To compute a group typically means finding a group that you already know that is isomorphic to the given group. In this case, the integers are a group under addition, and that group turns out to be isomorphic to the Fundamental Group of a circle
Math profs only regurgitate text book material while writing it on the blackboard. They present no insights that are not available in the text book. For instance they never give examples using real physical integers for functions or fields that would help explain abstract concepts. Their excuse for this abominable dereliction of duty. "If you need examples you don't belong here." LOL
Injective is dual to surjective synthesizes bijective or isomorphism -- duality! Being is dual to non-being creates becoming -- Plato. Thesis is dual to anti-thesis creates the converging thesis or synthesis -- the time independent Hegelian dialectic.
@@hyperduality2838 whilst i agree with duality, of course, mathematics is full of such a thing, but Hegel does not have any proof structure to his ontology (his model). also he made statements that were basically religious and non rational, some of his ''physics'' claims failed and generated the very worst ideologies in politics, marxism and fascism. Karl Popper's open society goes in details on hegel and how dangerous his ideas are.
@@Newtube_Channel they're asking what you mean because what you said didn't make any sense so they're confused. What instructors of AT don't write notes? Or of any math course? Do you just expect him to verbally speak the entire proof and not write anything?
Love the way he teaches, but can we just appreciate his persistence in saying "Gesundheit" with each cough without skipping a beat while teaching?
Really helpful lectures, thanks for uploading!
This is so helpful! Thank you so much for uploading.
Uf, that is a long proof. Excellent video :)
Could you please also upload chapter 3 and 4 of Allen Hatcher ? These are really helpful lectures. Thanks for uploading them.
@@kalanithalagoda6427 haha
Hatcher offers his book as a free download. Just go to his website.
@@robinbalean958 hes asking for albin to do lectures of those chapters, not for the chapters themeselves
54:00 Doesn't this require that Y is locally connected?
What does he say at 37:10 and at 37:13 ?
"Gesundheit", according to another comment, which is basically "bless you"
What does it mean to calculate a group?
To compute a group typically means finding a group that you already know that is isomorphic to the given group. In this case, the integers are a group under addition, and that group turns out to be isomorphic to the Fundamental Group of a circle
Filmed from an angle which makes it difficult to see the writing clearly.
Math profs only regurgitate text book material while writing it on the blackboard. They present no insights that are not available in the text book. For instance they never give examples using real physical integers for functions or fields that would help explain abstract concepts.
Their excuse for this abominable dereliction of duty. "If you need examples you don't belong here." LOL
Injective is dual to surjective synthesizes bijective or isomorphism -- duality!
Being is dual to non-being creates becoming -- Plato.
Thesis is dual to anti-thesis creates the converging thesis or synthesis -- the time independent Hegelian dialectic.
So true
Hegel was wrong and a pseudo intellectual.
@@gaulindidier5995 Perhaps|! Would you care to elaborate on your conjecture?
"Always two there are" -- Yoda.
@@gaulindidier5995 Homology is dual to co-homology -- Pierre Albin in a later lecture.
@@hyperduality2838 whilst i agree with duality, of course, mathematics is full of such a thing, but Hegel does not have any proof structure to his ontology (his model). also he made statements that were basically religious and non rational, some of his ''physics'' claims failed and generated the very worst ideologies in politics, marxism and fascism. Karl Popper's open society goes in details on hegel and how dangerous his ideas are.
I -like- hate the way instructors of AT insist on writing notes on the board as if it was a course in biology.
@DnB and Psy Production What do I mean?? Am I talking Chinese?
@@Newtube_Channel they're asking what you mean because what you said didn't make any sense so they're confused. What instructors of AT don't write notes? Or of any math course? Do you just expect him to verbally speak the entire proof and not write anything?
I don't see what's wrong with that?