Research paper

Mathematics

A Mathematics research paper is a qualitative work of scientific content that should correspond to the current level of the science development and the needs of the national economy, while its theme should be relevant. A research paper is the first step in research, scientific, and pedagogical activity leading to the graduate studies and preparation of a Ph.D. thesis. It is not yet an academic degree, but a level of academic training which indicates that the high school graduate possesses the skills and qualities inherent to a novice scientist. The writing of a research paper should be not only a solution to scientific problems but also an indication that its author studied a scientific problem independently and can recognize the professional issues and comprehend the general methods of its resolution.

When conducting the research, the student demonstrates the ability to apply the knowledge gained in practice. Regarding special training, it is intended to show how the student mastered a set of disciplines curriculum. At the same time, the correspondence of the received education with the professional qualification characteristics and the specialty is revealed when the undergraduate writes the mathematics research paper.

The preparation of a mathematics research paper involves solving the following tasks:

- Systematization, consolidation, and expansion of theoretical and practical knowledge obtained from the disciplines of technical direction and application of this knowledge in solving some specific scientific and production tasks;
- Conducting bibliographic work with the use of modern information technologies;
- The ability to critically evaluate and generalize theoretical positions;
- The ability to use legislative, normative, and instructional materials, and to critically understand the data of literary sources and documents of practice on the chosen topic;
- The ability to systematize and generalize the data of statistical collections and materials of business entities;
- The development of the author’s proposals for the improvement of the phenomenon or process;
- The development of the skills necessary for the independent work; improvement of skills in applying scientific knowledge methods to solve problems given to present in the research paper;
- Developing the skills of a public discussion, defending the personal scientific ideas, proposals, and recommendations;
- The presentation of the research results.

The mathematics research paper is characterized by an in-depth theoretical study of the problem, the presence of scientific originality, and the practical significance of the study. Depending on the nature of the research conducted, the subject of mathematics research papers can be worded as follows:

Tired of all the guides and never-ending instructions?

- The presence of an integrated theoretical approach regarding the study of the research object; student develops the methods of solving the problem associated with the subject of research;
- For the topics of practical orientation, scientific originality is determined by the results of the study obtained for the first time or as the development of previously formed experimental approaches.

The elements of originality that might be presented in the mathematics research paper include the following:

- The research object that is little investigated or isn’t investigated at all;
- The new production of known problems or tasks;
- The original usage of solutions or methods;
- The new application of a known solution or method;
- The original conclusions from the well-known theory in the new conditions;
- The new experimental results and their consequences;
- The new or improved criteria, indicators, and their justification;
- The development of original models of processes and phenomena; the data obtained from their use.

The topic for a mathematics research paper should reflect the specifics of the curriculum and correspond to the direction of research. There is also an option to work on the related topics.

- Economic-Mathematical Modeling in the Management of Enterprises in the Recreational Sphere;
- Modeling and Analyzing Adaptive and Rational Expectations at Different Levels of Management;
- Mathematical Methods and Models of Economic Development Analysis on the Macro-Economical Level;
- Modeling and Analyzing The Adaptive and Rational Expectations on Different Levels of Management.;
- 10 Mathematical Methods and Models of Analysis of the Processes in the Enterprise’s Innovative Development.

- The History of Mathematics as a Science;
- Mathematical Modeling as a Way to the Innovative Future;
- The Mathematical Prognosis as an Inseparable Component of the IT Sphere;
- 7 Famous Mathematical Investigators;
- The Impact of Mathematical Algorithms on Human’s Life.

Bad topics are considered to be too broad or too frequently explored. Look at the list and decide if it will be interesting for you to read a research paper on those topics. Build on this point – choose only that topic that is of interest for you as a researcher.

The selection of literature should begin immediately after selecting the topic of work. Textbooks, manuals, monographs, periodicals, legislative acts, collections of scientific articles and conference materials, databases, and reports from official Internet sites can serve as sources of information to write the mathematics research paper. When analyzing data, the student must follow the following recommendations:

- First of all, the literature should be considered to reveal the theoretical aspects of the subject under the study. The list includes monographs, textbooks, magazine articles, and the instructional materials;
- When studying the literature, there is no need to seek to master all the information, but only select the one that has a direct bearing on the topic of the work; the criterion for evaluating the read is the possibility of its practical use in the work;
- It should be guided by the latest data on the problem, relying on the most authoritative sources, including professional periodicals;
- Specify precisely where materials are taken from;
- The quotations are used to distribute the opinion of the author of the source without distortion and to identify the views when comparing different ideas.

However, the number of quotes should be optimal and determined by the needs for the development of the topic. Their large number can be perceived as an expression of the weakness of its author’s position. The material of mathematics research paper should be presented in a dense, holistic, and logical sequence, with the observance of linguistic rules.

- Schwartz, Judah L. “Can technology help us make the mathematics curriculum intellectually stimulating and socially responsible?.”
*International Journal of Computers for Mathematical Learning*4.2-3 (1999): 99-119. - Piggott, Jennifer. “Mathematics enrichment: What is it and who is it for?.”
*Paper presented at the British Educational Research Association Annual Conference.*Vol. 1. 2004. - Rihan, Fathalla A., and Bassel F. Rihan. “Numerical modelling of biological systems with memory using delay differential equations.”
*Applied Mathematics & Information Sciences*9.3 (2015): 1645. - Ho, Kwok-Pun. “Hardy-Littlewood-Pólya inequalities and Hausdorff operators on block spaces.”
*Math. Inequal.*Appl 19 (2016): 697-707. - Yanisko, Emily Joy. “Negotiating perceptions of tracked students: Novice teachers facilitating high-quality mathematics instruction.”
*Journal of Urban Mathematics Education*9.2 (2016).

