macosxnerd101's Profile
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Blog entries
Macosxnerd101's Blog > Discrete Calculus and Sums of Powers
Posted 03 August 2014
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...
We can actually derive this solution for any sum of powers using discrete calculus. We need a few...
Macosxnerd101's Blog > Knowing When to Write Code and Knowing When to Do Math
Posted 31 July 2014
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...
Macosxnerd101's Blog > Counting Subsets and the Binomial Theorem
Posted 06 July 2013
The Power Set on a finite set S, denoted P(S), has 2^{S} elements. Similarly enough, Sum_{i}^{n} C(n, i) = 2^{n}...
Macosxnerd101's Blog > The Importance of Multiplicative Functions
Posted 03 July 2013
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...
First, let's define two terms multiplicative and completely multiplicative. A multiplicative function f...
Macosxnerd101's Blog > Which Math Course(s) Should I Take?
Posted 09 June 2013
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...
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 January 5, 1993
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Comments
macosxnerd101
09 Jul 2014  14:54modi123_1
09 Jul 2014  11:58da1
17 Jun 2014  12:11macosxnerd101
02 Jun 2014  23:27jon.kiparsky
02 Jun 2014  23:24pbl
22 May 2014  13:26macosxnerd101
14 May 2014  10:31modi123_1
14 May 2014  09:35"Hexagonal Hyperbolic Honeycombs"
https://johncarlosbaez.wordpress.com/2014/05/14/hexagonalhyperbolichoneycombs/
modi123_1
24 Mar 2014  13:20http://jacquerie.github.io/hh/
macosxnerd101
12 Feb 2014  12:21Martyr2
11 Feb 2014  11:53Dogstopper
10 Feb 2014  11:21belgarion262
10 Feb 2014  09:49andrewsw
10 Feb 2014  02:48tarmizi_adam2005
09 Feb 2014  21:52