Okay the reason I asked is because I don't know too much about academia outside of one publication and didn't know if you wanted these books just for the sake of learning (which is not a bad thing) or if you wanted to study purely for maximizing your new grad salary. If you're goal is the latter, I can give you insight of what the new grad quant market is looking like right now and clear the misconceptions you have (I had a similiar naive mindset for you when I was an undergrad so I want to help you avoid the rude awakening you're going to get after you graduate). First off, my advice will be in terms of the US quant job market, which I'll just generalize to the Europe quant job market (I doubt there are significant differences though).
1)
4) The reason I'm starting out in the first year is that I want to maximize my luck surface area to bag a seat in one of the top programs in the world.
This is a really good mindset - I wish I grinded harder in first year; it only gets harder the later you start. But I don't think the direction you're going in is right at all if your goal is maximizing your new grad salary
2)
(If you are not an Indian you won't understand how biased the whole market is for the IITians).
Trust me I know, but it's not just the Indian job market that's biased for IITians. At the quant firm I currently work in, all the indian quant researchers (even the interns) are from an IIT. At Princeton Mfin, if you look at their 2023 resume book, again all the indian students are pretty top in their IIT program with quant internships in India. So the honest truth is you're already starting at a pretty big disadvantage, so grinding early is good but just make sure the direction you're going in is right. For example....
I believe an employer will value an Imperial guy over any IITian.
Simply not really true (at least its not true if I replace 'Imperial' with a top 5 MFE program). I reiterate this many times but the weight of your undergrad experience FAR exceeds what a professional masters will do for you. Employers understand the bar to get into these professional masters are typically lower (Princeton, Columbia, CMU undergrad is alot harder to get into for an international student than their MFE programs are), and they understand that MFE students are generally not the students who can get a great quant job straight after undergrad (they want the reason for this to be because of visa issues not because you weren't good enough in undergrad).
In general, I think you're misconceptions are that you think everything will work out and you'll seemlessly land a good quant job if you do well on all the required math prereqs and get into Imperial, but this is really really really not the case. As someone who got a 4.0 in all the relevent math courses in a top 3 school in my country, and has a 4.0+ in a top 5 MFE program, I can safely tell you that recruiting for quant FT positions/internships at a top firm is NOT a cake walk: I won't even get an interview in many of the tier 1 hedge funds. Perfect GPAs and MFEs alone is just not sufficient; that's just the way it is.
Okay so now onto actual advice:
1) I'm not sure how it works in India but can you just transfer to a better more quantitative school lol. Truth is these "online courses", even those offered by top schools, are not a good subsitute. Even if the online course teaches you better than your university does, from the perspective of employers and universities, they don't count as much compared to if you did the course at your university. The reason is that people typically aren't hellbent on getting the highest possible score on an online course, but students care ALOT abt their university courses - some value it even more than their lives (our school had to install nets around)
2)
4) Also, I want to start doing internships in my 2nd year and if I don't offer something extra to the employer I will get rejected solely because I'm not from IIT.
This mindset is very very good. Yes you're at a disadvantage so you need to compete in other ways. Your edge is not going to be your GPA because the same GPA in an IIT will always mean more. Cram as many internships as possible in your undergrad. There are some schools that let their undergrads do 6 internships before they graduate and their students are generally very succesful. But it's not just about quantity of your internships - make sure you're progressively landing a better internship every term. Like maybe start off with a not so well known internship --> for your later internships try landing a spot in a reputable firm in India --> for your final internships try aiming for a reputable firm in the US. This is the most well-established way of getting into a quant firm from the people I know at least. Also your internships don't even have to be in quant, I'd actually suggest aiming for a FAANG: I seen so many people with previous FAANG experience get an interview at quant firms for even QR roles. Yeah this isn't going to be easy but internships should be your MAIN focus - honestly school and grades is important only to the extent of helping you land these internships. Getting your foot in the door is hard but all my friends tell me the hardest part is landing your first quant firm or FAANG, then it becomes much easier from there because you already 'established' yourself
3) I'm not sure if Putnam is offered in India but if you just get a few questions right, you will be head hunted by hedge funds. Getting 2 questions right in putnam is far far more impressive to me than just getting A+s in your undergrad math course. Caveat is putnam is pretty hard though but the value in scoring well in putnam in terms of landing a quant firm is just so high - I know someone who got contacted by HRT for getting several questions right on putnam
4) I really don't think there's much value in reading all these books early. School is honestly pretty easy because everything is solved already - they won't make you solve something that no one has solved before. Like even the hardest questions on our ODE and PDE tests was just to think of a clever transformation to get the equation in a nice form where we already know what the general solution will look like. Also things like real analysis aren't
particular useful imo - like sure it can teach you how to rigorously prove something but at least in my quant firm, you're never really required to prove something with that amount of rigour (there's more emphasis on thinking of clever heuristics). For the foundational courses, I think you should put alot of emphasis on understanding linear algebra really well (alot of stats is just linear algebra, like a regression is just a projection on the column space). The parts of calculus that will be used ALOT later on is taylor expansions, and gradients and hessians. however, in general I think you get more value from spending your effort on things outside of school like landing great internships (ofc your first internship will be dependent on ur school and grades but this will decay in importance as you get more internships), or doing well in putnam.
