Магистратура
2019/2020
Научно-исследовательский семинар Магистерской программы 2
Лучший по критерию «Полезность курса для расширения кругозора и разностороннего развития»
Статус:
Курс обязательный (Математика и математическая физика)
Направление:
01.04.01. Математика
Кто читает:
Факультет математики
Где читается:
Факультет математики
Когда читается:
2-й курс, 3, 4 модуль
Формат изучения:
без онлайн-курса
Прогр. обучения:
Математика и математическая физика
Язык:
английский
Кредиты:
3
Контактные часы:
42
Course Syllabus
Abstract
This discipline belongs to the cycle of disciplines of theoretical education and the block of elective disciplines. The study of this discipline is based on the following disciplines: • basic courses in algebra and mathematical analysis; • course of the theory of dynamical systems; • courses of Hamiltonian mechanics and classical field theory; • partial differential equations course; • course of foundations of quantum mechanics.
Learning Objectives
- Acquitance the students with the most important physical principles and models, research methods and mathematical structures of modern theoretical and mathematical physics
- Experiencing with the algebraic and analytical machinery of modern mathematics, development of physical intuition and problem-solving skills, as well as the construction and study of mathematical models of physical phenomena
Expected Learning Outcomes
- understanding of the basic physical principles and mathematical models, become proficient in the mathematical technique used for the analysis of such models, including methods of representation theory and integrable systems, the technique of generalized functions, functional integration, methods of string theory and gauge theories
- possessing the skills of independent analysis of mathematical problems, show readiness for a creative approach in the implementation of scientific and technical problems, based on the systematic updating of acquired knowledge, skills and abilities and the use of the latest achievements in the field of mathematical physics; improvement of skills in scientific discussions and presentations at scientific seminars
Course Contents
- Supersymmetry and supersymmetric field theories. Superfield formalism
- Integrable models of statistical physics: Ising model and ice model
- The Yang-Baxter equation. Basics of the theory of quantum groups and the Bethe algebraic ansatz method
Bibliography
Recommended Core Bibliography
- Reed, M. (1972). Methods of Modern Mathematical Physics : Functional Analysis. Oxford: Academic Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=567963
Recommended Additional Bibliography
- Dubrovin, B. (1994). Geometry of 2d topological field theories. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsarx&AN=edsarx.hep-th%2f9407018