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Mathematics I Use
ce with real-world data sets and problems. Of course, I do not do all of this every day, but I have done all of it at one time or another and most of it regularly. Probably a lot more is based on observation, experience and heuristics than should be
programming  maths 
4 days ago by hashanp
All the Mathematics You Missed: But Need to Know for Graduate School: Thomas A. Garrity: 9780521797078: Books
Depending on what graduate school you go to (of course) students may or may not know such-and-such about field X but know a lot about field Y. For example, a student who does applied mathematics may not necessarily know a lot about topology. Instead of going over to Munkres, one need only skim the few pages that this book has on it to get the general idea.

That being said, this book is not (or, at least, should not be considered) the be-all-end-all of any topic. This is more like a chocolate sampling pack: it's a little bit of a lot of things. I'm glad, for example, that they included something about the Zariski topology, but I'm upset that they never actually calculate anything substantial in the parts about multivariable calculus. In particular, one of the questions asks the reader to "interpret" what the Jacobian means in such-and-such a case, but little is said in the chapter about such a thing.

I've read this book in the following way: skim the parts I knew well, read the parts I didn't know well, and write down topics that came up for the parts I didn't know well. Afterwards (using, in fact, the suggested reading that is conveniently at the end of each chapter) I would read in greater detail.
books  maths 
4 days ago by hashanp
What's the length of the shortest bit sequence that's never been sent over the internet? • Sean Cassidy
Sean Cassidy:
<p>A friend of mine posed this brain teaser to me recently: "What's the length of shortest bit sequence that's never been sent over the Internet?"

We can never know for sure because we don't have a comprehensive list of all the data.

But what can we say probabilistically? Restating it like so: "At what value for X is there a 50% chance there's a sequence of X-bits in length that hasn't been transmitted yet?"

What does your intuition say? Obviously every 8-bit sequence has been sent, since there's only 256 values. By downloading this HTML page over TLS you've probably used up every 8-bit value. Has every 100 byte message been sent?

This is how my intuition went: it's probably less than 128 bits because UUIDs are 128 bits, and they're universally unique. It's probably greater than 48 bits because of how common collisions are at that end for hashes and CRCs, and the Internet has generated a lot of traffic.

How would we determine the right value?

I decided to model data as each bit sent is like flipping a coin. This isn't strictly true, of course, but with encryption becoming more prevalent, it's getting to be close.</p>

If you're at all into maths, it's fun just to pause and try this before you go to his solution.
Maths  internet  bit  sequence 
5 days ago by charlesarthur

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