Why do managers need advanced mathematics?

Mr Zenkevich, why do applicants have to take the Unified State Examination in mathematics when seeking to pursue the "Management" speciality?

All applicants seeking to study at St Petersburg University should know that here they will receive a fundamental university education that implies acquiring a certain thinking paradigm depending on the selected field of study: based on mathematics in the field of mathematics, based on physics in the field of physics, etc. If young people study at the Graduate School of Management at St Petersburg University, they acquire an interdisciplinary mode of thinking. The field of management implies synthesis of multiple sciences and disciplines including comprehension and use of mathematical methods, models and tools. This is related to the major way of solving managerial problems, which includes working within interdisciplinary groups of specialists formed depending on the specific task.

How are mathematics and management related to each other? Will graduates really need mathematical theories and models?

Managers are different. Let us consider lower-level managers, for example, front shop managers or bank front line manager. Do they need advanced mathematics and mathematical methods? I am not sure. They have to be able to organise the work in the front space, answer customer’s questions and accurately perform the orders of their supervisor. The Graduate School of Management does not provide training for such managers. We train future leaders for subdivisions of large-scale Russian and international companies, directors and owners. At this level, management solves practical tasks of corporal governance. Imagine that a certain business has a problem and problems are always related to management. A manager who is not trained to use analytical and mathematical tools approaches it simply by formulating recommendations to a solution. We see this superficial approach all around. However, in order to really solve the issue, one should understand it, perform experimental research, analyse techniques, approaches and methods of solving it, formalise the task, conduct quantitative modelling, analyse the results, draw conclusions, and only then give recommendations stating the limitations on applicability and risk assessment instead of doing experiments on the business.

What managerial decisions require the use of mathematical modelling most often?

The main function of managers is taking decisions in the sphere of their functional responsibility. There are routine decisions that imply efficient information collection and the use of standard techniques. There are also non-standard but repeating tasks, for example, selecting a supplier, organising shipment, and production decisions to name just a few. Mathematical and further quantitative modelling is most effective for these recurring issues. Another sphere of mathematical (quantitative) modelling application includes strategic decisions that define the company economy in the mid-term and long-term period. In other words, mathematical modelling is required when the cost is high.

The Graduate School of Management at St Petersburg University trains top managers. Can graduates count on such positions immediately upon graduation?

No one will be accepted for a top manager position in a large company immediately after graduating from any business school. Any graduate has to go through certain stages in any case. However, if a young specialist is restricted in possibilities to use modern business analytic tools intelligently including mathematical modelling and information technologies, they will soon reach the ceiling of their career due to the lack of competence. This is not a verdict, since there are many different forms of further advancing their qualification. After the bachelor’s programme, one can pursue a master’s programme. If you are already taking a managerial position, you can enter MBA or EMBA programmes. If you want to become a competent manager, you will get to this point one way or another.

Can a top manager delegate everything related to finances and calculations to experts and specialists?

I would rephrase your question in the following way: can a top manager delegate decision making? Why do you need such a top manager then? Top managers are in charge of taking decisions. Specialists including mathematicians can efficiently help to develop the tools that support decision making. They can help, but they are not responsible for the ultimate result. For example, a top manager has to take a decision that will be assessed based on two criteria: profit (preferably, maximal) and costs (preferably, minimal). There is no universal answer. It is the top manager who has to choose the best option from a variety of efficient solutions. Another example is when the decision is taken in the situation of unpredictable impact from external conditions. Here, there is also no universal answer. In this case, the manager has to understand that all the suggested models are subjective, since they are based on a subjective understanding of the impact caused by external conditions. It is therefore the top manager who has to choose an optimal decision and take responsibility for the consequences related to uncertainty.

Can you please tell us about the role of mathematics in research?

