Hearing Perturbation Theory

In numerical linear algebra, we create ways for a computer to solve a linear system of equations A\vec{x} = \vec{b}. In doing so, we analyze how efficiently and accurately we can find the solution \vec{x}.

Perturbation theory concerns how much error we incur in the solution \vec{x} when we perturb (spoil) the data A and \vec{b}. A classic statement tells us that the amount of error depends on the condition number of the matrix A.

I will define and prove the statement, and help you understand it by “hearing” it.

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Math in Cross-Stitch

This year, I took up cross-stitching to decorate my place. I picked a complex design for the heck of it, too. Shortly after I inserted three strands into the fabric, I realized that we could cast cross-stitch as an optimization problem (shortest path).

See, if your strands haphazardly jump from one block to another, you will suffer a shortage of strands. The key is to, whenever possible, move from one block to an adjacent one horizontally or vertically by 1 unit. If that is not possible, then move diagonally in the fewest units possible.

By following these procedures, we get x’s on the front and a neat array of l’s on the back. I even saved enough strands to create a full border.

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15 Keywords

As an officer of Central Austin Toastmasters, I use Meetup to advertise my club and welcome new guests. Meetup allows me to set 15 keywords that best describe my club. It also lets you (a Meetup member) set keywords that describe your interests. Meetup uses your keywords to recommend groups that would interest you.

My goal is to attract more Meetup members so that more will visit my Toastmasters club. Hence, I should select keywords that are not only relevant to my club, but will also likely coincide with your interests.

Which 15 keywords should I use to attract more members?

I wrote a simple program to help me decide on these keywords.

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p@55w0rd$: Part 2

Last time, we looked at how passwords work. To confirm your identity, companies salt your password, they hash the salted password, and they check your hash. (For brevity, I won’t mention salts anymore. Assume that salts are used.)

We left out 3 important questions.

1. Can a hacker find out our passwords from hashes?

Yes and no. We will see that a hash function that is designed well acts like a trapdoor. We can change passwords to hashes, but there is no way to change hashes back to passwords. However, the hacker can still make guesses at our passwords and check which ones result in the stolen hashes. We call this an attack. I will cover 2 ways to make an attack.

2. Can the hash function stop attacks?

Yes, a hash function that is designed well makes attacks difficult. I will explain what I mean by a good design.

3. What can we do to protect ourselves?

We can’t completely rely on the hash function to protect us. We have to be vigilant, too. I will show you how to create good passwords and keep your accounts safe.

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