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
Tag: guide
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
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
Logical Implications
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.Here I'll be discussing the basic logic found in most mathematical arguments. We'll be learning … Continue reading Logical Implications
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
Bijective 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. Hello! In this post I'll be explaining bijective functions. To do that, I first need to cover some definitions. It is recommended to read Set Theory Part … Continue reading Bijective Functions
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
Word of Cole 