There's a saying that "Google knows you better than you know yourself" (it probably isn't a saying, but I just said it, so it is). It's well known that search engines like Google build profiles about you from your searches. You may forget about the time you were reading Wikipedia articles about the SCP foundation or the Liberian Civil Wars, but Google never forgets. They remember every search since yesterday, a year ago, ten years ago: storing more information about you as a person than you ever could.

So for the last two weeks I haven't really been online, due to the fact that I messed up my computer beyond repair. For some reason it brings a strange sense of comfort that I was the one that bricked it, as opposed to Microsoft or something. Yay for user freedoms! This is what happened— Google was being annoying as usual and sent me my photos with each day having its own directory or something like that, preventing me from using my file manager to quickly live preview the photos.

I just came back from attending the 1052nd AMS (sectional) meeting at Penn State, last weekend, and realized that the Kingdom of Mathematics is dead. Instead we have a disjoint union of narrow specialties, and people who know everything about nothing, and nothing about anything (except their very narrow acre). Not only do they know nothing besides their narrow expertise, they don't care! –Doron Zeilberger, Oct. 28, 2009 Here's a hot take: all the ideas we describe in math are relatively easy to grasp, but mathematicians make things complicated because of our poor short term memory.

I mentioned in my introduction post that this series would probably end up being about the applications of Linear Algebra to other fields of math or something. Well it's the first post, and we already stopped talking about real life applications! Whoops. Consider the vector space with basis \[ \mathscr{B} = \{ 1, x, x^2, ... , x^n \} \] over $\mathbb{R}.$ This is known as the vector space of polynomials with real coefficients of degree n or less, denoted by $\mathbb{R}[x]$ (some texts may use $P_n)$.

There's an interesting discussion about relating your mathematical field of study to the way you eat corn on the cob. This sounds ridiculous, but if you look closer, it's actually very interesting. Here's the hypothesis: the algebraists will eat their corn in rows, whereas analysts go in spirals. Of course, this isn't a theorem because we have no way to prove this. It's also non-trivial to partition the set of mathematicians by the "