An arithmetic sequence of numbers, sometimes alternatively called an arithmetic progression, is a sequence of numbers in which the difference between all pairs of consecutive numbers is constant. A very simple arithmetic sequence consists of the natural numbers: 1, 2, 3, 4, … where the difference between any number and the number before it is …

# Tag: math

Mar 09 2016

## Unsigned Binary Integers and Internal Congruence

This is going to be another one of my “selfish” posts – written primarily for me to refer back to in the future and not because I believe it will benefit anyone other than me. The idea is one that I always took for granted but had a hard time proving to myself once I decided …

Jan 12 2016

## Modular Exponentiation Rule Proof

It is no big secret that exponentiation is just multiplication in disguise. It is a short hand way to write an integer times itself multiple times and is especially space saving the larger the exponent becomes. In the same vein, a serious problem with calculating numbers raised to exponents is that they very quickly become …

Jan 03 2016

## The Complete Idiots Guide to Calculus

Title: The Complete Idiot's Guide to Calculus Author: W. Michael Kelley Genre: Mathematics Publisher: Penguin Release Date: 2006 Pages: 336 Let’s face it: most students don’t take calculus because they find it intellectually stimulating. It’s not . . . at least for those who come up on the wrong side of the bell curve! There …

Jan 02 2016

## Modular Multiplication Rule Proof

I must stay focused. I must stay focused. I must stay … I wonder what’s new on Facebook. I don’t really feel like writing this post mostly because I know that it will be very similar to the other two I have already done: modular addition rule proof and modular subtraction rule proof, but my New …

Dec 31 2015

## Modular Subtraction Rule Proof

I’ve already presented and proved the rule for modular addition, so for a sense of completeness, but mostly to satisfy my OCD, now I’ll cover the rule for modular subtraction. When doing subtraction in modular arithmetic, the rule is: If we subtract integer from integer and calculate the difference modulo , we get the same answer …

Dec 31 2015

## Modular Addition Rule Proof

Addition in modular arithmetic is much simpler than it would first appear thanks to the following rule: This says that if we are adding two integers and and then calculating their sum modulo , the answer is the same as if we added modulo to modulo and then calculated that sum modulo . Note that …

Nov 15 2014

## Euler’s Formula

Besides being an obvious lady killer, Swiss mathematician Leonhard Euler gifted the world with some pretty important mathematical concepts, notational conventions, and formulas. I almost feel bad about the fact that I couldn’t even spell his name correctly until I was well into adulthood. You are probably thinking, “Sure, he had a bitchin’ robe, and for …

Nov 10 2014

## Complex Numbers and their Geometry

(Note: I lied. This will be my first “neural dump.” I began writing about Euler’s Formula, but felt what follows was worthy of its own post and a better foundation for what will follow when I tackle Euler.) Complex numbers arose from the fact that there is no solution for in the equation in , …