I have a similar story. The NSA hires entry level mathematicians for a pittance. They money they offered wasn't enough to raise a family, so I went with a job at a defense contractor that paid 50% more.
This "crating" thing you mention... I've never heard the term, but I've seen the effects. Some people settle down for a nice, steady, mind-numbing job in a SCIF because they know it's basically guaranteed employment for as long as the program lasts. You can spend your entire career doing the same thing for the same project, all while tidily walled off from the world because of security constraints. My peers and I joke that it's welfare for engineers.
How much latency did the network have? If latency was anything more than minimal, window scaling (disabled by default in XP) would allow the Ubuntu machine to better fill the connection.
How much packet loss, if any? Selective ACKs and Timestamps can affect recovery time after lost packets and transmission timeouts. XP does not use either option by default.
A quick look at/proc/sys/net/ipv4/tcp_congestion_control indicates that the default on the ubuntu machine where I'm typing this is the "cubic" flavor of TCP congestion control. I believe that XP uses the "New Reno" variety.
All of these can have an impact, and obviously TCP can be tuned on either OS. The discrepancy is probably due to TCP options that are relevant to his connection (and configurable in XP), but disabled by default.
Having recently graduated from the University of California, Irvine, with a degree in Mathematics I can tell you that it seems very unlikely to me that the exams are any easier at the college level. Many of the texts we used in partial differential equations, Fourier analysis, complex analysis, etc. dated back to the 1950s an onward. The exams I took were based on the material in the books, so if this is how exams were made 50 years ago, the only way they can be easier is if they are based on the "easier" concepts being covered. I find that unlikely.
Even the more modern textbooks were by no means simple to understand. The book I used for a course in cryptography and number theory was written in the 1990s, and the exams in that class were as hard as everything else.
The point of the encryption is transport layer security and privacy. The point of the certificate is TRUST. Having an encrypted session makes no difference if you are communicating with an impostor.
The prompt about unrecognized certs certainly SHOULD off-put the customer; it's likely to be that customer's only warning that the party on the other end of the connection isn't who it claims to be.
Re:What do you mean by unknown?
on
Happy Pi Day
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· Score: 1
This is true, but placing the branch cut along the x-axis works well with the real-valued definition of the natural logarithm as the area under the curve 1/t from 1 to x, where x > 0, i.e. since the natural logarithm is strictly undefined for negative real numbers.
Re:What do you mean by unknown?
on
Happy Pi Day
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· Score: 2, Informative
Not exactly. I see what you are trying to do, though.
The problem with trying to write ln(e^(pi*i)) = ln(-1) is that the natural logarithm function defined over the complex numbers has a branch cut along the negative x-axis. Anywhere along that line, ln is not a single-valued function. One may alternately say that ln is holomorphic for all complex numbers whose imaginary part is nonzero, or whose imaginary part is zero and real part is positive.
The only legitimate reason I can see NOT to include a proof for any theorem discussed on Wikipedia is if the author of the article knows of no proof he is free to cite (because of copyright or attrribution). Proofs aren't something "extra" you add to a mathematical discussion, they ARE the math. Once you are discussing math on a serious level--say, anything beyond the elementary higher math usually taught to Engineers--it is nonsensical to say you know anything about a theorem if you have not read and understood a proof of it, or a good discussion of why no proof exists. The fact that some theorems are easy to state (see Fermat's Last Theorem, Goldbach's Conjecture, etc.) yet profoundly difficult to prove if you have not really understood the underlying ideas has led many an amateur mathematician toward becoming a crackpot.
In my opinion, articles about mathematical theorems without proofs are an invitation to circle-squarers and other well-intentioned but misinformed souls to contribute nonsense to Wikipedia.
Most Americans go to college to "get a better job" or because they want to enter a certain field. They are, to coin a phrase, "goal oriented" -- school is a funnel into which they jump and once they get out the other end they can go back to living their lives, only now they will have been granted permission to enter into the career of their choice. So-called elite schools are desirable, not because they offer a better learning experience, but because they will "look better" to potential employers. I was certainly goal-oriented when I went to college, but probably not in the way you meant it here. I graduated High School in 1994 homeless and sleeping in a vacant lot out in the California desert. I made some bad choices and spent some years cleaning up the mess those choices left behind. I finally made it to college at age 27 and graduated in 4 years with a BS in Mathematics, cum laude. I spent the summer looking for work and I start my new career on Monday.
My goal was to get as far from where I started in life as I possibly could. A lot of my foreign born peers at the University seemed to relate with this.
I'll make it to grad school, but it'll take a while. I have a family now and have to support them while I pursue my education. Call me crazy, but I have a hunch that is also something some of my immigrant peers will be able to relate to. As for my compatriots: I suspect the reason that many of them don't seem metaphysically "hungry" enough to chase the hard goals is that they have never really experienced being the usual kind of hungry.
