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Upcoming Tutorials

This summer, I began working on a tutorial for the 128-bit AES cryptosystem. I ended up putting it down for quite a few months and am now just getting back to it. I hope to have it done in the next three weeks, pending school work and such. If it doesn't get done by the end of Thanksgiving break, it will get finished over winter break.

After...

Discrete Calculus and Sums of Powers

Have you ever wanted to know why \sum_{i=0}^{n} i = n(n+1)/2? The obvious proof is by induction, but it doesn't give us insight as to how we got the formula. I'll show you how to derive these formulas using discrete calculus.

We can actually derive this solution for any sum of powers using discrete calculus. We need a few...

Knowing When to Write Code and Knowing When to Do Math

As some of you all may know, this summer I'm working doing summer research related to graph theory and dynamical systems over graphs. In a graph dynamical systems setting, each vertex has a state (such as a binary state) and an update function. The update function looks at the current state of the vertex and its neighbors and produces a new...

Counting Subsets and the Binomial Theorem

The Power Set on a finite set S, denoted P(S), has 2|S| elements. Similarly enough, Sum_{i}^{n} C(n, i) = 2n...

The Importance of Multiplicative Functions

I came across this thread today, where the OP was attempting to solve a problem regarding counting divisors. Here, the use of a multiplicative function provided means to optimize when counting divisors for larger numbers.

First, let's define two terms- multiplicative and completely multiplicative. A multiplicative function f...

Which Math Course(s) Should I Take?

There are a lot of threads asking about math courses to take, so I figured it was time to put together a blog entry on this. I'm making the assumption that you, the reader, are some sort of an IT or CS major, so I'm starting at Calculus and moving my way up. This isn't a complete or comprehensive list of math courses commonly available...

Graph Theory Love- Four Color Theorem

This semester, I am taking a class called Applied Combinatorics, which has a large Graph Theory component. Today, my professor was introducing planar graphs. We got sidetracked on the Four Color Theorem, which states that a planar graph requires no more than four distinct colors so that no adjacent faces have the same color. I have been working on...

Getting Even Better at Programming Java

If you haven't checked out my thread Getting Better at Programming Java yet (or even if you have), you should check it out (again). It has now been updated with links to relevant tutorials on Dream.in.Code for most of the topics. If you have a tutorial that you feel belongs on the list, shoot me a PM and we'll look at placing it!

I...

Successful Credit By Exam

So a couple weeks back, I was ranting about my Data Structures I class. I heard back today that my credit by exam was successful. In order to complete my credit by exam, I had to complete a program and a written test, getting a 70% or greater on both. The program was representative of the major project taking about half of the semester. I had to...

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