This research paper, “On the relationship between the Collatz conjecture and Mersenne prime numbers” by J. Kaiser, a mathematician, explains a connection between the numbers in the Collatz Conjecture and prime numbers. The article uses mathematical proofs and observations as evidence to explain concepts. The audience is a mathematical and academic one given the difficulty of equations. In short, the article explains mathematically a similarity between two patterns and sequences of numbers.

This article is very important for my research because it represents a simple pattern and observation in mathematics which I could use to empower my readers in terms of giving them confidence in finding such patterns and becoming a mathematician or studying mathematics. I could also use this for the last section of my book for mathematical proofs where I could write some equations from this paper to explain concepts to a more mathematical and academic audience. While the article is very evidence-based and can be cited, only certain parts stated above of it are useful for my research because the audience of my book and this paper differ greatly in terms of experience in mathematics and their academic situations

In this video, “Collatz Conjecture in Color – Numberphile”, Alex Bellos, a columnist for the Guardian and a mathematical communicator, talks about representing the Collatz conjecture in an innovative and artistic way. He uses his experience working with mathematician Edmund Hariss as evidence. The audience once again is a non-academic audience that is interested in mathematics. He explains the modifications made to trees of Hailstone numbers in terms of rotating the number logs and produces a coral like looking natural structure, which shows the beauty of mathematics and its natural presence.

This video is very useful in terms of illustrating my book because it gives a number of images and the way to make them that would be nice and easy to understand for my audience. It also helps me convey the message to my readers that mathematics is a beautiful area of study and is very useful not only for engineering but for the arts and natural studies

In this video, “UNCRACKABLE? The Collatz Conjecture – Numberphile”, David Eisenbud, a professor of Mathematics at the University of California, Berkeley, describes the Collatz Conjecture as a problem that any fourth grader can understand. He uses as evidence various examples he writes down and refers to books by credible mathematicians. The audience is a big one containing inquisitive learners who may not be academicians, with the video having more than 1 million views. In short, the video introduces the Collatz Conjecture in a very nice way, showing why it is so easy to understand and in short, why it is so difficult to prove.

This could be very useful for my research because it pointed me to terms like trees and gave me a nice way to introduce the conjecture by comparing it to Hailstones falling down as the numbers following the mathematical formula in the problem. I got introduced to papers like the, “The Undeniability of the General Collatz Problem, ” which I could use for future research. This video was very useful in terms of the content it had and the papers it pointed me to.

In this article, Mr. Dilip D, a mathematical article writer for the reputed Indian magazine, the Mint, explains the Collatz Conjecture and paints its picture as a very challenging to prove yet easy to understand problem. The author uses as evidence quotes and experiences of renowned mathematicians like Terence Tao and Richard Lipton in order to create credibility in the article. The main audience includes people who are interested in mathematics and want to know more about new concepts. In short, the article introduces a non-academic audience to the Collatz Conjecture and its history.

This article could be useful for me because it is from a credible website and it lists mathematicians whose papers I could read and use for my book. It also is very useful because it has a similar audience as my book and I can position myself as the author of this article did – a writer with an interest in mathematics.