Although considered as one of the most euphemism, math research remains as a pragmatic discipline that demands extensive skill set for writing help to comprehensively grasp the conception all framework and apply the suitable criterion to yield expected results. Furthermore skeptical disorientation of the subject by some of its critics has been a deterrence in the overall embracing of the subject and as such limited mathematics research proposals conducted under the subject.

The purpose of this paper is not to provide research topics in mathematics but rather to provide a predefined layout that students alongside other practitioners who may be seeking to exhaust the various topical algorithms under the subject to offer more accurate and coherent presentation of their work.

As such the connotations are not to provide a math research paper but rather offer a template that will ascertain that all the essential pertinent features that qualify the paper as a research paper are embedded within the case study based on the given subject matter. This will attempt to shrink down and outline some of the critical essential elements of the mathematical research given the dissimilarity that mathematical languages and symbolism that are encompassed within the discipline.

In order to effectively write a research paper, there is need to adapt and restructure the anticipated essay in a Mathematical language and syntax that will not only demonstrate with the clarity of the sampled topical subject under discussion but accompany the presented theorem with examples to ease the understanding.

In contrast to the conventional essay format, research in mathematics papers are dissimilar in that the symbolic nature in addition to extensive proof of the theorems will often create an abstract presentation of the discipline to the end user. As a result, this will often inculcate a barrier that if not further exposed to illustrate the underlying concepts that the end users will not capture the various propositions.

## How to do research in mathematics

In order to effectively present the symbolical notation that distinguishes the mathematical paper from the conventional essays, the paper will adopt two formats and structures that will define the paper setting it apart as precarious sampled in maths research. This includes the formal and informal expository patterns.

### Formal exposition research in mathematics

This structure demands a linear presentation of the hypothesis and possible deduction based on the subject matter be predefined in an orderly sequence where the flow of algorithms form definitions to theorems and proof that support the exposure of the fore stated theorem. As a result, this structure is limited to the theoretical framework for the proposed hypothesis plus only the descriptions to illustrate the theorems with little or no support caption all feature to further illustrate the proposed hypothesis.

### Informal exposition areas of mathematics

This is a complementary substrate that accompanies the first formal syntax but will offer logical explanations of the latter propositions and proofs that have been predefined under the formal section. The mathematical connotations that are presented under the formal sector such as figurative language, proofs, and equation are often denoted in a symbolic language limiting comprehensive understanding of the subject if the user is not acquainted with the language. Analogies alongside other essential illustrative features are attached to support the proposed hypothesis are also incorporated under the informal approach.

## The predefined layout structure of math research topic

However, in order to present and cover the broad spectrum of fundamental and application of mathematics, there are critical topological and axiomatic formats that each of the papers has to adhere in order to construe as the ordinary conventional math research paper. Though significantly dissimilar to the conventional paper, each publication will be effected based on the standardized criterion where the essential elementary factors and structured features have been complied with. These variants could be outlined as follows:

- Conception understanding of the mathematical paper – This is a title or an epilogue that will define the theorem under the case study
- Title, acknowledgment and conventional list of authors – This is an outline of the possible quoted contributor to the paper in addition to the topical summary of the thesis under investigation.
- Abstract – prologue of the paper outlining previous works that had been conducted under the subject matter.
- Introduction – will briefly present what is incorporated under the program
- Body – These includes computation, comparisons and possible interpretation of the problem subject
- Conclusion, appendix, and references – will present the synopsis and acknowledgment of other publications that have been exhibited under the thesis
- Publication of a math paper – actual dissemination of the paper for general or specified audience based on the initial purpose for such publications.
- Preprint archive – based on the paper format whether scholarly or scientific there is preceding articles or presentation that been previously undertaken
- Choice of the journal, submission –
- Decision
- Publication

## Mathematical axioms in maths

For ease of understanding and usability, mathematical papers must be complied with specific protocols from punctuation to fonts to footnotes alongside other constraints that will ascertain the validity of the thesis or paper investigation. As such it is critical that the various connotations such as the theorems, definitions, symbols, and other notations are clearly defined to ensure that subject matter is well presented to the audience. There are however minimal guidelines that are essential conventions that core in presenting the paper.

### Logic –

each of the argumentative representation of the subject matter must flow comprehensively in a logical pattern to ensure that the author’s ideas are communicated clearly to the audience.

### Definitions

any new ideological statements must be outlined to present the standardized structure of communication.

### Theorems and equations –

any hypothesis attached and possible deductions that may be drawn from propositions may also be defined vividly or shortened under the equations to present the expected background knowledge that is under review adequately. As such each of the theorems should be clearly defined to illustrate the actual usability and application.

### Maths symbols and Notations

adherence to the rules and the standard connotations is critical to avoid confusion in case of presentation or general communication to the audience.

## Language Presentations in maths

Based on the symbolical language characterizing most mathematical research, the composition of typical software packages such as word documents may be limited as they lack the full set notation that may be utilized in drafting the papers. Two packages are available within the market offer more professional and sample research papers that cover the topographical features that are essential in presenting the mathematical research papers. This includes open-ended LaTeX program and the closed Wolfram dependent on the user’s cost implications and availability. The Wolfram is a somewhat costly product in contrast to LaTeX that is free with product quality being slightly indifferent as Wolfram versions are of a higher valuation.