Бакалавриат
2024/2025
Линейная алгебра
Статус:
Курс обязательный (Международный бакалавриат по бизнесу и экономике)
Направление:
38.03.01. Экономика
Кто читает:
Департамент математики
Где читается:
Санкт-Петербургская школа экономики и менеджмента
Когда читается:
1-й курс, 2, 3 модуль
Формат изучения:
без онлайн-курса
Охват аудитории:
для своего кампуса
Язык:
английский
Кредиты:
6
Course Syllabus
Abstract
The course is oriented to the first-year students of the direction of Economics and Management, educational program International Bachelor's in Business and Economics. The aim of the course is to study the basic concepts, to learn the basic methods of Linear Algebra and their application to construct economic and mathematical models. The course covers the theory of matrices and determinants, the structure of solutions to systems of linear algebraic equations, linear spaces, Euclidean spaces, the theory of self-adjoint operators and second-order curves.As a result of mastering the discipline, the student should know the theory of solving matrix equations, elements of vector analysis and analytical geometry; be able to apply the apparatus of linear algebra in the problems of forming economic models and solving applied problems used in the courses "Mathematical Analysis", "Methods of Optimal Solutions", "Probability Theory and Mathematical Statistics", "Applied Statistics", "Game Theory", "Dynamic Systems in Economics"; have skills in solving systems of linear equations, performing operations with vectors and matrices.
Learning Objectives
- The objectives of learning the course "Linear Algebra" are the study of units of Matrix Algebra, the solution of systems of Linear Equations and Vector Analysis, allowing the student to navigate in such courses as "Probability Theory and Mathematical Statistics", "Methods of Optimal Solutions", "Mathematical Models in Economics". The course "Linear Algebra" is used in the theory and applications of multivariate mathematical analysis, differential equations, mathematical economics, econometrics. The content of the course can be used to design and apply numerical methods for solving problems from many areas of knowledge, for constructing and researching mathematical models of similar problems. The discipline is a model applied apparatus for studying the mathematical components of professional education of students of the Economics and Management.
Expected Learning Outcomes
- to construct and use equations of lines and planes
- to construct a set of solutions to systems of linear inequalities in the plane
- to apply inner product, cross product and triple product
- to analyze the sign-definiteness of a quadratic form using Sylvester's criterion
- to find the eigenvalues and eigenvectors of a linear transformation
- to build an orthogonal projection onto a subspace
- to find a fundamental system of solutions
Course Contents
- 1. . Systems of Linear Equations
- 2. Euclidean Spaces, Analytic Geometry
- 3. Linear Operators and Quadratic Forms
Interim Assessment
- 2024/2025 3rd module0.4 * Exam + 0.15 * Self-work + 0.15 * Test 1 + 0.15 * Test 2 + 0.15 * Test 3
Bibliography
Recommended Core Bibliography
- Fuad Aleskerov, Hasan Ersel, & Dmitri Piontkovski. (2011). Linear Algebra for Economists. Springer. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsrep&AN=edsrep.b.spr.sptbec.978.3.642.20570.5
Recommended Additional Bibliography
- Williams, G. (2019). Linear Algebra with Applications (Vol. Ninth edition). Burlington, MA: Jones & Bartlett Learning. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1708709