Number Theory is one of the most pure fields of mathematics. Many people look to it when trying illustrate the beauty of math. Staying true to the name of this site, I hope to help you see some of that beauty for yourself. Before reading posts from this series, there some important foundational concepts you … Continue reading Number Theory
Tag: theory
Group Types Part 2
Hello! This posts belongs to a series Group Theory. I recommend checking that out before reading this post. You should definitely read Intro to Groups and Group Types Part 1. The groups we've seen so far have been aproached from the perspective of elements. This is a very useful tool, but sometimes it's nice to … Continue reading Group Types Part 2
Group Types Part 1
Hello! This post belongs to my series Group Theory, I recommend starting there to get the basics before reading this post. Specific to the groups presented here, you should also read Modulo and Equivalence Relations. We've seen some examples of infinite groups in Intro to Groups such as $latex G = (\mathbb{Z}, +)&bg=ffffff&fg=4E4E4E&s=1$ and $latex G = (\mathbb{R} \setminus … Continue reading Group Types Part 1
Group Theory
Abstract Algebra is a rich, massive field of mathematics. It is the study of many mathematical structures such as groups, rings, fields, modules, etc. Groups are the simplest of these structures and are the focus of this series. Before you begin this topic, I reccomend working through Intro Math, as this will give you a nice … Continue reading Group Theory
Intro to Groups
Hello! This is the first post in my series on group theory. For an overview of this series, see Group Theory (link to be added). I recommend working through Intro Math before starting this topic (especially Logical Implications, Set Theory Part 1, Set Theory Part 2, and Binary Functions). The vocabulary from Binary Functions is … Continue reading Intro to Groups
Intro Math
Welcome to my Intro Math series! Here I'll offer some info about the series, and you can find links to all the topics below. The standard mathematics education has students working through Calculus, then moves into proof-based math. This is a significant jump and can be jarring for many students. Lots of new concepts and … Continue reading Intro Math
Quantifiers
This post belongs to my "Intro Math" series, a set of posts designed to give the foundations to advanced mathematics. More info can be found in Intro Math.Before reading, I recommend Set Theory Part 1 for a brief overview of sets.In mathematics, there are two main quantifiers $latex \forall &bg=ffffff&fg=4E4E4E&s=1$ and $latex \exists&bg=ffffff&fg=4E4E4E&s=1$. These symbols are … Continue reading Quantifiers
Set Theory Part 2
Hello! Be sure to read Set Theory Part 1 before reading this post This post belongs to my "Intro Math" series, a set of posts designed to give the foundations to advanced mathematics. More info can be found in Intro Math. There are a couple sets that everyone learning math should know. The first is … Continue reading Set Theory Part 2
Set Theory Part 1
Hello! This post belongs to my "Intro Math" series, a set of posts designed to give the foundations to advanced mathematics. More info can be found in Intro Math. Here, I'll be introducing sets - one of the most fundamental ideas you'll encounter in math. Pay careful attention as these concepts will show up in … Continue reading Set Theory Part 1
Word of Cole 