Recent content by Markjdb

Hi everyone, For integrable f,g:\left[a,b\right]\rightarrow\mathbb{R} with f(x)\leq g(x) for all x\in\left[a,b\right], it's a basic property of the riemann integral that \[\int_a^b f(x)\,dx \leq \int_a^b g(x)\,dx\] My question is whether the strict version of this inequality holds...

Hm, I suppose it really depends on how you define 'prepared'...I didn't do any prior reading before taking the course; it's hard to say how much it would've helped in retrospect. For linear algebra, pretty much everything in the text that wasn't covered in 146 is covered, as well as some...

It depends a lot on the profs, but I just finished math 245/7/9 this term, and linear algebra 2 was by far the hardest of any of the advanced courses. There was a certain amount of material covered that wasn't in the textbook, and a huge amount of material covered overall.

Let p be a prime number. Let Zp denote the field of integers modulo p. Determine the number of points (x, y) with x, y in Zp such that y^2 = x^3 + x^2. I just don't really have any idea how to approach this; the last problem was to find all rational points on the above curve, which I did...

I came across this problem today and haven't been able to figure it out... Give an example of a vector space V which isomorphic to a proper subspace W, i.e. V != W. It seems to me that V can't have a finite basis, but can't think of any examples regardless...any thoughts?

Homework Statement Find the integral from 0 to pi/2 of sin(x)dx/(cos(x)+sin(x)). The Attempt at a Solution You can easily make it into the integral of tan(x)dx/(1+tan(x)), but the substitution u=tanx can't work because tan(pi/2) is undefined. Any ideas for a good substitution?

Homework Statement Let f be positive and bounded over [a,b]. If f^2 is integrable over [a,b], then show that f is as well. The Attempt at a Solution I'm just trying to use the fact that the upper and lower sums of f^2 over a partition P are arbitrarily close, and then somehow find an...

Wow...quite impressive...

This one I remember after Vladimir Putin was on Larry King live: Larry King: Let's get to the part that may not have been enjoyable. What can -- what happened? You tell me. What happened with the submarine? Vladimir Putin: It sunk. He has a bunch of other good ones, but they're funnier...

I work full time as a butcher during the summer at the St Lawrence Market in Toronto, which basically means being there at 6 am (it takes me an hour to get there), and working till about 6 - 7 pm, 5 days a week. And sometimes 5 and a half. And summer's coming. Although the pay isn't half...

Stay away from Shostakovich :biggrin: (Although I personally love his music)

I find this to be very true as well as an effective way to get high marks: listen in class and question all the underlying ideas of the lesson. All the people in my science and math classes blindly take notes and copy examples, as a result, miss what the teacher is explaining. Although the notes...

Thanks to all who responded to my post. I...I get it now! :smile:

I never meant to say that it's better to be self-taught than to have a teacher. I'm just trying to emphasize that it is an option, and that having a teacher is not a prerequisite to becoming a good musician, and nor does it ensure that you will.

In my experience as a completely self-taught double bassist, a music teacher isn't necessary if you are self-motivated and have a goal. I play for enjoyment because I don't really want to study music at a university level, I've found it very important to listen to music that includes your...