# Sylabus predmetu OPT136C - Optimization Methods (VŠPP - SS 2019/2020)

Čeština          Angličtina

Course code:
OPT136C
Course title in Czech:
Optimization Methods
Course title in English:
Optimization Methods
Mode of completion and number of credits:
Exam (6 credits)
Mode of delivery:
full-time, 2/2 (hours of lectures per week / hours of seminars per week)
part-time, 8/0 (lectures per period / seminars per period)
Language of instruction:
Czech
Course supervisor: RNDr. Michal Bejček, Ph.D.
Name of lecturer:
RNDr. Michal Bejček, Ph.D. (supervisor)
Mgr. Dana Sobotová (examiner, instructor, lecturer)
Prerequisites: none
Annotation:
The course covers theoretical tools for problem analysis and solving, mainly in the context of economic sciences. Students will become familiar with those aspects of Mathematics that are useful in dealing with important optimisation problems. The course develops the student's ability to reason logically and to correctly analyse and grasp the essence of practical issues. Emphasis is laid on understanding and on practical applications.

Course contents:
 1 Vectors, linear dependence and independence, vector space and its base. (allowance 0/0) 2 Addition of matrices, multiplying a matrix with a real number, scalar product of vectors, multiplication of matrices. (allowance 0/0) 3 The rank of a matrix, simplifying a matrix without changing the rank, computing the rank of a matrix. (allowance 0/0) 4 Systems of linear equations, Frobenius norm, matrix norm. (allowance 0/0) 5 Determinants, using determinants to solve systems of linear equations, Cramer's rule. (allowance 0/0) 6 Systems of linear inequalities, solving a system of two inequalities in two variables by graphing. (allowance 0/0) 7 Linear programming, solving model problems. (allowance 0/0) 8 Functions of two variables, domain of definition, patrial derivative. (allowance 0/0) 9 Local extrema of functions of two variables, examples of. (allowance 0/0) 10 Constraint local extrema, method of substitution, Lagrange's method. (allowance 0/0) 11 Global extrema of functions of two variables. (allowance 0/0) 12 Solving a traffic control problem using linear programming. (allowance 0/0) 13 Basics of graph theory, vertex of a graph, edge of a graph, degree of a vertex, walk of a graph, tree of a graph, spanning tree of a graph. (allowance 0/0)

Learning outcomes:
Expert knowledge; you should be able to:

- solve a system of linear equations using matrices and determinants,

- solve a system of linear inequalities graphically and explain its use in linear programming,

- describe the way of finding local extrema (also constraint extrema) of a function of two variables.

Expert skills; you should be able to:

- use the rank of a matrix to determine vector dependence or independence,

- solve a system of multiple equations with multiple unknowns using matrices,

- find local extrema (also constraint extrema) of a function of two variables.

General competences; you should be able to:

- understand and appreciate the importance of Mathematics in everyday life,

- show how to implement the acquired aspects of Mathematics in your own field of study.

Input knowledge:
No preliminary courses precede this course in the curriculum.

This course assumes basic skills in high school Mathematics.

Learning activities and teaching methods:
Revise regularly using relevant lecture notes and the recommended materials. Complete assignments conscientiously and, if needed, request an appointment with the lecturer. Try to deal with the problems considered during the lectures and tutorials on your own as a homework assignment. Mastering basic definitions, equations, and algorithms is essential.

Rámcové podmínky zápočtu:
The pass mark for the final test is 50%.

Rámcové podmínky zkoušky:
The examination is oral and covers the following: The examination is oral and covers the following: - Basic vectors, vector space and its base. - Matrix addition and multiplication. Rank of a matrix. - Solving systems of linear equations using martices, number of solutions. - Determinants, Cramer's rule. - Solving systems of linear inequalities graphically. - Functions of two variables, local extrema. - Constraint local extrema, substitution methods, Lagrange's method. - Basic graph theory.