Mathematics is a method and language of cognition of the surrounding world. Mathematics is an exact science that does not tolerate arbitrariness in interpretation and various speculations. This is the embodiment of order and rigid logic. It helps to understand the world around us, to learn more about its laws, since these laws are subject to the same order that prevails in mathematics. One way to understand universal mathematical laws is to write a study on this subject. In this article, we will explain how to do this and what mistakes to avoid.
Studying mathematics, students:
Basically, every math project writing is carried out according to the four following stages:
1.Preparation. Defining the theme and goals of the project.
3.Research. Information gathering, solution of intermediate tasks. Basic tools to use are:
4.Results and (or) conclusions.
Let’s find out in detail what should you do on each stage of your paper writing in order to make it well-researched, structured and logical.
In order to begin research, you need to find a problem that you can investigate and that you would like to solve. This problem will tell you how to formulate a research topic. The ability to see the problem is sometimes valued higher than the ability to solve it.
The main task of any researcher is to find something unusual in the ordinary, to see the difficulties and contradictions in those things where for others everything seems habitual, clear and simple. The easiest way to develop the ability to see problems is to learn to look at the same objects from different points of view.
The crucial stage in the preparation of the study is the stage of justifying the relevance of the topic. To substantiate the relevance means to explain the necessity of this topic in the context of the general process of scientific knowledge. Justifying the relevance of the chosen topic, you should indicate why this particular mathematical problem is currently relevant. The relevance may consist of the need to obtain new data and the need to test new methods, etc.
Justifying the relevance, it is necessary to briefly highlight the practical reasons and difficulties for which the study of this topic has become necessary.
Once the mathematical problem is found and justified, the researcher can begin to develop a hypothesis. Translated from the ancient Greek language, the hypothesis means “the basis, the assumption, the judgment about the natural connection of phenomena”
The hypothesis must satisfy a number of requirements:
The hypothesis is formulated as a complex sentence: ‘if …, then …’. Such a formulation should direct the attention of the student to the disclosure of the essence of the phenomenon, the establishment of cause-effect relationships. In the course of the experiment (or using another scientific method), the hypothesis is refined, supplemented, developed or rejected.
Before finding the list of references online, follow this algorithm of actions:
The specific content of the main part of your work depends on the type of mathematical research, which can be:
This type may include computational-graphic works or case studies, which imply, for example, the development of a physical model or the solution of a specific mathematical problem.
If your task is to do theoretical and analytical research, then the started research is developed in the main part. In this case, the main part of the work is the in-depth continuation of the problem analysis based on the theoretical framework tools (the methods listed in the introduction). This can be a comparison and detailed consideration of the views of different scientists and authors in order to substantiate their own point of view, which will be demonstrated in the conclusions.
You should start the main part of this study by listing the tasks indicated in the introduction. Then propose ways to solve them and describe the results of the application development. As a confirmation of the effectiveness of the methods, data of experiments, observations, as well as illustrations and help on implementation are systematized using tables, graphs, diagrams.
Usually, such works are written by future engineers, technologists, in order to suggest ways to improve the subject of research or to develop an independent project from scratch. In this case, the main share of the main part of the work consists of drawings, formulas, calculations, dependency graphs, and the like.
Of course, mathematical research is impossible without mathematical calculations. However, the main task of the student is not only to make the correct calculations, use the necessary formula or approach, but also to be able to explain his choice with words. Therefore, when you write a study in mathematics, you must explain each of your actions logically, using mathematical terms, and do so in such a way that the reader cannot make a double interpretation of your words. Explain each point from the new line and make sure that your paper is convenient to read and perceive. It is not recommended to use arrows when you move from one step to another, just write about your intentions with the help of the words.
To better understand the basics of the correct approach to writing math research, we consider the most common mistakes of students who lead them to a dead-end and do not allow them to test their hypothesis in the right way and get the correct result.
Of course, math research writing cannot be easy because you face two tasks at the same time – to calculate correctly and to write properly. Be sure to follow the right scientific methods and use up-to-date sources, and this will facilitate achieving your goal several times.