Learning Math with Mathman

  Welcome to my blog! My name is Emily and I'm an incoming applied math graduate student who really wants more people (even those without a math background) to explore upper level mathematics without becoming overwhelmed with notation. This blog is open for anyone to read, and are not intended to need too many prerequisites to understand (and any you need will be mentioned in the beginning of the blog). Each blog is a mix of my explanations and some comics featuring Mathman, who is definitely not just Adam West Batman with a Pi symbol. I want to cover a wide variety of topics within mathematics and more mathematical topics in computer science, but currently focus on topology and graph theory. I also will occasionally cover topics related grad school when inspiration strikes me. Hope you enjoy!

  If you clicked on this link to learn about topology after seeing the word Mathman, you clearly aren’t looking for a serious article that throws a bunch of formal definitions at you. Especially when it comes to higher level concepts in mathematics, there are few sources that attempt to give an intuitive explanation without assuming that the reader is basically a math major. Luckily for you, Mathman and I assume you only know the following: Basic geometric shapes (circles, squares, triangles, etc) How to describe a shape (How many sides does a shape have, etc) How to change the characteristics of a shape (By rotating a shape, moving the shape around a space, changing the size of the shape, etc) So, assuming that you remember some basic geometry (even if you don’t, many geometric concepts are reexplained along the way), let’s get back to the question at hand. What is a topology? This can be a difficult question to unpack. What does the word even mean? Well, if we look at the root words,

  For this blog, let's take a brief break from making silly blogs about topology and graph theory and focus on the math PhD application process! Hopefully, as someone who has just applied and gotten into a couple of math PhD programs, I can give my few nuggets of wisdom to you. While I could ramble all day about the process, I'll try to limit myself to 10 pieces of advice.  As you read this, keep in mind that you should take all my advice with a grain of salt and every applicant's experience is different! Additionally, there is no standard way that a math department conducts their PhD admissions, so any of this advice could not be true for some departments. Anyways, I will split my general advice into 3 sections: applying to grad school, the grad school cycle, and deciding your future. Applying to Grad School Advice #1: Don't look for schools until you figure out the areas of research that you want to focus on! Before you run off to find schools to apply to, you need to

  If you are following along with the Mathman Explains series, you might be really confused by how coloring maps connects to topology and graph theory. If this is the first article that you're reading, you'll probably even more confused to how this is a researched problem in mathematics! Don't worry, today we will go on a short adventure into the confusing world of map coloring, where we discover why coloring maps is secretly a complicated nightmare... All you need to know is the little bit of graph theory that was covered in part 2 of this series! When discussing the coloring of maps, we will mostly talk about the 4 Color Problem! So, what is the 4 Color Problem? Well, if given a map divided into sections, what is the minimum number of colors that you need to color the map in a way where the colors of two sections touching each other don't have the same color? While it is easy to just color every section of a map with a different color, finding the minimum amount of co

  This article is part 2 of a series where Mathman and I intuitively cover various topics in topology. If you don’t know what a topology is or what topological properties are, check out the first part of the series. Other than the basic topology covered in part 1, this article doesn’t assume that you know anything about graph theory! So what is graph theory? What is a graph? How does graph theory relate to topology?   These feel like difficult questions to answer. We should try to look at the 3rd question first since we all know what a topology is. Maybe Mathman can help? Interesting, so we can somehow represent a topology (the original map) with this 1D topological structure that retains how the bridges were connected. Lucky for us, this 1D topological structure is a graph! Much like how we make maps of the world, the connection between graph theory and topology is that we can represent topologies using graphs. So, what is a graph? Figure 1: an example of a graph Well, let’s l