Author Archives: Ryan

About Ryan

I'm a software developer at Hudl where I work on awesome software. Before that, I was a grad student in mathematics, interested in probability theory as well as analysis, more on the side of functional analysis and less on the side of PDEs. Apart from that I'm pretty lame. Though I do enjoy watching football, playing golf, and playing the trumpet.

If you are like me, you’ve probably got lots to do for final exams and things of the like as the semester (trimester, quarter, whatever your school uses) comes to a close. In an effort to take a bit of … Continue reading →

Posted on 12/11/2012 by Ryan | 1 Comment

To Converge or Not to Converge – Hilbert Spaces Part 4/Banach Spaces 1

Posted on 11/04/2012 by Ryan

Last time I introduced the notion of the weak topology on a Banach space . I defined the topology in terms of net convergence, but remarked that this was equivalent to the weak topology generated by . The purpose of … Continue reading →

Posted in Analysis | Leave a comment

Moving Around a Sphere – Hilbert Spaces Part 3

Posted on 10/27/2012 by Ryan

Well, it’s been a long time since I’ve written a post, but I have a bit of time tonight and I really don’t feel like doing homework tonight, so let’s talk about some mathematics! Last time I wrote, I promised … Continue reading →

Posted in Analysis, Set theory | Leave a comment

Hilbert Spaces – Part 2

Posted on 05/28/2012 by Ryan

Recall that in the finite dimensional world, two vector spaces are isometrically isomorphic if and only if they have the same dimension. In the last post, I mentioned that, by using the appropriate definition of a basis and dimension, one … Continue reading →

Posted in Analysis, Linear Algebra | 1 Comment

Some Physics – Part 2

Posted on 04/16/2012 by Ryan

Imagine a drop of water splashing into a small bowl of water. When the drop hits, it will create water waves that will propagate through the bowl. If we place a screen with two small openings in the path of … Continue reading →

Posted in Physics | 2 Comments

Some Physics – Part 1

Posted on 04/13/2012 by Ryan

And now for something completely different! I’ve decided to write another series of posts in conjunction with my discussion of Hilbert spaces. As many of you know, I did quite a bit of undergraduate work in physics, and I thought … Continue reading →

Posted in Physics | Leave a comment

Digression: Hilbert Spaces – Part 1

Posted on 03/15/2012 by Ryan

Hello all, I hope your semesters are going well! I am on spring break this week, so I’ve got a bit of time, and I figured instead of getting a head start on my homework for next week, I’d write … Continue reading →

Posted in Analysis, Linear Algebra | 1 Comment

The Riesz Representation Theorem – Part 2

Posted on 02/28/2012 by Ryan

So I should explain: this is one of those weird weeks where I have actually finished all my homework for the week two days early, so I actually have some time to write on the blog! So, let’s talk about … Continue reading →

Posted in Analysis, Linear Algebra | 3 Comments

The Riesz Representation Theorem – Part 1

Posted on 02/27/2012 by Ryan

Hello everyone! I realize it’s been far too long since I’ve last posted, and I decided I don’t really want to write about Radon-Nikodym anymore. Maybe someday if I get requests I’ll write a couple more posts in that series, … Continue reading →

Posted in Analysis, Linear Algebra | 3 Comments

Differentiation of Measures – The Radon-Nikodym Theorem Part 2

Posted on 11/27/2011 by Ryan

Hello everyone! My apologies for the long delay between posts in this series, these last few weeks have been a bit crazy with the NSF fellowship application due as well as an exam and a boatload of homework. Anyways, I’m … Continue reading →

Posted in Analysis | 3 Comments