As shown in the textbook all compact sets in the space of real numbers must be closed and bounded (Abbot 96). However, topological spaces go far beyond just a set that is a subset of the reals. This brings to our attention the idea that the proof for sets being compact if and only if […]
When I started trying to think about applications of infinite series outside of mathematics, my mind quickly went to the business school where I spend the majority of my time when I am not in math classes. Early in introductory finance or economics classes, students are introduced to the idea of the Time Value of […]
In class last week, we learned about the uniqueness of limits. Specifically, the limit of a sequence, when it exists, must be unique. But what if I told you that there existed a place in mathematics where this is not always the case? Today, I’d like to briefly define that context and then illustrate some basic examples. […]
I remember when I started learning mathematics in elementary school, particularly counting the number of balloons on a printed piece of paper and writing that number down at the bottom. Fast-forward 15 years, and I’m in college studying about set theory and still counting – this time the elements in a set, also called the cardinality […]
Many would claim that organization is a basic aspect of being human–but organization in mathematics seems to be essential. The most basic thing organized in math are the numbers we use as a part of our tool kit. Just like the various ways to organize tools, there too exists ways to organize the numbers we […]
Blogging has gained in popularity drastically in recent years, and mathematics-oriented blogs are likewise growing in both content and variety. Academics of all specializations are finding an active audience for their current, past, and future research endeavors. A blog is also a great place to explore ideas that may pertain to research, teaching, and learning, without being […]
You must be logged in to post a comment.