Hello! This post belongs to a series called Number Theory. You should read Divisibility and Prime Numbers. I'll also be introducing induction in this post - a common mathematical tool. Fundamental Theorem of Arithmetic - Every integer greater than $latex 1 &bg=ffffff&fg=4E4E4E&s=1$ can be written as a product of prime numbers. Before I prove this, … Continue reading Fundamental Theorem of Arithmetic
Tag: math
Number Theory
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
The Division Algorithm
Hello! This post belongs to a series called Number Theory. Before reading this post, I recommend going to that page and making sure you have the prerequisite material. You should be familiar with Set Theory Part 1, Set Theory Part 2, Quantifiers, Modulo and Equivalence Relations, and Divisibility and Prime Numbers. Before I introduce the … Continue reading The Division Algorithm
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
Divisibility and Prime Numbers
Hello! This post belongs to my series Intro Math, a set of posts designed to help bridge the gap between "plug and chug" type math and proof-based ideas. I reccomend reading Quantifiers, Logical Implications, Set Theory Part 1, and Set Theory Part 2 before this post. You will only need minor concepts from each, and may be able to get … Continue reading Divisibility and Prime Numbers
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
Modulo and Equivalence Relations
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. I suggest reading Set Theory Part 1 and Set Theory Part 2 before this post. Typically when dealing with integers, we think of them as unbounded. We can keep adding $latex 5 … Continue reading Modulo and Equivalence Relations
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
Binary Functions
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. I've done a few posts talking about functions that take one input, such as $latex x^{2}&bg=ffffff&fg=4E4E4E&s=1$ , $latex x-5&bg=ffffff&fg=4E4E4E&s=1$ , etc. Another class of functions, known as Binary … Continue reading Binary Functions
Word of Cole 