yep this guh has even forgot what unitary matrix were. (representation theory )
but right now ai teaching me revisiting basic very most nicest abstract algebra book whihc is amazing that Idont have to restudy it but rather ai summarizes to me chapters so that my illiteracy (since i forgot some of basic literacy in abstract algebra during last 3 years which I worked to side projects studying etc) illiteracy issue gets fixed.
its that I have remnant intuition knowledge to craft some theorems, but when you need to do mental gymnastics of represesnting/redefining/approaching (mimicing limit behaviour etc) or any such alteration and any representation, then surely absolutely definitely exactly one needs to get reliterate in this topics and more of that i need to study to topos 2.d semester to get to the definite literacy in sheaf gluing topic.
so that I very liked the ai's suggested alternate hull design ideas (that without rebco) but some of them I couldnt even understand group theoretic definition there . so thereby to keep up follow up on ai's suggestions reading and to share my own ideas to develop to ai afterwards, i needed to pause a while, study to bascis to refresh knowledge in abstract algebra and then learn study some commutative algebra (which i hadnt had chance to study yet|) and topos knowledge revisiting and studying to later topics in topos then.
hmm so now i return to ai teacher now ai sharing brief summaries of chapters of one most famous introduction to abstract algebra book. (since guh forgotten even some of basic concepts there in abstrac talgebra, some knowledge remains but some does not since hadnt been doing abstract algebra awhile)
its utterly cool that this happens because that book is at least 500 pages or so. to restudy it just to revisit concepts would taken alot effort right? but now i can with much less effort with teacher ai telling concepts of chapters basically, can study it in such less effort version.
its unimaginable nice for me to ai teach the introductionary algebra book briefly so that I dont have to read 500 pages or so. nice! I liked this! yayyy! i dont have to study to 500 pages or so any!
hmm but in yet unstudied books I dont know If this method would work. for instance some group theory book or some algebra book I hadnt studied, I dont know whether this brief studying would work. might not work. but i think I would with chatting ai, would get to learn more of commutative algebra and topos sheaf gluing alike topics. hmm in topoi book, I had studied like 65% of the book itself, because I went to Lawvere's most famous one introduction to topos book awhile and then during this time i were also studying hmm that nlp tasks (along wiht studyingt asks of group theoretic books and representation theory that being before than topos) then hmm I paused a while whilst doing side project studying. but then so I also need to restudy to topios book. hmm for Lawvere's topoi book I actually only yet studied to some half of the book by then. so i would might need to study to review it also with ai. yep. then some new topic: commutative algebra which is indeed required some literacy of seems as. then i think i hadnt studied to topology domain (since we can take methods from there. even if we dont study with continous functions (indeed topology also includes methods to deifne a continuity concept for point topology concepts where there is discreteness but not default riemann contiunouty. so topology already has a methods there and there to have its concepts be defined for this commute graphs side i think, but for that, i also need to restudy to the topology books there and there. hmm and for the commute graph's curvature concepts, hmm differential geometry concept, that i studied to decades ago, when studied i created some static lib method for optimizing verlet integrator with taking method from different domain of differential geometry. but that were then. i also now need to revisit differential geometry book also since has been decades then. of course curvature concept I recall intuitonally, but surely i lost lots of knowledge there in that domain and need to definitely revisit. since ai defined new abstract concepts of curvature concept there in commute graph in hysteresis side of microloops side so there an dthere I think i would also revisit differential geometry side. so i need to study also to revisit the methods of set theoretic rigorous methods including borel sets etc.
but current task is indeed after not all of these books but initial some of them, I would also tackle the group theoretic reverse substitution task also myself alike ai did. since that seems most curious. what else other group definitions which we can define to then have similar convergence limit behaviours etc. means e.g. that means figure out some algebraic topology methods to accomplish the mechanism of H-> 0 in the commute graphs that does not require higher resolution commute graph sections (but sections might not be the correct term, i also forgot section term's meaning in category theory side stupid i ) but i just meant its very cruious to figure out some topological (algebraically commutative graph wise topologlical methods) to program commutators in a graph. (which is the poset) so that ai already understood what i meant by free groups definition just in a minute and then ai already generated such hull designs itself, but i am curious whether even more divergent methods might exist or not in that. so I wish to tackle tihs algebraic topology task myself to extend ai's mehtods there although I hadnt understood this ai's alternate hull design methods some algebra there yet since yep stupid guh has forgotten even saome basic abstract algebra knowledge there and there. but i dont believe i can generate more than what ai generated in its alternate topology methods in algebra mentality wise generated alternate commute graph programming methods to create hull design. and lets check. since I just got envied of ai's algebra skills, and right away at this point of this project, i started to not be able to keep up with ai's ideas, right at this point, i need to restudy/study. since this topology methods mindset in algebra side of commute graphs, is requires some definite knowlege in advance knowledge revisiting/relearning and learning missing knowledge yet from such books.
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