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Poll: With which topics in Mathematics should the average high school senior be comfortable?

I have a PhD in Mathematics and am a Tenured Faculty (10yrs) at a 4-year public University. To me there's really two different answers here. If someone isn't going to college, I'd say a basic understanding of Algebra would be fine. For those going to College, I'd say a strong background in...
- Unitary
- Post #33
- Oct 29, 2016
- Forum: OT Discussion Club
U
CostCo USA dropping Amex for Citigroup VISA

Currently only Executive members get the Costco 2% back. This page seems to imply that everyone will now get 2% back at Costco. Wonder if that's the case.
- Unitary
- Post #383
- Mar 24, 2016
- Forum: OT Discussion Club
U
Stumped on math problem

I know I'm a bit late, but I thought I'd share another possible solution. Again using properties of mod, you first know that 7^2=49 is congruent to -1 (mod 10). In other words 7^2==-1 (mod 10) Take 16 powers of each side, (7^2)^16==(-1)^16 (mod 10), or (7^32)==1 (mod 10) Multiply each...
- Unitary
- Post #13
- May 20, 2014
- Forum: OT Discussion Club
U
Turn on, tune in, drop out. Falling objects question.

I don't think that they will land at the same time as the masses don't cancel out when you include wind resistance. True, when looking at the standard gravitational motion equation F=ma (without wind resistance) the masses do cancel out, it no longer does when you include the wind resistance...
- Unitary
- Post #39
- Oct 30, 2013
- Forum: OT Discussion Club
U
the event horizon of a black hole should be colorful

For a static black hole a photon would have a circular orbit at radius 3Gm (or 50% larger than the Schwarzshild radius) Unfortunately, no photons are trapped by this orbit as it is unstable. In other words, any perturbation from this orbit causes the photon to fall into the black hole or fly...
- Unitary
- Post #13
- Oct 25, 2013
- Forum: Ask a Technical Professional
U
[TOM'S] AMD inter-generational CPU shootout

This was certainly an interesting article, but I don't understand their constant Athlon II x4 bashing. Sure, it was the slowest processor of the bunch, but it is a budget cpu that came out four years ago. I'd instead offer a different conclusion, one that highlights that paired with a modern...
- Unitary
- Post #221
- Aug 22, 2013
- Forum: CPUs and Overclocking
U
f(a + b) = f(a) + f(b)

But that top limit doesn't exist.
- Unitary
- Post #29
- Jan 12, 2012
- Forum: OT Discussion Club
U
Non-linear springs, specifically "constant" force springs

If the spring gave the same force, no matter its displacement from equilibrium, it would be a linear spring as its force would be F_s=C. As for the physicality of a spring with these characteristics I think it would be hard to really call it a "spring".
- Unitary
- Post #2
- Oct 22, 2011
- Forum: Ask a Technical Professional
U
Anyone go to community college & transfer to a 4 year university?

I transferred from a CC to a Univ of California. The CC and UC had a transfer agreement where if I took certain classes and maintained a 3.0 gpa, I had automatic acceptance to the UC. The best part was that when I transferred all my lower division requirements were automatically satisfied and...
- Unitary
- Post #27
- May 20, 2011
- Forum: OT Discussion Club
U
What degree do you have?

General area is partial differential equations. More specifically I looked at the existence of shock wave solutions in relativistic gas dynamics.
- Unitary
- Post #62
- May 6, 2011
- Forum: OT Discussion Club
U
What degree do you have?

Ph.D. Mathematics, 10 years total, 5 years for B.S., 5 more for graduate work.
- Unitary
- Post #57
- May 6, 2011
- Forum: OT Discussion Club
U
for you math geniuses out there...

Please be more specific about your question. For example, where does "i=3" come into play in your sum?
- Unitary
- Post #10
- Sep 8, 2009
- Forum: OT Discussion Club
U
Linear Algebra

Linear Algebra is essentially the backbone for most of advanced mathematics. Unfortunately, most undergraduate classes focus too much on matrices for computation and vector space examples for this to be seen. It's too bad because there are many accessible and interesting examples of linear...
- Unitary
- Post #29
- Sep 3, 2009
- Forum: OT Discussion Club
U
Inverse function

Unfortunately, what you want to do is impossible. The function doesn't have an inverse on the domain x>0 because it is not one to one. Moreover, I think that even if you restrict the domain to where it does have an inverse (say x>1), it cannot be written in an elementary form (using roots logs...
- Unitary
- Post #2
- Jul 19, 2009
- Forum: OT Discussion Club
U
Math help - eigenvalues

Too bad that you believe this... couldn't be farther from the truth.
- Unitary
- Post #20
- Apr 12, 2009
- Forum: OT Discussion Club
U
Math help - eigenvalues

This is a pretty straight foward problem from PDE's: (Heat equation with one insulated end and another held at zero?) Using the hint, if L=0 then the ODE becomes y''=0. The general solution is y(x)=a+bx. Now y'(x)=b, so the condition y'(x)=0 gives b=0. Similarly, if y(P/2)=0, then we get...
- Unitary
- Post #16
- Apr 12, 2009
- Forum: OT Discussion Club
U
Gonna go to San Diego Wild Animal park this weekend...

It's been a while since I've been there, but I think it's a California Condor. And yes they were HUGE!
- Unitary
- Post #18
- Mar 19, 2009
- Forum: OT Discussion Club
U
calculus help

Assuming logb(x) means log base b we get, f(bx)=logb(bx) =logb(b)+logb(x) (Product to Sum for Logs) =1+logb(x) =1+f(x)
- Unitary
- Post #7
- Mar 18, 2009
- Forum: OT Discussion Club
U
Who wants to explain linear algebra to me?

