Hello, and welcome back, and today we’re going to be pausing our discussion of Pascal’s triangle temporarily, and discussing some proof writing! (Don’t worry, this will only be a 2 part series, so we will be back on to Pascal’s triangle in no time!) What is proof? A proof is a series of statements, each… Continue reading Proof Writing (Part 1): An introduction to a couple types of proof.
Hello, and welcome to the 3rd episode in this 5 part series! In this blog we will be formally writing the Hockey-stick Principle showcased in the last blog, see what it has to do with multi-dimensional triangles, and finish our study on this pattern of Pascal’s triangle. Formal writing of the Hockey-stick Principle To begin,… Continue reading Pascal’s Triangle (Part 3):
Hello everyone! Welcome back to my blog series on Pascal’s Triangle. Today we will be looking at the first pattern covered in the last blog–triangular numbers, and their relation to the Hockey Stick Principle. A short proof To begin this blog, we will first prove the property of the triangular numbers shown in part 1:… Continue reading Pascal’s Triangle (Part 2)
In this blog, we discus some of the more basic properties in Pascal’s triangle, and lay a foundation for the future blogs in this series!
The pinnacle of this series of modular arithmetic, we prove a theorem that ties everything together!
In the penultimate episode of modular arithmetic, we discuss the relation between inverses, and multiplication tables, and set the scene for part 5!
Explore the world of proofs while learning about the inner workings of modular arithmetic!
Delve more into the realm of modular arithmetic as we learn about doing operations in it!
An elementary level look at one of the most interesting subjects in number theory.