extremely well done : being very precautions about explaining the concepts so well : thank you . I do think you should have used a bigger paper triangle with some brighter and a bit bigger blobs of colours . Thanks a gain and keep on teaching us please . H.H (Capetown )
2 месяца назад+1
Thank you very much, sir! You are absolutely right about the triangle - I didn't realize this until cutting of the video, and then it was already too late (the blackboard was wiped clean...).
2 месяца назад
PS: In case you're also watching lesson 2 and wondering why the triangle is still too small: I have prerecorded the first lessons before starting the series, so I can't make any changes there. But in the videos I'm recording now I try to zoom in better.
I think I was already 2 years into my math undergrad and had finished Linear Algebra 1 + 2 before I started to think about what groups have to do with symmetries :) And I feel like I'm still learning something from this video. For me personally, math can also be fun just thinking about the abstract rules directly, but it is really nice to see how it all comes together :)
2 месяца назад+1
Awesome! I'm also on the "thinking-abstractly-is-also-fun-side", but especially for beginners the motivation for the definition of a group becomes much clearer through these examples. Very happy to hear from you and that you're actually watching the videos.
Thank you very much - I will (try). So far, the first 10 lessons (plus solutions) have been recorded and will be released one after another every week. Hopefully I can uphold the weekly posts, but family- and school-duties might have priority at times.
Nice job. I recently had a university course in abstract algebra and your video reinforced concepts that are still rather new to me. I like the problem sets.
2 месяца назад+2
That's great to hear, as this is exactly one of the goals of this course. Keep me posted, also if the solution videos are helpful.
It already has helped bridge the gap between the intuition and the formality of textbooks. I look forward to the next lectures!
2 месяца назад+2
@@casaroli That's awesome since this is exactly the intention of this series. Every saturday at 3 p.m. (German time zone) the new lesson will be released (except for lessons where the problem set is so extensive that I will spread the solutions out over two weeks). Looking forward to hearing from you again!
I'm a bit confused. Is the set a collection of objects or operations (various spins and rotations) and if so, then why do you need an operation along with the set?
2 месяца назад+2
"Operation" here does not refer to the objects (here: symmetries of a triangle or more general "maps") but to the law of composition of these objects, i.e., how to combine two symmetries to obtain another symmetry.
Thanks for clarifying this. Operation in your group refers to operation on two elements in the set of different rotations and flips, namely the operation of composition of two elements.
If you rotate the triangle about - 120 degrees you would end up with the same constellation as if you rotate about 240 degrees. So while you would move different the end result would be the same and for most applications of these concepts it's not important how you get to the new constellation. Therefore the D3-Group contains only 2 rotations.
Für die ersten ca. 20 Lektionen wäre das mein Büchlein amzn.eu/d/7gP9CxI (Ist inzwischen aber leider recht teuer ... ) Ich könnte ein handgeschriebenes Uni-Skript von mir hochladen, das passt allerdings nicht 1:1 zu den Videos und ist zu Beginn recht knapp gehalten. Interesse?
Da steckt ja Ihre Arbeit drin. Von daher wäre es ja fairer, das Buch zu erwerben als ein kostenloses Skript zu fordern. Vielen Dank auf jeden Fall für die Videos!
2 месяца назад+1
@@matthias7790 Respekt - das ist aber sehr rücksichtsvoll (so gar nicht passend zur "her damit"-Mentalität, die heute viele an den Tag legen). Allein schon aufgrund dieses Kommentars werde ich überlegen, ob ich das Skript nicht verfügbar mache. Danke.
2 месяца назад+1
Handschriftliches Skript jetzt verfügbar unter matherialien.jimdofree.com/
If by "Skript," you mean a transcript, RUclips provides an transcript when you push the transcript button at the bottom of the author's description, which you can see by clicking on "more."
Subtraction can be associative if you turn it around to addition, i.e. if instead of subtracting you add up negative numbers. 3-2-1 is the same as 3+[(-2)+(-1)]
2 месяца назад+1
@@DaLiJeIOvoImeZauzeto Nice, but then you simply have addition in the integers (and the question was about an elementary operation that is not associative). Interestingly this does not work with division when writing it as multiplication with the inverse.
I use lowercase letters for maps (e.g., f, g, ...), so "id" is consistent with that. Besides, it's standard notation, at least in German texts. But thanks for caring and commenting twice. PS: I'm about 10 weeks ahead in recording the videos, so even if I wanted to, I couldn't make imminent changes.
extremely well done : being very precautions about explaining the concepts so well : thank you . I do think you should have used a bigger paper triangle with some brighter and a bit bigger blobs of colours . Thanks a gain and keep on teaching us please . H.H (Capetown )
Thank you very much, sir!
You are absolutely right about the triangle - I didn't realize this until cutting of the video, and then it was already too late (the blackboard was wiped clean...).
