Vyacheslav Savin: “Integration Is an Art”

On October 11, MEPhI will host the 1st All-Russian Interuniversity Speed Integration Championship “Integrate”. We talk about the idea of this competition and what is special about integration as a branch of mathematics with the organizer of the championship, senior lecturer at the Department of Higher Mathematics of the MEPhI Vyacheslav Savin.

Senior lecturer at the Department of Higher Mathematics of the MEPhI Vyacheslav Savin

- How did the idea of this championship come about?

- Generally speaking, we started holding such a competition within the university 4 years ago. Let me note: since the last century, an integration championship has been held at the Massachusetts Institute of Technology. At Moscow State University, integration competitions were also held at the relevant faculties. But at MEPhI, over the course of several years, our competition expanded to an interuniversity format.

- Why was integration chosen from different branches of mathematics?

- This question is not difficult to answer. Among other branches of higher mathematics that involve solving certain problems, integration is a separate art. If differentiation, that is, the inverse operation of integration, is a craft where it is known which algorithm needs to be followed in order to get to the answer, then each integral, regardless of its type, is a separate task, which in a short time, as we We assume it’s quite difficult to decide at the event itself, at the championship.

- So simply knowing algorithms is not enough?

- Moreover, as a rule, there are no specific algorithms.

- What qualities are required for successful integration?

- First of all, this is still knowledge of the table of integrals. You can't go anywhere without this. And secondly, probably, this is non-standard thinking, that is, the ability, in an extreme situation, in a short time, among all possible paths that at first glance seem simple, to find the right one and use it.

- In what application areas is integration used most fully and most often? Relatively speaking, when solving which problems will a MEPhI graduate have to deal with integrals?

- It is definitely difficult for me to answer this question, because there are a lot of these areas of science, technology, and life in general, in which integration is used in one way or another. Moreover, each of them is described by integration quite completely. It is widely known, for example, that almost all processes in the physical world, in the world of economics, in the world of demography are described by differential equations. And everything that is described by differential equations involves integration to find a solution to this very differential equation.

- Does winning this competition give you any privileges?

- The title of the best “integrator” of the “Integrate!” Championship, in my opinion, is the most important privilege, the most significant. This is, firstly. And yet, we are holding this championship, first of all, so that the guys feel the spirit of team competition within the framework of such an event for integrating speed, so that they get some pleasure, test their skills in extreme situations. Well, and secondly, from the point of view of awards, we promise not to offend anyone.