This paper was a research paper written by me explaining a novel representation of Hailstone numbers I used inductive and direct proofs as evidence in this paper. The audience is an academic one given the technical nature of the proofs. The main point of the paper is to showcase to readers my observations and proofs to readers and to introduce a new way to view the Collat Conjecture.

This article while not directly useful to my book, is very useful to the chapter about mathematical explanations. It can also be used as an example of how an inexperienced non-academic person interested in mathematics can observe and prove intriguing results in mathematics. I think that this paper could be very useful because it is easy to understand and can give confidence to my readers in their mathematical capabilities.

In this guide written for UC Davis students, the author talks about how to write mathematical papers for a given audience. Examples from fiction book authors like Herman Melville and examples of equations have been used and not much quantitative evidence has been used given the explanatory nature of the article. The audience is that of mathematics students learning to write mathematical books and papers. The main point is to take care of the audience and to write accordingly explaining all steps and not writing only the final equation.

This was very useful and informative because I learnt about explaining concepts to inexperienced mathematicians. However, I do not agree with the fact that the audience should be assumed to be as knowledgeable as the writer. This would not be true in my case because I would be writing for non-STEM audiences. However, I think learning about things like TeX mentioned in the article could be very useful in terms of formatting my artice

This research paper by a mathematician Erhan T., introduces fractional sum notation for odd numbers and reverse reduced sequences. This paper uses mathematical proofs as evidence and explains points through corollaries, theorems and lemmas. The audience once again is that of academicians who study mathematics. The main point of the article is to introduce the author’s findings about the Collati conjecture.

This acts as a very important research paper for my book for the chapter giving mathematical proofs and explanations. Given that the writer is a Master’s Student, it shows that even inexperienced mathematicians can try to prove very big problems, thereby representing the equity and equality in mathematics that I want to show to my readers to empower them.

This article, “The Collatz Conjecture: Beauty or Conundrum of Mathematics?”, Arghyadeep Das, a writer for Medium.com explains the problem and the probability of finding a counterexample. The author uses quotes and proofs by famous mathematicians as evidence. The audience is a more of a non-academic and mathematically inclined one. In short, the author introduces the problem and explains the seaweed representation while talking about how a counterexample could spill water over the work of many mathematicians.

This article is not very credible alone because of the non-mathematjical credentials of the author. However, the facts are consistent with what I read in other articles, making the information correct. I think the main use of this article could be explaining to the audience how finding a counterexample is a current focus of mathematicians in the chapter relating to current attempts to tackle the problem. However, I think this article was more of a repetition of old facts than it was an introduction to new information.