Overview

This book contains new research material in the field of pure mathematics and has solely been written to advance the subject and provide new insight in the field. It can be used by research academics and students alike or by anyone who is interested in mathematics research and needs a research topic. It can further assist with new methods that can be applied to real world examples. The book introduces irregular sequences and functions and initiates a way to work them out. It further gives application examples to show that these sequences and functions can be applied in the real world. It should be clear that the research is not conclusive and can be further researched and refined for clarity and advancement. The book also covers second-degree irregular functions and provides derivatives to support the work. The irregular sequences dealt with herein are characterized by two or more common differences.

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Author Information

I, Mfanufikile Emmanuel Mbele was born in 15 September 1979.at a small town called Hammanskraal, outside Pretoria. I started school at Lepono Primary school in Mathibestad and later moved to higher grades at Bahwaduba Middle School and finished Grade 12 at Sekitla High School in 1998 (all schools in the same area). I loved mathematics from as early as grade 6 and got a good grade in the finishing grade after upgrading. Below are links to my other preprint works available at ScienceOpen.com: https: //doi.org/10.14293/PR2199.001317.v2 https: //doi.org/10.14293/PR2199.001288.v2 https: //doi.org/10.14293/PR2199.001625.v2 https: //doi.org/10.14293/PR2199.002077.v1 The current book is based on the above preprint articles. I love the development that has already been done in mathematics and are glad to also provide a hand to assist. I would like to see a better world for everyone, where everyone enjoys the life made simple by scientific development and human achievements. The research work that I have done so far has not been funded, and it brings a lot of challenges. The challenges are all laid in the path of open publishing.

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