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Author Archives: Ryan
A quick, cool result to distract you from finals
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
To Converge or Not to Converge – Hilbert Spaces Part 4/Banach Spaces 1
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
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Moving Around a Sphere – Hilbert Spaces Part 3
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
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Hilbert Spaces – Part 2
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
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Some Physics – Part 2
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
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Some Physics – Part 1
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
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Digression: Hilbert Spaces – Part 1
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
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