Okay this turns out to be pretty straight forward with the right notation. First, A, B, C and D are vectors and we will denote the i th component as A_i ect. (Typically we use both up and down indicees, but here it won't be needed.) Using this notation, the dot product between A and B...
- Unitary
- Post #19
- Sep 29, 2008
- Forum: OT Discussion Club
U
Who is graduating this year?

Congratulations to everyone graduating! I'm finishing up too, 6/14, Ph.D. Mathematics.
- Unitary
- Post #31
- May 1, 2007
- Forum: OT Discussion Club
U
Why does gravity propagate at the speed of light?

Certainly, from the (linearlized) GR point of view gravity waves should propagate at the speed of light like Biftheunderstudy mentioned. Does anyone know if this has this been verified experimentally?
- Unitary
- Post #10
- Apr 29, 2007
- Forum: Ask a Technical Professional
U
OK blood pressure people....

It would probably be best to talk to a doctor about it just to be safe. Personally, I'm in my late 20's and my BP is regularly be between 135/95 and 145/95 whenever it is taken. When I spoke with my doctor, he suggested that I wear a monitor that took my BP every 15 minutes for 24 hours to see...
- Unitary
- Post #9
- Apr 26, 2007
- Forum: OT Discussion Club
U
So you keep fliping a coin. 50/50 chances

It certainly can! It's another time our intuition fails when we deal with infinite things. Take, for example, the Riemann integral. We estimate the area under the curve by approximating it by rectangles. In the limit, the width of the rectangles goes to zero. So the area under the curve...
- Unitary
- Post #62
- Apr 7, 2007
- Forum: Ask a Technical Professional
U
So you keep fliping a coin. 50/50 chances

Assuming idealized coin flips, the correct language would be to say that the coin flips will "almost surely" not repeat forever. The outcomes that repeat forever form a set of measure zero within our probablility space, meaning it's not likely at all (probability zero), but sill possible for...
- Unitary
- Post #59
- Apr 7, 2007
- Forum: Ask a Technical Professional
U
How much did you make straight out of college?

University Assistant Professor and it pays in the mid 50's. It seems low for someone with a Ph.D., but academics nearly always pays crap (as compared to similarly qualified industry jobs) and it's only 9 month's of work each year. One big plus, however, is the health/retirement benefits...
- Unitary
- Post #36
- Apr 5, 2007
- Forum: OT Discussion Club
U
Math wiz! Partial DE help

I'm certainly no expert at solving problems like this, but here are my first thoughts: I would try to use separation of variables, i.e. assume u(x,t)=u(x)v(t). Plugging this into the heat equation, you will get two ODE's, one first order and one second order. I would try to solve these and...
- Unitary
- Post #4
- Mar 28, 2007
- Forum: OT Discussion Club
U
Math wiz! Partial DE help

It may be a typo, but ut=uxx is the heat equation. Did you mean utt=uxx?
- Unitary
- Post #2
- Mar 28, 2007
- Forum: OT Discussion Club
U
Honda: Odometers too fast, Settle Lawsuit

My wife and I purchased a 2006 Toyota Camry and the speedometer reads exactly 5mph too fast at any speed above 40mph. (It's slightly less under 40.) One would think this would make the odometer read incorrectly, but it's spot on with the actual speed. The dealer even changed out the...
- Unitary
- Post #50
- Feb 19, 2007
- Forum: OT Discussion Club
U
help evaluating integral........

Okay, I figured it out. It's a little tricky because you use both integration by parts and substitution. Since I don't want to deal with constants, I'll drop the 4/9 in my calculations. Start by doing integration by parts with u=(1+x^(-2/3))^(1/2) and dv=dx. Then...
- Unitary
- Post #18
- Jan 10, 2007
- Forum: OT Discussion Club
U
Resume (CV) question: Education-related

I'm assuming that you attended the same college both times right? Then I think it's clear from the dates that you took some time off and have returned to continue your studies. If you feel like it would be benificial to list some of the classes you took as a Mathematics major you should do...
- Unitary
- Post #4
- Dec 28, 2006
- Forum: OT Discussion Club
U
Resume (CV) question: Education-related

I think it would be okay to put down both. Also, having an estimated graduation date for the degree wouldn't hurt too. Putting all these together, maybe something like this would work: 1998-2001, 2006-Current, University name, Town, State Bachelor of Arts in Liberal Studies, June 2007...
- Unitary
- Post #2
- Dec 28, 2006
- Forum: OT Discussion Club
U
linearly independent/linearly dependent sets

You can do it both ways. Put your vectors into the columns or rows of a matrix then row reduce. If you end up with less "leading ones" than vectors, your set is linearly dependent. Of course there is a more indepth answer explaning why this works, but this is the quick explanation. This...
- Unitary
- Post #9
- Dec 17, 2006
- Forum: Ask a Technical Professional
U
Which class should I take.

I agree with the other poster and go for Numerical Analysis if you are interested in an applied graduate math degree. After that I would choose Complex analysis. By the way, why Financial Mathematics?
- Unitary
- Post #9
- Dec 17, 2006
- Forum: OT Discussion Club
U
Which colleges have you guys been accepted to?

I too applied to Rose-Hulman, but for a faculty position in the mathematics department. :beer: at the outside chance that you become my student!
- Unitary
- Post #25
- Dec 13, 2006
- Forum: OT Discussion Club
U
Easy elementary school level math problem.

It seems like you are leaving out a few crucial details, but I'll give you my thoughts: You have an iterative integral operator, so my first inclination was to somehow use the contraction mapping theorem to get existence of a limit. I am guessing these are probablilities so the kernal...
- Unitary
- Post #9
- Dec 7, 2006
- Forum: OT Discussion Club

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