In high school and even the first year of university I was pretty much a natural at math. I'd been doing algebra and trigonometry since I was 10, calculus since I was 13 and started on differential equations at 15.
Not that this made me any kind of child prodigy mind you but it was a fairly isolating experience because my first 18 years took places in isolated towns with <15,000 people so I just didn't come across other people like me or with similar interests. But I digress...
The second year of university maths bored me senseless and it sucked all the fun out of maths for me. Three hour proofs, numerical methods (in particular) and so on. So I stopped doing it and just did CS instead (originally I'd been intending some kind of double major equivalent).
Having not used calculus (for example) for years I can still remember how to derive/integrate, etc. So I retain a decent part of what I knew (or so it seems). But the one area I suffer in, largely because I never got that far, is in deciphering academic papers. This applies to CS too, which is where it's a pain.
I like dealing with actual code rather than abstract ideas put in text (and the vaguest of algorithms that you can't just take an implement, or at least I can't).
So my situation isn't identical to yours but I really would like to know how I could improve my maths and CS in this area.
There's an incredibly common roadblock in math education when you make the jump from mechanical maths to creative maths. On one side, math makes sense as a set of powerful rules which help to guide you to understand and analyze the world. On the other side, math is more like a penpal friend while you're living in a foreign country. It offers advice, but largely you're on your own in a confusing land.
Academic papers are written from the far side of that roadblock. They're often best considered anecdotal pointers to how to survive abroad rather than comprehensive guides like textbooks (or review papers) offer. Reading them is thus both an exercise in deciphering something distant from your comfort zone and learning to apply its vague knowledge to your own situation.
In order to understand academic papers then, you've kind of got to become a traveler yourself. At that point you appreciate the vague note passing because even though it's difficult, there's a real opportunity there to see something few ever have before.
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So practically, academic papers are never easy to decipher unless you're basically part of the same communities as the authors (or they are really dedicated and skillful communicators who have an uncommonly deep understanding of the topics they're writing about). If you're doing work that cannot be solved by what exists and is common knowledge today, however, they're your best bet at finding a guide and no matter how difficult they are you want to read them through.
I shudder to think how many hours I spent poring over textbooks and lecture notes just so I could have the "AHA" moment that comes along with dealing with abstract entities.
In high school and even the first year of university I was pretty much a natural at math. I'd been doing algebra and trigonometry since I was 10, calculus since I was 13 and started on differential equations at 15.
Not that this made me any kind of child prodigy mind you but it was a fairly isolating experience because my first 18 years took places in isolated towns with <15,000 people so I just didn't come across other people like me or with similar interests. But I digress...
The second year of university maths bored me senseless and it sucked all the fun out of maths for me. Three hour proofs, numerical methods (in particular) and so on. So I stopped doing it and just did CS instead (originally I'd been intending some kind of double major equivalent).
Having not used calculus (for example) for years I can still remember how to derive/integrate, etc. So I retain a decent part of what I knew (or so it seems). But the one area I suffer in, largely because I never got that far, is in deciphering academic papers. This applies to CS too, which is where it's a pain.
I like dealing with actual code rather than abstract ideas put in text (and the vaguest of algorithms that you can't just take an implement, or at least I can't).
So my situation isn't identical to yours but I really would like to know how I could improve my maths and CS in this area.