446 reputation
38
bio website dfan.org/blog
location Boston, MA
age
visits member for 3 years
seen 1 hour ago

Game programmer and designer (PC and consoles) since 1991, in C at first and then C++. I also use Python seriously and other languages semi-seriously (currently doing some hobby stuff in Clojure). Emacs zealot.

Games include Ultima Underworld, System Shock, Terra Nova: Strike Force Centauri, Frequency, Amplitude, Eyetoy: Antigrav, Guitar Hero (plus 2), Rock Band (plus 2, Beatles, 3).


Apr
17
comment Is there any shorthand notation for linear interpolation?
pic also accepts a of the way between p and q, which I suppose demonstrates the lack of a common notation.
Apr
17
comment Is there any shorthand notation for linear interpolation?
@MJD Thanks. After a little searching, it looks like the pic notation is a<p,q> and metafont's is a[p,q], so they do have the same general form.
Apr
4
comment how to calculate this convolution:
That function looks a little funny. Is it possible that $u(t) - (t-T)$ is really $u(t) - u(t-T)$ and you copied it down incorrectly? I'm also a little surprised that the problem bothers to give two names $x(t)$ and $h(t)$ to the same function.
Apr
3
comment Solving $y'-y=2\cos 5t$ using the Laplace Transform
Note by the way that you can do the partial fractions part of this problem (which is most of it!) a lot easier by using the cover-up method. The time spent learning this method will have paid for itself by the time you've done two Laplace transform problems.
Apr
3
comment Solving $y'-y=2\cos 5t$ using the Laplace Transform
You can easily check your answer for $y(t)$ by just seeing whether the original differential equation holds for it.
Apr
1
comment Confusing rational numbers
I haven't checked your intermediate math, but perhaps you are expected to rationalize the denominator in your final answer?
Mar
30
comment Strategies for developing explicit formulas for nth term given recurrence relation?
The closest thing to a general method for solving recurrences is the use of generating functions, which will definitely work in this case. Searching for "generating functions recurrence" will turn up some material. If you want a textbook reference, try Concrete Mathematics by Graham, Knuth, and Patashnik, or An Introduction to the Analysis of Algorithms by Sedgewick and Flajolet.
Mar
28
comment Probability of getting no worms in your box
One quick check for whether your formula for exactly $n$ infested boxes is correct is that if you sum the probabilities for $n=0$ through $n=6$, you should get $1$, since that covers all the cases.
Mar
28
comment Probability of getting no worms in your box
The probability that exactly $n$ out of the $6$ boxes are infested is a more complicated problem, and you would have to use the formula for a binomial distribution.
Mar
28
comment Uniform Distribution Probability
Your reasoning for 1/6 seems sound to me.
Mar
23
comment Roulette with extraordinary strategy
Do you have any knowledge of probability theory already or are you solving this totally from first principles?
Mar
22
comment Limit question involving L'Hospitals rule
I agree with you!
Mar
11
comment Step by Step explanation of derivative of a matrix
Looks good to me. What you are saying is that the change in your matrix when you modify $x$ by $\Delta x$ is $\Delta x I$, which it is.
Mar
10
comment Prove that the cardinality of $\Bbb N$ is less than the cardinality of $\Bbb R$
$\mathbb N$ is countable.
Mar
9
comment Solving Augmented Matrices (3 systems) at once
OK, but that's not Gauss-Jordan elimination. I'll write about Gauss-Jordan elimination in an answer.
Mar
9
comment Solving Augmented Matrices (3 systems) at once
How would you solve the system if you only had to solve for $Ax = b_1$?
Mar
9
comment Find the diameter. Integrate
A couple of things I don't understand about the problem statement: 1) Your picture has the tank centered on the $x$-$y$ plane at $(0, k/2)$ rather than $(0, 0)$ as the formula would indicate. Is it really the latter? 2) You call it a "cylindrical tank" which would indicate to me that the height is constant, but from the formula the roof seems to be more of an inverted cone. Is that right?
Mar
7
comment Use Lagrange multipliers to find the maximum(s) and minimum(s)
@user106342 Yes, once you've found all the critical points, you need to plug them back into $f$ to see what their actual values are; no shortcuts there.
Mar
7
comment Use Lagrange multipliers to find the maximum(s) and minimum(s)
@Mathster Why doesn't $\lambda = 3$ work? $\lambda = 3$, $x = -2$, $y = \pm \sqrt{12}$ looks OK to me.
Mar
7
comment Use Lagrange multipliers to find the maximum(s) and minimum(s)
Don't forget that you have three constraints to find your three variables $x$, $y$, and $\lambda$: the two equations you got from equating partial derivatives, and the original constraint $x^2+y^2=16$.