Welcome to the second installment of this three-part series on set theory. The first piece, Set Theory Defined (recently updated with code samples), detailed requisite foundational knowledge. It is highly recommended that readers begin there if they haven’t already.
The first piece in this series introduced sets and exhibited how ES6 arrays are analogous to them. It also depicted how to transform, or map, a set into a related set. This post expands on set theory by probing into set operations.
Set theory is incredibly intuitive and has many practical applications in software engineering. In fact, any professional programmer without an understanding is at a disadvantage. Unfortunately, many in the industry relegate it to the purview of mathematicians. This is understandable because most material on the subject delineates set theory with first order logic as a basis for math. The good news is that it doesn’t have to be this way. As this series demonstrates, it is accessible to anyone regardless of background.
Welcome to the final installment of this three-part series on coding theory. If you have not had the opportunity to read the first two pieces, it is highly recommended that you do before continuing on. They are available here:
- Coding Theory (Part 1 of 3) - Coding Theory Defined
- Coding Theory (Part 2 of 3) - Coding Theory Defined
Having covered cogent concepts in previous posts, this article aims to dive into a demonstration which consists of defining a code using a generator matrix and correcting errors using a parity check matrix. The example is a bit contrived and thoroughly simplified for the sake of brevity. However, the intent is not to provide an exhaustive resource; it is to familiarize the reader with coding theory and hopefully entice him/her into further inquiry.
Welcome to the second installment of this three-part series on coding theory. If you have not had the opportunity to read the first piece, it is highly recommended that you do before continuing on. It is available here: Coding Theory (Part 1 of 3) - Coding Theory Defined
It’s rare to find concepts simple yet adroit at the same time. However, Hamming’s contributions to coding theory “fits the bill”. This post begins with a brief introduction to Hamming and a short history lesson before diving into Hamming Distance, and Perfect Codes. Additionally, it delves into a few simple math concepts requisite for understanding the final post. These concepts all come together in the final installment by providing examples of how to generate and decode the most powerful and efficient error correcting codes in use today.
Coding theory stands as a cornerstone for most of computer science. However, many programmers today have a diminutive understanding of the field at best. This three-part series of blog posts describes what coding theory is and delves into Richard Hamming’s contributions. Although derived in the 1950s, Hamming’s ideas are so visionary that they still permeate modern coding applications. If a person truly comprehends Hamming’s work, they can fully appreciate coding theory and its significance to computer science.
23 post articles, 5 pages.