An ideal approach to research entails conceiving each research problem as being attached to another series of research problems that have been resolved, but where the current issue is qualitatively different from the previous elementary component attributes. And that when all the solutions are run together, the whole group forms an entity that resolves most problems exhaustively plus helping generate sets of engagements aimed at resolving future and emergent problems. Under the circumstances, basic research leads to problem-oriented research, that then transitions to qualitative research that describes inexpensive but effective solutions. Then we move on to quantitative research that directs the actualization of the anticipated reality. When this is done and a problem area will receive the entire package of research treatment and more often than not, a novel solution or novel solutions are generated that pass the test of complex structures requirements. Complex structural requirements demand stability because a change in one part of the system affects the remaining components in unanticipated ways. To avert such problems, the research plan ought to be fractal in design and execution.

In this article, we focus on how to write dissertation proposal that fits into the qualitative aspect of the research and that prepares the researcher or the research teams for the final stage of the research process of actualizing results and intentions. This implies using the dissertation proposal template to generate a sample of dissertation proposal that working along a qualitative bent. To prepare dissertation proposal writing initial conditions must be stated as follows:

- An argument highlighting qualitative possibilities relating to items contained in a dissertation proposal wholesomely that are met so that the corresponding proposal remains relevant, urgent, executable plus desirable.
- Dissertation proposal example created must be specified by 4 scientific and numeric rudimentary features.
- Planning a dissertation proposal outline involves crafting the body of the text to a union of groups corresponding to the 4 basic constituents
- A dissertation proposal sample generated naturally ought to accomplish a qualitative task of reaching an objective efficiently and effectively.

*Hence as an Example:*

The next scenario in our dissertation proposal sample is satisfied by saying: “For every component of a dissertation proposal template there are groups of circumstances described using the four basic elements represented by the archetypes of the numbers 1, 2, 3, and 4 that combine to provide the appropriate compounds. Hence the title of the sample of dissertation proposal must have the first element as a declaration of identity, the second component describes the method of conflict resolution, the third resolve the situation of the problem that needs to be resolved, and the fourth is the stabilization of the whole form to unity.

Such a formal definition allows us to derive the best kind of title that will direct our dissertation proposal given that the necessary components are specified by a predetermined structure and method of generating the required variables.

The entire dissertation proposal template is as follows:

- Title
- Starter/introduction
- Goals plus Objectives
- Technique of operation
- Review of literature works
- Limitations examination
- Resources needed
- General presentation structure
- Resource management strategy
- References

Now, if the dissertation proposal aims to generate a solution to a specified problem, then there is a need for the problem to be stated formally. In this case, the problem is stated as: “How do we best meet the effects of not having a clear theory on the origin of man when developing knowledge?”

Hence for every item in the dissertation proposal template, a mathematical function is created to meet the requirements of the problem statement in a way that fulfills the conditions of compounding the basic elements together in a way that fits.

Therefore the title for our dissertation proposal example is derived from a function that states that “There exists a set for the title T’ whose condition is such that:

- 1 = Promise to resolve the problem statement
- 2 = Method of operation
- 3 = Emergent component that resolves the tension
- 4 = Desired reality that needs to be affirmed

Therefore the mathematical function for the title is:

Title = (A statement that fulfills the conditions 1, 2, 3, and 4 of the problem to be resolved).

“Introduction” = (A union of statements with elements 1, 2, 3, and 4, that support and elaborate the title)

“Aims + Objectives” = (A list of statements of Aims corresponding to the elements 1, 2, 3, and 4: Plus a list of statements on HOW each of the listed statements as AIMS demands actions with corresponding basic elements)

“Method of Operation” = (For each of the objectives’ there is a list of ACTIONS having the basic elements 1, 2, 3 and 4 which if ADDED then the result is the accomplishment of the target objective’)

“Literature Review” = (All literature sources supporting and articulating the AIMS + OBJECTIVES and METHOD OF OPERATION where each source has a structure that corresponds with the basic elements)

“Limitations Analysis” = (The generation of a list of ALL requirements for achieving AIMS and OBJECTIVES as stated in the AIMS + OBJECTIVES’ function)

“Resources” = (An enumeration of entities whose utility meets the conditions stated after Limitations Analysis’)

“General Presentation Structure” = (The organization structure that outlines the list of ALL requirements for meeting the PROBLEM STATEMENT through executing the METHOD OF OPERATION’ and is supported by LITERATURE REVIEW’)

“Resource Management Strategy” = (The sequence of activities for executing the General Presentation Structure’ with consideration for Limitation’ and Resource’ availability; to satisfy the least cost requirement for utilizing any given resource under consideration)

“References” = (The list of entities consulted to help in satisfying ALL the conditions in AIMS and OBJECTIVES’ and Literature Review’)

After having all the elements of the dissertation proposal template defined as numerical functions the remaining task is that of operating on each function by inputting the problem statement and deriving an output that satisfies the function. The task is easily done by posing the generic question: “What does the function (f) under consideration, generate given the input of the problem statement P and the basic elements 1, 2, 3, and 4?

We now come to the point where we can know how to write dissertation proposal that satisfies the conditions implied by the dissertation proposal template, and the resonance conditions demanded by the basic elements as applied to each item in the dissertation proposal template. Hence by using the numeric function of the General Presentation Structure’ we can create a dissertation proposal outline of the draft dissertation proposal. Once we have the outline, we can then use descriptive language that makes good use of appropriate connector statements to create the first draft of our dissertation proposal.

Given the resultant draft, the next steps to be undertaken are those of checking the whole draft for:

- Logical consistency
- The credibility of the entire argument
- How effective the action plans generated are, and
- How feasible the solutions generated are likely to be considering the conditions posed by the problem statement

Once this iterative process has led to satisfactory results, we can be certain that dissertation proposal is likely to be approved. Or rather, we can be certain that the necessary conditions for gaining approval by your supervisors have been met, and that we can now make the final draft of our sample of dissertation proposal.

Since the intended document is a dissertation proposal rather than the entire dissertation, it is only necessary to state the most necessary and urgent reasons corresponding to the dissertation proposal template that is adequate for effective decision making and approval. This will help us to have a scope that is narrow enough to allow for critical thinking and for a deeper visualization of the dissertation making process.

The foregoing discussion has taught us about how to write dissertation proposal via basic numerical analysis, functions, and operations applied to the dissertation proposal template. This then helped us to generate a sample of dissertation proposal that is relevant, urgent, and effective in resolving the intended focus of the dissertation. The dissertation proposal has been created out of a problem statement derived from previous research that originated with basic research that stated the knowledge under consideration in abstract terms, then the research evolved into problem-oriented research and finally moved to the present level of solution creation.

At each level, care has been taken that the research is done and the results produced are limited in scope and are specifically limited to the four basic elements of the Pythagorean tradition that is also the traditional approach to knowledge creation and development. This, as we have shown is because the basic elements can be proven Numerically and that they provide a robust mechanism for accurate Numerical description and use in the case of creating functions that generate answers or solutions that are objective and easily demonstrable to others.

Therefore the above method is effective when coming to how to write dissertation proposal and is a resource when seeking ideas that fulfill the research requirements.