бұрын
Crystal clear, thank you sir.
@LucyMuthoni
4 жыл бұрын
Thank you very much for this video. Be blessed!
@clu5ter892
5 жыл бұрын
Thanks for this vid from Russia)
@MunkyChunk
4 жыл бұрын
You are a... GENIUS!!! Thank you!!
@YoutubeModeratorsSuckMyBalls
Жыл бұрын
Why in rings case addition should be commutative? What if one operation is commutative, but it is distributive over second which is not? Can this structure be considered ring? What if none of the operation is commutative but one of them distributes over another? What is the point of distributive properity? Why is it even introduced? Is it states superiority of one operation over another or what? What if both operations are distributive over each other, like conjuction and disjunction? Should all those cases be considered as rings?
@c0t556
6 жыл бұрын
Very good explanation! Thank you so much!
@fraktallyfractals2083
5 ай бұрын
About Z as a group, at the beginning of the video, does that mean that zero is its own opposite?
@DavidVonR
Жыл бұрын
Too cool! I love group and ring theory :)
@anantrelan4071
5 жыл бұрын
@12:01 Field is a ring with two operations . @18:12 F is a Field under (only) Multiplication . Q. Why is there only 1 operation for the field F at @18:12 ? Thanks
@HamblinMath
5 жыл бұрын
A field always has two operations, addition and multiplication. I'm distinguishing the field multiplication (scalar times scalar) from "scalar multiplication" (scalar times vector).
@anantrelan4071
5 жыл бұрын
@@HamblinMath oh ok Thanks for the Reply !!
@Caleb-qr6lo
6 жыл бұрын
lol I see xor symbol and get really confused.
@asmamokr1345
7 жыл бұрын
thk'x a lot but i have a question ... for groups the first example for the inverse (-a) don't belong to Z ( but in the rule it should belong ) ...i am confusing 😣😣
@MathMaster19
7 жыл бұрын
-a belongs to Z, it doesn't belong to N
@josvandeneynde5849
6 жыл бұрын
Great video! I thank you!
@katelikesrectangles
6 жыл бұрын
That was really helpful, thank you!
@arnabdasphysics
Жыл бұрын
Superb!
@gunjanrathore9337
3 жыл бұрын
Is division for any R' N' Q' is made an algebraic structure??? R set of real no N set of natural no (1, 2,3...) Q set of rational no
@shrimp8594
3 жыл бұрын
Thank you:) Really helpful video.
@TheHuggableEmpire
3 жыл бұрын
So addition and multiplication in rings doesn't necessarily mean the usual sum and product?
@janoprivracki1992
Жыл бұрын
Correct, these are abstractions. Don't mind me commenting a year later... rofl. Hopefully it's helpful to someone in the future
@evrenunal3644
Жыл бұрын
@@janoprivracki1992 it indeed helped me, thanks
@osebrainquestfoundation9631
2 жыл бұрын
It knowledgeable. Thanks
@ebrimagajaga4639
6 ай бұрын
Please help me answer this question… Is (N, +) a group ? N is a set of natural numbers…
@HamblinMath
6 ай бұрын
No, because not every element of N has an inverse.
@SzechSauce
4 жыл бұрын
Great explnantions thanks!
@AyushSharma-ux4fk
4 жыл бұрын
can you please share the slides that you are using to teach?
@48_subhambanerjee22
2 жыл бұрын
love it
@rushikeshkavar6128
6 жыл бұрын
Nice video. But is Ring Definition correct? According to Wikipedia, There should be additive identity and additive inverse. Am i wrong? Please clarify.
@HamblinMath
6 жыл бұрын
Kavar Rushikesh R being a commutative group under addition includes those properties.
@harirao12345
5 жыл бұрын
very clear ... thank you!
@pragyapathak8660
6 жыл бұрын
Nice vedio sir but in group definition closure property is not mentioned
@HamblinMath
6 жыл бұрын
Closure is typically understood to be part of what you mean when you say that the operation is "on" the set G.
