131–140 of 227 posts
What I understood after studying CS for over 10 years at a few universities regularly ranked highly at ACM ICPC is that math is unnecessarily obfuscated to most people. There is even an excellent book "Concrete Mathematics" from Stanford that tries to bring fun back to math instead of drying people with some formal stuff without explaining how people over the centuries got to that structure. I honestly believe math l…
It reads as a high level false-historical account of how math might have been developed, in its entirety, if it unfolded in the most direct and logical way from the human experiences we all share (guided by understanding of where mathematics has ended up in the modern age).
The false-historical expose is fantastic. The goal becomes less to express things as accurately and comprehensively as modernly possible—which you'll experience as you take on graduate level books or modern papers—but instead to demonstrate large-scope intuition for why whole fields evolved as they did and how they are all intermingled.
I hated math from elementary up until i learned Fourier theory. That was a pivotal moment in my education ; math went from wrote excercise to pure beauty in a single lecture. Now im trying to self learn lie algebra. I need to find out what prerequisites i need. A ton of math at this level is notation and terminology.
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For your analogy with Turing machines, do you have a better mathematical model of a computer? Nobody works directly with the TM model when they're doing theoretical CS anyway, they just describe the algorithm and everyone understands that if you really really wanted to you could work it down to a TM. The same is true of mathematics. It might be hard to get everything precise, but that's not the point of mathematics.…
And, of course, the point of the oracles is for proofs of non-existence.
What I understood after studying CS for over 10 years at a few universities regularly ranked highly at ACM ICPC is that math is unnecessarily obfuscated to most people. There is even an excellent book "Concrete Mathematics" from Stanford that tries to bring fun back to math instead of drying people with some formal stuff without explaining how people over the centuries got to that structure. I honestly believe math l…
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Actually I think this is fairly non-trivial. Sure you could make a "compiler" that compiles a JavaScript interpreter down to a Turing machine, but you would almost certainly not understand the generated states and transitions.
A more elegant model of computation is the lambda calculus. It's also very bare-bones, but it's easy to imagine writing real programs in it. Functional programming languages, at their core, are just lambda calculi with some syntactic sugar.
It's practical, but it's also a good foundational model. It's easy to reason about, due in part to the fact that it models familiar math (partial functions).
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Right, I understand your point. I said in an earlier post that an engineer is one who obtains an engineering degree from a certified university. I realize that it's pedantic and elitist, and there's definitely a part of me who thinks it's idiotic. Because it is. It's a title, who cares right? It doesn't lessen the worth of my degree. I've been trying to come up with valid reasons for why it's important for only peopl…
To say that a professor is the best person to learn from isn't 100% true. I had a linear algebra professor who simply lectured by reading straight from the book and then occasionally drew the diagrams. Alas, he apparently was a valuable research professor and had tenure, so there's little that could be done. In this case, the professor was hardly the best approach towards learning the subject. And as for experience,…
But the best professors I've had (and I've had a bunch) were the ones that really did combine both. (And frankly, I can forgive a lot of poor teaching in return for a "well, this is technically true, but no one really does it that way; they use this shortcut...."
As for a university education not providing immediately applicable industrial experience, well, that's kinda not the point of it. Sort of the difference between passing the FE exam and being a PE.
Awesome. Good for you. Keep at it. Keep a journal. Share with others what you learn. Learn from others when they share it. I'd add a few of books to your list: Graph Theory by W. T. Tufte: http://www.chapters.indigo.ca/en-ca/books/product/9780521794... On Numbers and Games by John H. Conway: http://www.amazon.com/On-Numbers-Games-John-Conway/dp/156881... And for good re-introduction to geometry and it's practical app…
The author for Graph Theory is W. T. Tutte, not Tufte, and much appreciate the link which helped clear up my initial confusion.
I hated math from elementary up until i learned Fourier theory. That was a pivotal moment in my education ; math went from wrote excercise to pure beauty in a single lecture. Now im trying to self learn lie algebra. I need to find out what prerequisites i need. A ton of math at this level is notation and terminology.
For me it was vector algebra. I was trying to write space games with real motion, and that was the key to efficient code.
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Can't stress this enough- in Canada (Ontario specifically) it is a serious fine for anyone caught using the term without being certified by a professional organization.
what about in the US? Is there such a fine?
Don't go near any dark alleys.