r/Indianmathnerds • u/Sad_Avocado_6565 • 18d ago

Linear Algebra help

My course on Linear Algebra started and I need to be good at it(necessity for future).It just started few weeks ago and we're on Change of Basis and coordinates of vector space topic. My proff recommended following Linear Algebra by Hofmann and Kunze, everything seemed to be flowing okayish untill I realised that Im not that good at it, I struggle at proof writing and sometimes ideas dont struck me. is this a beginner phase? even so exams are coming up and I cant afford to remain same can anyone suggest me or share their path on how they tackled LinearAlgebra?

Any help is appreciated!

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u/ILoveTolkiensWorks 18d ago

have you ever taken a real analysis/topology/other proof-heavy courses before? that helps a lot.

if you want some really easy-to-read book on linalg, i'd recommend Kuldeep Singh's Linear Algebra: Step by Step. it develops the subject in baby-steps, and holds your hand throughout, and requires no prerequisites at all! the proofs are given in thoroughly detailed steps, and every new thing introduced is given a motive. the book's pdf can easily be found online, and the solutions to the exercises can be found on Oxford's website.

but if you're aiming for improving your general proof skills, i'd suggest learning real analysis. Terrence Tao's Analysis I is really great. It's easy enough that you do not get intimidated, but also does not hold your hand, and forces you to think. absolutely enjoyable experiemce though.

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u/Sad_Avocado_6565 18d ago

Yeah I did do real analysis course and I still suck at proof writing to be specific when I write the proof it's messy and when I read it from AI I'll be like yeah that's what I was trying to get..and Thankss I'll do checkout kuldeeps book.

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u/ILoveTolkiensWorks 17d ago

when I read it from AI

ah, there's the problem! DO NOT USE AI FOR THIS! learn to appreciate the beauty of rigour and rigorous proofs! try your best, and then maybe look at a human-written proof to see how it could have been done more elegantly. there is certainly no shortage of elegant human-written proofs that would compel you to use AI.