If we have our statement p then q:

The inverse is inverting the signs think of i as the square root of -1. You are negating each element.

~p -> ~q

Converse, reverse.

q -> p.

Once you remember those, just remember that the contrapositive is converse and inverse combined.

~q -> ~p

In Calculus II we learn the wretched “Trigonometric substitution” and it can be hard to remember them. I came up with this little pneumonic device to help me out. Is it good? Not at all. Did it help? Yes, it did.

a^2-x^2 = sin^2x: Sine gets the mine.

a^2+x^2 = tan^2x: Remember the A in tAngent and the A in Add. Taddgent.

x^2-a^2 = sec^2x: She cant keep that constant = secant keep that constant.

These are stupid but I hope that they help.

Well now you do! Ian is the name and blogging is the game, so let me quickly answer some hypothetical FAQs.

Who is Ian Cooper?

I am a Computer Science and Mathematics major here at UW-Whitewater. I have been known to dabble in other areas such as music and 3d art from time to time. I am incredibly passionate when it comes to learning about subjects that I think give me the best advantages when thinking about, discovering, and creating cool things. Computers are magic and math is the language that the spells are written in. I want to wield this wizardry.

Why make a blog?

I want to go through my academic journey keeping a clear and concise record of what I have learned, explained in a way that anyone can understand. Explaining hard concepts in a digestible form is a key element of achieving true understanding of a concept, and reinforces its contents. Also, it’s kind of cool having a little soap box I can stand on and yell about whatever creative obsessions I currently have.

What do you think of the song “Hey, Soul Sister” by Train?

“Your lipstick stains, on the front lobe of my left side brain.” Are you kidding me? This song has made more people cry in human history than sliced onions; with its poor insertion of “tonight” at the end of the chorus (huge lyrical copout in any song), cheesy ukulele I-V-VI-IV chord progression, and who can forgot the obnoxious “heyeys.” I could go on; objectively, the worst song of all time. Seriously, if you disagree just read the lyrics. “Oh! But you must admit, it is just so catchy!” Yeah? So is the gummy bear song but you guys aren’t defending that one now are you?

If you were abducted by rats and they take you to their rat king and the rat king says to you, “If you kill thirty of my mightiest rats (which you know 100% you would beat, no doubt at all), and you will become rat king; or walk out right now, no questions asked, and the rats will never bother you again.” would you fight the thirty mighty rats or, eternally abandon the incredible opportunity of becoming the rat king?

Wow, miscellaneous reader, that is an extremely powerful question you just asked pertaining to moral philosophy. Should I take the power of the rat kingdom for personal gain at the expense of other conscious agents, or should I forfeit the power and spare the thirty rats? Perhaps I will investigate this later on in my blogging career.