A candidate dissertation is always a qualification work. You defend a job in which you show your qualifications. This does not have to be some breakthrough in science, practice. But sometimes this concept - qualification work - is somehow simplified. It is believed that if you wrote several formulas or 150 pages of reasoning, the qualification work is ready and you can go to defend it. However, it is not. In any case, the Ph.D. thesis should contain at least a new look at some well-known statements of problems or some new solutions. Why do people even defend dissertations?
Who should set the tasks and how? This is a crucial issue. Graduate students and masters themselves do not know how to set tasks, this is a normal phenomenon, you don’t need to be surprised and worry about this. The ability to set goals we'll always come with experience. To be able to set goals well, you need to work hard. Therefore, we are faced with two problems here: the choice of the supervisor and the choice of the topic of the dissertation.
The choice of supervisor. You need to choose managers who have the time, opportunity and interest in you and your work. A graduate student or a master’s student, who is left to chance, find themselves in a very bad situation precisely because they do not know how to set tasks. For self-sufficient people, there are other recipes. The leader for them should be a super professional in their field, this is a person from whom to learn. I now understand that they just watched me “floundering” from the side, it was a harsh school of life if it comes up, it’s worth doing. Then they dealt with me and dealt a lot.
Now about the tasks.
The problem is a little different. It is known what is given, but what we get is far from known. Moreover, apparatus and equipment are often unknown. They have to invent a problem or modify some existing ones. Where the problems come from and how they are solved, many books have been written on this topic. Another model of threshold aggregation also occurred to me when several years ago a situation was shown on television when several houses in. The perception quality of a television program depends on two parameters: sound and image quality. If we summarize these two parameters, then image degradation can be compensated for by an increase in sound level. It is clear that the more the image quality deteriorates, the more you need to increase the sound, which, of course, is wrong. In those areas where I understand something, for example, in the theory of aggregation, one cannot pose the problem to a graduate student: to develop a general theory of non local aggregation operators. This is not a problem, it is a good intention. In my opinion, these are not scientific topics at all, so we will not talk about them.
Every dissertation is the expenditure of some intellectual and physical resources. Never waste time on 'narrow' topics that are of no interest to anyone. You can not spend time on a dissertation, which will become obsolete before you have time to defend it, you cannot spend time on a dissertation, which will go to the shelf and be forgotten in six months. Always try to choose the right balance of work value and effort. Any dissertation is an expended effort. Once, one of my co-authors decided to do a job on car sales; he was ordered by the association of car dealers. He worked on this topic for some time, analyzed sales, built a regression model, and before handing it over to the customer, he told me what he had done. I told him that everything worked out well, but macro factors that affect the economy as a whole were not taken into account. Therefore, if now something “sways” in the system, everything can change.
Less than a week passed, a crisis happened, and all these regression models turned into nothing. I want to warn you, do not deal with models that turn into nothing in an instant.
There should be an element of fundamentality in the work, do not just do technical work, substitute values, substitute parameters, the computer calculated, received some conclusions. You see, there must be some new look at the problem, this is not necessarily some kind of breakthrough in science, but at least something new must be. And fundamentality is achieved very simply - we need models, even quite simple ones, but there must be models. This applies to any sciences, not only mathematics, economics, political science, there should be new models in the work, leading to new views. Very often the tasks to be solved arise from the needs of the practice.
Planning effort and time.
Problem-solving is always a waste of time. And graduate students often can not do science, need free days. There was such a load in this company that when she came tired of me in the evening, I understood that I was telling her something, but she did not perceive anything. I can not deal with graduate students in this mode. Moreover, your output at such a load will be zero.
Today you are investing in yourself, defending dissertations. Therefore, arrange with the employer that you have one free day a week, that you go to the library and do science 16 hours that day, then there is some chance.
Balance effort and time spent. There is such a problem in mathematics about the dimension of a partial order. A year of intensive work on this problem and I still use the knowledge gained during the solution of this problem, and only 1 page of results was included in the dissertation online.
Analysis of publications. The most important thing for all graduate students: you need to read a lot, if you do not read, you cannot pretend that you know something in your field. You need to view all the major magazines and, most importantly, books. It takes time. A dissertation without a good, qualified review is not a dissertation.
The structure of the dissertation. Firstly, never write an autobiography, do not write how you came to the results, you should state the theory, and not how you came to this. A dissertation, on the contrary, may contain a solution to several problems. This shows a person’s qualifications in various naturally related fields.
Annotation. I have been taught many times that they read the annotation first, then read the introduction, then read the conclusion and after all, this, if you like it, begins to read the text. Therefore, annotation and introduction should be extremely clear and well built. In this case, there should be a clear and concise description of what you have done and the place of your task in the class of tasks to which it relates. The person reading this text must understand where your dissertation fits.
Now, the abstract. The abstract repeats the structure of the dissertation, everything should be more concise, the only feature that I do not understand in my abstracts is why it is impossible to refer to other people's works.
