The course will cover the basic mathematical background needed for economics MA students and partly for social data science MS students. While our topic is the mathematical theory, albeit application oriented, still some applications in economics and data science will be touched.

**Course schedule and materials for each week:**

The course consists of 9 lectures and 9 problem-solving class. For data science students the first 6+6 lectures and seminars are mandatory. They will not cover higher dimensional calculus and optimization.

- Inverse matrix, determinant. Eigenvalues and eigenvectors. Basics of function calculus (continuity, differentiation, derived function). Functions of several variables, their graphs. Partial derivatives, gradients, total derivatives, chain rule. Level curves. (5+5)
- Basics of probability theory. (1+1)
- Implicit functions. Hessian of a function. Convexity, concaveness. Unconstrained and constrained optimisation. Shadow value.
*(3+3, only for economics students)*

Additional topics covered by individual work: complex numbers, operations with matrices, integral calculus

The students will learn the basic notions and results of calculus, real analysis, linear algebra, and probability theory. Emphasis will be placed on constrained optimization (only economics students). Students will gain expertise in using the theory in various, but simple contexts of economics and data science. Some expertise in problem solving will also be earned.

For economics students, there will be a final test at the end of the course, on the 18th of September. The passing threshold is 50%. For the social data science students, there will be a homework assessment at the end of the 12 sessions.