Thursday, May 31, 2007

The Summinator


The Summinator
Originally uploaded by USUDave
9 January 2007: Graph Theory
[Said in Deep Voice] The Summinator.
I left the other doodles in there just because I thought they were kinda cool. That, and I hope that whenever I look at "The Summinator" I get a brief reminder of the cyclic and transitive graphs.

Grid


Grid
Originally uploaded by USUDave
9 April 2007: Graph Theory
This is just a grid, but it's actually made out of the characters between 2551 and 256C in the character map (Times New Roman). See ╬║╝╔╚ ╗╦ ╣╩ . They just all happen to fit nicely when arranged properly.

Minimal Vertex Separator For A Complete Graph


Minimal Vertex Separator For A Complete Graph
Originally uploaded by USUDave

2 April 2007: Graph Theory.
I don't remember exactly how the relationship goes, but I remember how we, as a class, decided that this illustration represented the Minimal Vertex Separator For A Complete Graph

Dave


Dave
Originally uploaded by USUDave
19 March 2007: Graph Theory
Dave
This is an illustration of my professor. He was wearing black slacks, a blue shirt, and sandals with flaming socks that day. And these are the actual graphs that he was drawing on the board as well.

Monday, May 28, 2007

Bipartite Hand


Bipartite Hand
Originally uploaded by USUDave
10 March 2007:
First day of spring break, 2007. It was nice to take a few minutes to sit and doodle to relieve the stress of the semester thus far. There's a hand hidden in there.

SnowFlake Fractal


SnowFlake Fractal
Originally uploaded by USUDave
Spring 2007 Semester.
Something that I whipped up really quickly in photoshop.

Wednesday, May 23, 2007

Poisson Distribution


Poisson Distribution
Originally uploaded by USUDave.
Stats 3000: Sometime Fall 2006.
The poisson distribution is a distribution in Statistics, but poisson is actually french for "fish". These are my two fish. The big guy is an 8-10" Oscar, and the little guy is a 3-4" Green Terror.

The Poisson Distribution (quoted from my stats book itself here) is; "A random variable X distributed as a Poisson random variable with parameter λ, which is written X ~ P(λ) and has a probability mass function P(X=x) = (e^-λ * λ^x) / x! for x = 0,1,2,3.... The Poisson distribution is often useful to model the number of times that a certain event occurs per unit of time, distance, or volume, and it has a mean and variance both equal to the parameter λ."

Maiden Voyage of USS Linear Algebra

Linear Algebra: Sometime Fall 2006
Just a doodle of a Maine Lobster Boat that I did in Linear Algebra.

Galaxy


Galaxy
Originally uploaded by USUDave.
Stats 3000: 31 October 2006
I don't know what this is..... connect the dots gone wrong?

Old Main


Old Main
Originally uploaded by USUDave.
Linear Algebra: Sometime Fall 2006
This is Old Main, the first building on the Utah State Campus. The first parts of it were built in 1888.

Nash Island


Nash Island
Originally uploaded by USUDave.
Linear Algebra: Sometime Fall 2006
The Nash Island Light, off the coast of home in Maine.

Home Sweet Home


Home Sweet Home
Originally uploaded by USUDave.
Linear Algebra: Sometime Fall 2006
A sketch of my apartment, from memory, during linear algebra.

Binary Search Tree


Binary Search Tree
Originally uploaded by USUDave.
CS 5050: Advanced Algorithms
January 2007


We had to draw a Binary Search Tree of height=7. I thought "I Can't Fit That Onto A Piece of Paper Neatly.... I Need A Bigger Canvas....Hrm..."

I drew this on the sidewalk on campus, took digital photos of it, and then turned those photos for my homework. Dr. Yan Really liked it. :-)

More Photos


Root
Theorem: Let T be a (proper) binary tree with n nodes, and let h denote the height of T. Then T has the following properties:





Leaves
1. The number of external nodes in T is at least h+1 and at most 2^h .

2. The number of internal nodes in T is at leasat h and at most 2^h - 1.
Binary Tree Zoomed

3. The total number of nodes in T is at leasat 2h + 1 and at most 2^(h+1).

4. The height of T is at least log(n+1)-1 and at most (n-1)/2, that is, log(n+1)-1 < h <(n-1)/2.



Binary Tree
That Means that this binary tree has
  • 128 leaves
  • 127 Internal Nodes
  • 255 Total Nodes
Binary Search Tree
BST