Set theory is the branch of mathematics that, unsurprisingly, deals with sets. It’s an area of great importance in a number of fields, including computer science. In this post, I’ll go over a brief review of basic set theory as it pertains to those pursuing an interest in computer science. Let’s just jump right in! What is a Set? The first and most logical question we can answer about set theory is just what is a set?...
I previously posted a logic rules cheat sheet and figured it was about time that I do the same for boolean algebra. Expression Equivalent To Name of the Rule $$ X + Y $$ $$ Y + X $$ Commutative $$ X \cdot Y $$ $$ Y \cdot X $$ Commutative $$ (X + Y) + Z $$ $$ X + (Y + Z) $$ Associative $$ (X \cdot Y) \cdot Z $$ $$ X \cdot (y \cdot Z) $$ Associative $$ X + (Y \cdot Z) $$ $$ (X + Y) \cdot (Z + Z) $$ Distributive $$ X \cdot (Y + Z) $$ $$ (X \cdot Y) + (X \cdot Z) $$ Distributive $$ X + 0 $$ $$ X $$ Identity $$ X \cdot 1 $$ $$ X $$ Identity $$ X + X' $$ $$ 1 $$ Complement $$ X \cdot X' $$ $$ 0 $$ Complement $$ X + X $$ $$ X $$ Idempotence $$ X \cdot X $$ $$ X $$ Idempotence
When working with logic in discrete math appliations there are a plethora of rules you can use for working with the well formed formulas. Remembering them all can be a daunting task, which is why I like to have a cheat sheet available. As such, here’s a simple one that I like to use when working with these problems. Equivalence Rules Expression Equivalent To Name of the Rule $$ P \lor Q $$ $$ Q \lor P $$ Commutative - comm....
Welcome to what will be the first in an ongoing series aimed at reviewing computer science topics. Today we will be diving into binary number representation. Understanding binary is an important step in gaining a better understanding of how the computer works on a lower level. Recall that a computer is made up a whole bunch of integrated circuits, which are in turn made up of a bunch of transistors. These transitors can have one of two states: on or off....
The uses for prime numbers in computer science are nearly endless. They are useful for everything from hashing, cryptology, factorization, and all sorts of applications in-between. There exists a great number of algorithms that allow us to quickly generate primes, but today we are going to take a look at a popular method known as a prime sieve. There are a number of different implementations of prime sieves, but one of the simplest to implement is known as the Sieve of Eratosthenes....