The introduction reveals the essence of the problem, the elements of scientific novelty, the relevance of the topic, the necessity of its research, the source data for the development of the subject, the purpose, the object, the methods of research, and the practical value of the mathematical research. The names of scientists and practitioners whose works include the issues under consideration and the chosen research methods are mentioned briefly.

It is advisable to construct an entry with the coverage of the following elements:

- The urgency of the topic is determined by a critical analysis and comparison with the known approaches for solving this problem, justification of the importance of work for the development of a particular industry;
- The purpose of the study is to predict the results and determine the optimal ways to solve problems in the selection of the research methods;
- The objectives of the study are identified by the goal and detailed ways to solve the problem.
- The subject of research is a process that is studied within the object of investigation;
- The object of research is a process or phenomenon that generates a problematic situation and examines the subject of research in all its interrelations;
- Research methods are a way of gaining reliable scientific knowledge and practical skills in different spheres of activity;
- Information about the use of information technologies, standard, and author’s software (as a rule, the author indicates that a set of tasks for the automation of analytical and predictive calculations on the PC has been developed using MS Excel);

The bulk of the work consists of sections and divisions (if necessary – items). The main text of each section is preceded by a brief description of the chosen direction and the justification of the research methods used in this section. At the end of each section, it is recommended to formulate conclusions with a brief statement of the scientific and practical results presented therein. Each section begins with a new page. The first section of mathematics research paper should be of a theoretical nature and contain several paragraphs. The section covers the analytical substantiation of the problem being studied, examines its essence, significance, classification characteristics, history, current trends of the subject of research, and methodological approaches. The disclosure of theoretical issues should have the elements of scientific originality with the formation of their position on the research issues, contain the author’s suggestions on improving the definitions of individual terms, supplementing the classifications, and clarifying the methods.

It is advisable to illustrate text with the graphic materials – charts and graphs. It is also recommended to use the modern literary sources devoted to the problems studied in work: monographs, scientific articles, conferences materials, and Internet publications. It is obligatory to compare the points of view of representatives from various mathematical schools. The same is about the use of statistical data with a mandatory reference to the sources. The volume of the first section should not exceed 30% of the total size of the mathematics research paper. Its second section has an analytical and researching character and consists from two to three points. All calculations, tables, graphs, and charts in the mathematics research paper accompany the interpretations and conclusions that allow to determine the nature and the state of the phenomena and processes under investigation, to disclose their peculiarities and trends of development, and to create a basis for identifying the unused reserves for the improvement of the research.

If possible, the text is illustrated with the real documents (placed in applications and accompanied by a brief commentary). The sources of information are the planned and actual performance indicators, statistical, financial, tax, and management reporting, orders, primary informational materials regarding the individual business processes, observations, surveys, and other methods of collecting the primary information. It is mandatory to use modern information technology during completion of the mathematics research paper and apply the software for the mathematical calculations. In the case of the use of standard application software, the student reveals the features of its application, necessary revisions, and settings, especially the preparation of input data and interpretation of output results. A general concept should be given in the case of the development of the author’s software for mathematical operations. The information and methodological support are also to be provided together with the description of the algorithms and circuits of the computational process, the form of the source documents (tables, diagrams, graphs), and the requirements for the use of the established software.

In the third design and advisory section of the mathematics research paper it is necessary to put forward proposals on the prospects for the development and improvement of the selected research object (as a whole or its separate structural units) basing it on the principal theoretical positions, methodological approaches, and tools set forth in the first section. The results of the analysis carried out in the second section of the paper should also be taken into account. Such proposals should be reasonable and based on the relevant forecast calculations. The student could indicate which economic and mathematical methods, models, and software tools are used or will be appropriate in the future. It is advisable to cite the results of questionnaires conducted among other students and the results of the expert assessments organized by the student-author. The volume of the third section is 30-35% of the total size of work.

In the conclusions, the student needs to outline the results of the research on the mathematical subject, to indicate the obtained scientific and practical novelties, and to give recommendations for their experimental and efficient use. In this part of the mathematics research paper, the writers present their suggestions for solving the problem issues of the relevant research object. The conclusions should be based on the materials of the paper’s central part. The presentation of the content of each issue in the mathematics research paper should be demonstrative, explanatory, and scientifically substantiated. The theoretical positions should be based on the real and precise materials with the typical examples.

Appendixes to the mathematics research paper must contain informational materials that are the basis of analytical research on the chosen topic and appear on the latest pages. It is also advisable to provide the supplementary material necessary for the fullness of the paper. It includes:

- The real accounting and management documents related to the research object and statistics;
- Some intermediate mathematical proofs, formulas, and calculations;
- Some tables of auxiliary digital data; instructions and techniques (full or extracts from them);
- The description of algorithms and programs for solving the problems on PC developed in the course of completion of a mathematics research paper;
- Some illustrations of auxiliary character.

Make final touches in your research paper and submit it with confidence, “I am submitting a good research paper in Mathematics. Pythagor would appreciate my work”. If you follow all the maths research paper writing tips from this guide, your instructor will surely be proud of you. Arm yourself with patience and impress everyone with your research paper in Mathematics.