Any scientific research is based on the use of scientific methods. In its turn, any scientific method has certain stages: formulating and determining the problem; formulating a hypothesis; holding experiments if necessary; creating models; collecting data; and verifying the model. Modelling is therefore one of the main elements in applying scientific methodology. In the era of information technology, in 95 % of cases, modelling implies quantitative modelling that comprises implementation of a mathematical model designed in the form of software. Currently, this approach provides valid scientific and practical results.

How much mathematics will students have during their studies in the bachelor’s and master’s programmes?

Students of the Graduate School of Management at St Petersburg University study mathematics precisely in the required amount. In the first term, students will take a traditional course in advanced mathematics: mathematical analysis, algebra and geometry (Mathematics I). In the second term, students take only the course in the probability theory required to model the influence of external conditions in case of risks during the decision-making process (Mathematics II). In the third term, there will be a course in statistics (Mathematics III). Statistics including mathematical statistics is a fundamental basis to conduct empirical research in economics and management. A mandatory discipline of "Econometrics" is delivered in the "Public Administration" programme being optional in other fields of study. In the fourth term, all bachelor’s programmes include the mandatory course "Quantitative Methods for Decision Making" based on the Management Science discipline. Additionally, students can take various elective courses that use mathematical methods and tools. Students select their major after the second year. Quantitative methods and mathematical models are used in finances, logistics and even marketing and human resources management. "Mathematics I" provides a foundation for such disciplines as "Microeconomics" and "Macroeconomics". Where else is mathematics required? It is used in writing term papers and graduation projects, for which quantitative modelling is a necessary element to develop and propose further solutions and recommendations.

What makes you confident that students have the right amount of mathematics?

This year, the Graduate School of Management at St Petersburg University have created an interdisciplinary working group that monitors and improves the teaching process for disciplines and courses on mathematics and mathematical modelling. The studies of mathematics have two purposes: forming a mathematical approach within the framework of interdisciplinary thinking; and providing for the curriculum disciplines that use mathematical methods and tools. The major current issue is to find out how we can make it possible for students to master the required competencies and tools in mathematics that will be further applied during the studies and in practical work in the course of extremely limited number of academic classes.

Is the school level of training enough to keep up with mathematics during the studies?

It is certainly easier for the students with high grades in the Unified State Examination. However, I believe that any student enrolled in our programme is capable of mastering all disciplines in the curriculum. Some students may require to take more efforts in the first and second terms to pass the interim assessment. The most important thing is to have a desire to master mathematical disciplines in the required amount and perform all the mandatory tasks in due time. However, problems may arise if a student is poorly trained and has no such desire.

What about those young people, for whom mathematics is hard? Should they pursue the programme and further career in management?

If a person does not like mathematics, but wants to become a manager of the level that the Graduate School of Management trains at St Petersburg University, they should understand the need in this knowledge and learn to overcome difficulties. Lack of appreciation towards mathematics is usually related to the lack of proper training. On the contrary, if you understand why you need it, you will be able to fill the gaps in knowledge and master the required skills.

Are there any additional disciplines in mathematics?

There are elective courses. For example, I deliver an elective course in "Game Theory" attended by those who want to attend it and sign up for it. Game theory is a theory of mathematical models of decision making in the situation of conflict between the sides. We are planning to introduce other elective disciplines in applied mathematics: applied models of mass service, and mathematical experimental methods to name just a few. This is a complicated process, though, and the curriculum possibilities are limited.

How is mathematics represented in extracurricular activity of students?

I will give only one example. The Graduate School of Management at St Petersburg University has a joint project with the Faculty of Applied Mathematics and Control Processes at St Petersburg University that we started in 2007 and have continued till the present moment. It is related to organising and holding the annual international research conference "Game Theory and Management". This project has enabled us to form sustainable scientific ties with renowned specialists in game theory as well as with domestic and international journals in the field. Students take part in the conference both as speakers and as audience. In particular, some of my students including bachelor’s students, but mostly master’s students managed to obtain significant research results in their master’s dissertations and graduation papers with the use of game theory modelling. They have presented their results in front of serious high-status academic audience including the stars of modern science and Nobel laureates.