Why is it a stretch to prove the irrationality of sqrt(2)? This is trivial undergrad math stuff. sqrt(2) is a root of the polynomial equation x^2 - 2 = 0. By the rational roots theorem, if p/q is a root of the polynomial equation, then q divides 1 and p divides 2. Thus the only possible choices are +- 1 and +- 2. Neither of these is a solution so sqrt must not be rational.
I would not want to be asked to prove the rational roots theorem on an interview, but it's not impossible to work out from scratch just by thinking about it.
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I have a similar story. The NSA hires entry level mathematicians for a pittance. They money they offered wasn't enough to raise a family, so I went with a job at a defense contractor that paid 50% more.
This "crating" thing you mention... I've never heard the term, but I've seen the effects. Some people settle down for a nice, steady, mind-numbing job in a SCIF because they know it's basically guaranteed employment for as long as the program lasts. You can spend your entire career doing the same thing for the same project, all while tidily walled off from the world because of security constraints. My peers and I joke that it's welfare for engineers.
This article is idiotic.
How much latency did the network have? If latency was anything more than minimal, window scaling (disabled by default in XP) would allow the Ubuntu machine to better fill the connection.
How much packet loss, if any? Selective ACKs and Timestamps can affect recovery time after lost packets and transmission timeouts. XP does not use either option by default.
A quick look at /proc/sys/net/ipv4/tcp_congestion_control indicates that the default on the ubuntu machine where I'm typing this is the "cubic" flavor of TCP congestion control. I believe that XP uses the "New Reno" variety.
All of these can have an impact, and obviously TCP can be tuned on either OS. The discrepancy is probably due to TCP options that are relevant to his connection (and configurable in XP), but disabled by default.
Having recently graduated from the University of California, Irvine, with a degree in Mathematics I can tell you that it seems very unlikely to me that the exams are any easier at the college level. Many of the texts we used in partial differential equations, Fourier analysis, complex analysis, etc. dated back to the 1950s an onward. The exams I took were based on the material in the books, so if this is how exams were made 50 years ago, the only way they can be easier is if they are based on the "easier" concepts being covered. I find that unlikely.
Even the more modern textbooks were by no means simple to understand. The book I used for a course in cryptography and number theory was written in the 1990s, and the exams in that class were as hard as everything else.
I think you may be a little mixed up.
The point of the encryption is transport layer security and privacy. The point of the certificate is TRUST. Having an encrypted session makes no difference if you are communicating with an impostor.
The prompt about unrecognized certs certainly SHOULD off-put the customer; it's likely to be that customer's only warning that the party on the other end of the connection isn't who it claims to be.
This is true, but placing the branch cut along the x-axis works well with the real-valued definition of the natural logarithm as the area under the curve 1/t from 1 to x, where x > 0, i.e. since the natural logarithm is strictly undefined for negative real numbers.
Not exactly. I see what you are trying to do, though.
The problem with trying to write ln(e^(pi*i)) = ln(-1) is that the natural logarithm function defined over the complex numbers has a branch cut along the negative x-axis. Anywhere along that line, ln is not a single-valued function. One may alternately say that ln is holomorphic for all complex numbers whose imaginary part is nonzero, or whose imaginary part is zero and real part is positive.
This is why ln(x) is undefined for all x 0.
The only legitimate reason I can see NOT to include a proof for any theorem discussed on Wikipedia is if the author of the article knows of no proof he is free to cite (because of copyright or attrribution). Proofs aren't something "extra" you add to a mathematical discussion, they ARE the math. Once you are discussing math on a serious level--say, anything beyond the elementary higher math usually taught to Engineers--it is nonsensical to say you know anything about a theorem if you have not read and understood a proof of it, or a good discussion of why no proof exists. The fact that some theorems are easy to state (see Fermat's Last Theorem, Goldbach's Conjecture, etc.) yet profoundly difficult to prove if you have not really understood the underlying ideas has led many an amateur mathematician toward becoming a crackpot.
In my opinion, articles about mathematical theorems without proofs are an invitation to circle-squarers and other well-intentioned but misinformed souls to contribute nonsense to Wikipedia.
My goal was to get as far from where I started in life as I possibly could. A lot of my foreign born peers at the University seemed to relate with this.
I'll make it to grad school, but it'll take a while. I have a family now and have to support them while I pursue my education. Call me crazy, but I have a hunch that is also something some of my immigrant peers will be able to relate to. As for my compatriots: I suspect the reason that many of them don't seem metaphysically "hungry" enough to chase the hard goals is that they have never really experienced being the usual kind of hungry.
Why is it a stretch to prove the irrationality of sqrt(2)? This is trivial undergrad math stuff. sqrt(2) is a root of the polynomial equation x^2 - 2 = 0. By the rational roots theorem, if p/q is a root of the polynomial equation, then q divides 1 and p divides 2. Thus the only possible choices are +- 1 and +- 2. Neither of these is a solution so sqrt must not be rational.
I would not want to be asked to prove the rational roots theorem on an interview, but it's not impossible to work out from scratch just by thinking about it.