cs241

Relating Things Together Through the use of functions, we can define a lot of the things that we use in general, such as operations like $+$ and $\cdot$. As of right now though, we don’t really have a good way of comparing things together.

Always More Terminology 📖 Now that we have relations, we can define some properties about them and see how our examples from the previous page compare. In all of our definitions, we will use $*$ to represent some generic placeholder symbol, with $R(*)\subseteq A\times A$ being our relation set.

Why Duplicate Effort? Suppose we have some equivalence relation $\approx$; note here $\approx$ does not mean “approximately equal”, it just is a generic symbol for any equivalence relation. Since $\approx$ is an equivalence relation, then we know that it is reflexive, symmetric, and transitive.

What are we Counting? 🍎🍊🍐 So if we have two pieces of code, how do we know which piece of code will be “faster”? Yeah sure we can run the two of them side by side, but how fast code runs depends on a lot of factors, such as what device it was run on and what other programs were running at the same time.

Hijacked Notation Like many things in computer science, Big $O$ has a very specific definition and has a use case designed for number theory. Computer Scientists then took that notation, changed nothing about the notation, and then proceeded to use it in whatever way they felt was convenient1.

You Can Go Your Own Way 🎵 🎶 In this page I will explain one way of proving that two sets or set identities are equal. Obviously, there is never exclusively one way to do these things, so if you (for example) decide to learn algebraic identities for sets, then you are totally free to do so.

Why Do Mathematicians Do Something Different? In case my salty ranting on the previous page couldn’t clue you in, I will now take the time to explain what the notation of $\mathcal{O}, \Omega, \Theta$ truly mean in mathematics.

A Victim of my Own Design Prior, we have been working on very nice and fun programs that have been super straightforward to do counting on, but many algorithms that are taught in classes are self referential and recursive.

The Best You Can Get Prove why n log(n) is the best comparison based sorting algorithm Whats Up With QuickSort? Prove why quicksort is n log(n)

An Intro to Git Most people, in some capacity, have heard of git, or at least one of the many, many services that utilize git. Some of these services are such staples in the industry that I know that I personally didn’t know that git was entirely seperate than Github the website!