Study program / study programs: INFORMATION TECHNOLOGY, E-BUSINESS, INFORMATION SYSTEMS

Type and level of studies: Undergraduate applied studies

Subject: COMPUTER MATHEMATICS

Status: Compulsory

ECTS credits: 8

## Course objective

The objective of the Computer Mathematics course is mastering algebra, mathematical analysis, the basics of differential and integral calculus and discrete structures, which is of fundamental importance for computer sciences. This knowledge will allow future IT experts and IT managers to design mathematical models in programming projects and the implementation in information technology. Closely related to algorithms and data structures, discrete structures are an integral part of the necessary mathematical foundation for future IT experts.

## Course outcome

Through lectures, exercise and individual work on problem solving, the students will be able to define and create truth tables for the basic logical operations (functions), to differentiate between and properly implement universal and existential quantifier, describe logical functions, to solve problems requiring the connection between logic, sets and algebra, to define set union, intersection and difference and solve problems involving these set operations, to find the Cartesian product of sets, to define a function as mapping, to differentiate between one-to-one mapping (injection), NA (surjection) and bijection, to define the limit value of a function, to define the asymptotes of a function using limit values, to be able to prove identities by mathematical induction, to perform tasks using the binomial formula, to be able to represent sets of real and imaginary numbers on coordinate axes, to define vector values, to differentiate between vectors and scalars, to be able to add and subtract vecords and multiple them by a scalar, to define a definite integral and solve problems with definite integral, to define arithmetic and geometric sequence, to perform computational operations with sequence limit values, to define d’Alembert’s,Cauchy’s and Leibniz’s criteria for series convergence, to define differential equations, to recognize the type of a differential equation, to solve differential equations.

## Course content

Theoretical classes:

• Functions
• Mapping
• Fundamentals of mathematical logic
• Relations
• Operations
• Proving techniques
• Mathematical induction
• Linear algebra
• Matrices
• Determinants
• Vector algebra
• Polynoms
• Limit value of a function
• Continuity of function
• Differential calculus
• Derivative – concept and characteristics
• Function differential
• Function derivatives of several variables
• Integral calculus
• Indefinite integral
• Integration methods
• Definite integrals, using definite integrals
• Series
• Functions of several variables
• First and second order differential equations