# Course: Mathematics for Statisticians

Course type: programme-based elective

Lecturer: Gregor Dolinar, Ph.D., Full Professor

Study programme and level | Study field | Academic year | Semester |
---|---|---|---|

Applied statistics, second level | All modules | 1st | 1st |

For the timeline see Curriculum.

Prerequisites:

- Enrolment into the first year of the programme.

Content (Syllabus outline):

Analysis and Linear algebra

- Sequences and number series.
- Functions (domain, range, continuity, limit).
- Derivatives (differentiation rules, geometric interpretation, applications of derivatives).
- Integrals (antiderivative, definite integral, applications of integrals).
- Function series (Taylor series).
- Functions of more variables (domain, range, partial derivatives and their applications, multiple integrals).
- Vectors (basic operations, scalar product, vector product, basis of the vector space).
- Matrices (basic operations, multiplication, rank, determinant, special kinds of matrices, eigenvalues, eigenvectors, linear transformations, similarity of matrices, square form).
- Systems of linear equations (Gauss method)

Probability

- Sample spaces, events, probability.
- Conditional probability and independence.
- Random variables, discrete and continuous distributions.
- Expectation, variance, moments.
- Joint distributions; distributions of functions of random variables and random vectors.
- Conditional distributions, conditional expectations.
- Convergence of random variables.
- Laws of large numbers.
- Convergence in distribution, central limit theorem.
- Estimating parameters of random variables distributions.

Objectives and competences:

The objective of this course is to provide the students the fundamental mathematical concepts, methods and principles indispensable for the study of statistics, and to unify the mathematical background of students coming from different first level university programmes.

Provide the students with computer skills to do mathematical calculations. The development of analytical thinking and careful and precise inference.

Intended learning outcomes:

Knowledge and understanding of basic concepts of mathematical analysis (including sequences, functions, derivatives, integrals, function series) and linear algebra (including vectors, determinant, matrices, systems of linear equations).

Acquaintance with the basic concepts of probability calculus.

The ability to analyze and give mathematical interpretation of fundamental statistical problems. The ability to apply mathematical concepts in real world problems.