@joeflaubert5597
6 жыл бұрын
Thank you
@lamalamalex
10 ай бұрын
I don’t understand why y’all want to hide the operations of ➕ and ✖️ and then just talk about those. I mean, what else is there? Why the back and forth?
@privateaccount1266
3 ай бұрын
Because the operation symbol could be either + or x. For example when you saw the properties that characterise a group there was a symbol. And something could be a group with + or a group with x. You use + or x depending on the question.
@sunildhull8878
5 жыл бұрын
at 5:43 set of integers mod n became non negative integer which not follow inverse property over addition so it not supposed to be grp i.e. |-3|+|3|=6 not 0 plssss reply
@HamblinMath
5 жыл бұрын
Sunil, in arithmetic mod n, you take the remainder when the number is divided by n. For example, in arithmetic mod 7, the inverse of 3 is 4 because 3+4 = 0.
@goumuk
3 жыл бұрын
One more property of Groups - Closure property. If A , B belong to G, then if A ⊕ B = C, C also belongs to G.
@HamblinMath
3 жыл бұрын
Using your notation, if "A ⊕ B" didn't belong to G, what are we even talking about? This is often rolled into the definition of what it means for "⊕" to be an operation on the set G.
@goumuk
3 жыл бұрын
@@HamblinMath I guess you are right, but making it explicit may help beginners, so thought of mentioning here.
@shiina_mahiru_9067
5 жыл бұрын
I dont think R is a field since 0 has no multiplicative inverse, but R* would be
@Enriquecav
5 жыл бұрын
The multiplicative inverse is defined for all numbers except 0, so R is a field
@poomalaip2620
6 жыл бұрын
Give each definition examples
@andreiparaschiv3257
5 жыл бұрын
great video one of my concerns is that people could get the idea that you can prove a property by trying out random examples, as you did with the multiplicative inverse over Q[radical 2] by choosing a=3 and b=4. it has to be generalised, and that means not assigning specific values. that could have been made a little clearer in the clip.
@HamblinMath
5 жыл бұрын
I do specifically say "this isn't a proof"...
@footage6402
6 жыл бұрын
How does a group differ from a field?
@levinicklas7885
5 жыл бұрын
a field has 2 operations and an inverse. A ring does not always have an inverse and a group only has 1 operation.
@safofoh
7 жыл бұрын
Thanks, it's very useful
@Okapi000
3 жыл бұрын
Why don't you include closure as a necessary property to be a group?
@HamblinMath
3 жыл бұрын
"Closure" is typically assumed when we say that "+ is an operation on G."
@DantalionNl
4 жыл бұрын
Why is the property A * B = B * A called identity and not commutativity ?
@HamblinMath
4 жыл бұрын
Commutativity says "for all A and B in the set, A*B=B*A." It's not called identity. Read the "identity" property carefully.
@Ambagaye
5 жыл бұрын
Closure
@alex-my8hp
5 жыл бұрын
you missed out closure
@HamblinMath
5 жыл бұрын
While "closure" is sometimes included as a group/ring axiom, it's not really necessary, since for the operation on two elements to make any sense, the result of the operation must be in the set you're talking about.
@alex-my8hp
5 жыл бұрын
@@HamblinMath oh, fair enough
@AlessandroZir
2 жыл бұрын
❤️❤️❤️🙏🙌
@haentertain8383
3 жыл бұрын
Please send to me solved ring examples all
@a_ghoul
4 жыл бұрын
i am only in the 2nd grade how do I find x 2x+2=6
@qusai05
Жыл бұрын
subtract 2 from both sides, u get 2x=4, then divide by 2 on both sides, u get x=2
@felixhsu9583
5 жыл бұрын
祝我信安数基能及格🌝
@soseipirialadick-iruenaber7273
Жыл бұрын
You're talking too fast and I'm not understanding 😔
Пікірлер: 91