# Notation and Beginners

You’re interested in learning a new mathematical topic. After reading some popular articles that speak in broad terms about the subject, you are energized to go on a deeper dive and learn the details.

You’re interested in learning a new mathematical topic. After reading some popular articles that speak in broad terms about the subject, you are energized to go on a deeper dive and learn the details.

I am very good at finding the bad aspects of any given idea or thing. I wouldn’t call myself cynical. Rather, I have a tendency to find ways to justify *not* doing something. This has to do with my reluctance to try new things, and I suspect I’m not the only one who does this.

It’s tempting as a student to think that nothing is in your control. We often feel like our whole lives revolve around the whims of professors and their decisions for assignments and tests. It can be easy to retreat into “reactive” mode, making sure that everything which is thrown at you gets done. When we operate like this, we tend to be exhausted, since we can never look further than a week.

In mathematics, there’s almost always an opportunity to make proofs more concise. For example, when you first learn a concept, it might take a while to prove a result using the definitions that were developed. The reason it’s longer to do is because the definitions require you to spell out ideas explicitly. As a result, you might get to the end of the proof, but it takes a bunch of little intermediate steps to do so.