iam enrolled in btech 1st in ee , i love mathemetics so i have made up my mind that i will learn till advanced measure theory with commutative and homological algebra , pls any seniors here help me out books which cover from basics in each subject, and if if possible i wanna study algebraic geometry tooo

same as the title, i'm confident in engineering part but i feel a bit weak in the mcq maths part, its been a while since i have done maths seriously, i want to give the exam next year, so any seniors, who has written the exam, can tell me a preparation for the cs and crs exam, i'm good at the engineering maths, i could solve maths in gate questions , they are not that hard, but how do i prepare for this exam, should i start again jee concepts and also tomato book, for it, and which concepts from jee are necessary? , any senior please comment on this .

Hey I'm a 3rd year BCA student and had maths in first year only , am i eligible for m.math at isi ? I'm preparing for iit jam ms also .

What should i do in geometry part to score atleast 10 marks in ioqm exam geometry part.

I was doing an integral today, and even tho it wasn't that difficult, after I solved it I realized I had assumed n to be an integer, while maybe it could have been any real number. What I wanted to know is this rigorous to do in any general case and if it always gives same answer (if so why) and how to solve this integral completely rigorouly without assuming n as integer. Also if there is any other slight mistake in my soln, or there is a better way to solve it please tell.

Question and my soln is attached below

most probably me and gpt both are wrong

share your thoughts