PS: In case you're also watching lesson 2 and wondering why the triangle is still too small: I have prerecorded the first lessons before starting the series, so I can't make any changes there. But in the videos I'm recording now I try to zoom in better.
I think I was already 2 years into my math undergrad and had finished Linear Algebra 1 + 2 before I started to think about what groups have to do with symmetries :) And I feel like I'm still learning something from this video. For me personally, math can also be fun just thinking about the abstract rules directly, but it is really nice to see how it all comes together :)
Awesome! I'm also on the "thinking-abstractly-is-also-fun-side", but especially for beginners the motivation for the definition of a group becomes much clearer through these examples.
Very happy to hear from you and that you're actually watching the videos.
Every RUclips video must be like this ❤❤
This is fantastic, please keep posting videos!!!
Thank you very much - I will (try). So far, the first 10 lessons (plus solutions) have been recorded and will be released one after another every week. Hopefully I can uphold the weekly posts, but family- and school-duties might have priority at times.
Do it comfortably
I’ve been hoping to find a good introductory series on Abstract Algebra. Great timing.
Great timing indeed. Hope you enjoy the course and that you benefit from it.
Nice job. I recently had a university course in abstract algebra and your video reinforced concepts that are still rather new to me. I like the problem sets.
That's great to hear, as this is exactly one of the goals of this course. Keep me posted, also if the solution videos are helpful.
Thank you.
I will follow the series as a course!
That's great to hear. Please let me know if you enjoy the series and if you find it helpful.
It already has helped bridge the gap between the intuition and the formality of textbooks.
I look forward to the next lectures!
@@casaroli That's awesome since this is exactly the intention of this series. Every saturday at 3 p.m. (German time zone) the new lesson will be released (except for lessons where the problem set is so extensive that I will spread the solutions out over two weeks). Looking forward to hearing from you again!
Great video!
Excellent video!
Thank you!
Thanks 🙏
Blink & Slow Motion joke made me laugh so hard.
I'm a bit confused. Is the set a collection of objects or operations (various spins and rotations) and if so, then why do you need an operation along with the set?
"Operation" here does not refer to the objects (here: symmetries of a triangle or more general "maps") but to the law of composition of these objects, i.e., how to combine two symmetries to obtain another symmetry.
Thanks for clarifying this. Operation in your group refers to operation on two elements in the set of different rotations and flips, namely the operation of composition of two elements.
Why are there only 2 ways to rotate? Could you not also rotate in the other direction? (+&-)
If you rotate the triangle about - 120 degrees you would end up with the same constellation as if you rotate about 240 degrees. So while you would move different the end result would be the same and for most applications of these concepts it's not important how you get to the new constellation. Therefore the D3-Group contains only 2 rotations.
Thanks, my dear colleague! :)
Gibt es ein Skript?
Für die ersten ca. 20 Lektionen wäre das mein Büchlein
amzn.eu/d/7gP9CxI
(Ist inzwischen aber leider recht teuer ... )
Ich könnte ein handgeschriebenes Uni-Skript von mir hochladen, das passt allerdings nicht 1:1 zu den Videos und ist zu Beginn recht knapp gehalten. Interesse?
Da steckt ja Ihre Arbeit drin. Von daher wäre es ja fairer, das Buch zu erwerben als ein kostenloses Skript zu fordern. Vielen Dank auf jeden Fall für die Videos!
@@matthias7790 Respekt - das ist aber sehr rücksichtsvoll (so gar nicht passend zur "her damit"-Mentalität, die heute viele an den Tag legen). Allein schon aufgrund dieses Kommentars werde ich überlegen, ob ich das Skript nicht verfügbar mache. Danke.
Handschriftliches Skript jetzt verfügbar unter
matherialien.jimdofree.com/
If by "Skript," you mean a transcript, RUclips provides an transcript when you push the transcript button at the bottom of the author's description, which you can see by clicking on "more."
There is one basic operation, namely division, which is not associative...
And subtraction as well: a - ( b - c ) is i.g. not the same as ( a - b ) - c.
Subtraction can be associative if you turn it around to addition, i.e. if instead of subtracting you add up negative numbers.
3-2-1 is the same as 3+[(-2)+(-1)]
@@DaLiJeIOvoImeZauzeto Nice, but then you simply have addition in the integers (and the question was about an elementary operation that is not associative). Interestingly this does not work with division when writing it as multiplication with the inverse.
triangle has 2 surfaces
It would be better not to call the identity element id. The letter i has such strong meaning that it could be potentially confusing.
Thanks for the suggestion. In general groups I call it "e" (or 0 in additive groups) but when working with maps, I will stick to "id".
Then maybe ID?
I use lowercase letters for maps (e.g., f, g, ...), so "id" is consistent with that. Besides, it's standard notation, at least in German texts.
But thanks for caring and commenting twice.
PS: I'm about 10 weeks ahead in recording the videos, so even if I wanted to, I couldn't make imminent changes.
Fair enough. At least you have a reason.
@@jamesfortune243 👍