Original Math Notes
All Seasons
Season 5
Episode 513: Trouble in Chinatown
Family of averaged 2-dimensional Levy walks
Scene 8:
                    CHARLIE
            (thoughtfully)
          We could apply frequency-domain
          processors.  Larry can help, he worked
          with the NSA on noise analysis...

Filtering a White Noise Sequence »

This Demonstration creates a white-noise sequence and then uses a low-pass filter to produce a red-noise sequence. The "filter cut-off" is the fractional point in [0, 1] on the spectral frequency axis to apply the filter, as measured from zero frequency. The rate of suppression of frequencies larger than the filter cut-off is given by the "filter roll-off" exponent n (1 to 4); larger values of n mean greater suppression of the higher frequencies. A new time sequence is generated with the "randomize" button. The amplitude spectrum of the time series is plotted simultaneously, with spectral values on a log scale, out to the Nyquist frequency.
Scene 9:
Where one computer shows the restaurant's plain password
request page, and another is filled with computer code, which
the FBI has started to decipher.

                    DON
          Amita, that's the restaurant's
          computer hard drive...
          
                    AMITA
          Multi-layer encryption...
          
                    DON
          Our techs could crack it -- but
          you're faster and I don't have a lot
          of time.

Strong RSA Cryptosystem »

The RSA cryptosystem was invented by R. Rivest, A. Shamir, and L. Adleman. This Demonstration 1) generates a large RSA modulus n (up to 700 decimal digits); 2) creates the corresponding public and private keys, e and d; 3) provides a simple, practical way to encrypt and decrypt messages in various UNICODE supported languages.
Scene 15:
                    CHARLIE (cont'd)
          Same in audiology.  We shrink sounds
          we don't want so the sound we do want
          becomes foreground.
          
                    LARRY
          We use filters to diminish or blur
          noise -- identifying each unwanted
          sound by its frequency, then
          discriminating against it.

Geometric Mean Filtering for Blurring »

The geometric mean filter is a member of a set of nonlinear filters that are used to remove Gaussian noise. It operates by replacing each pixel by the geometric mean of the values in its neighborhood.
Scene 34:
                    LARRY
            (intrigued)
          Or under the squares.
            (tries some keys)
          Like a dragon hiding in its lair.
          Seems Yoon had a thing for numbers 8
          and 9.
          
                    AMITA
          I've tried every number, and every
          combination of number.

Probabilities of Combinations »

After selecting the colors using the controls, imagine that one color is picked at random from each disk. The order of the combination of colors is not important; for example, red, blue, orange is considered the same combination as red, orange, blue.
 
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