PREPARATORY CLASSES 2025

A. Basic Information

Note: The application deadline for the preparatory programming course has been extended to 1:00 PM on September 21, 2025.

The Faculty of Computer Science and Engineering, during the period од 15 септември до 26 септември 2025 , will organise preparatory classes in mathematics and programming. The preparatory classes are organised to help new students follow the first-year mathematics and programming courses more easily across all study programmes.

The preparatory classes provide an excellent opportunity for students to identify the prior knowledge required to master first-semester courses and integrate more easily into the educational process, as well as to supplement and refresh their knowledge of mathematics and programming.

The classes will be organised provided that a sufficient number of students register to form a group for each of the two courses.

It is planned that 4 to 7 hours of classes and practical sessions will be held each day. Classes will begin at 9:00 at the FCSE campus (the detailed timetable will be announced after candidate registration has closed).

The mathematics and programming classes will be delivered in a hybrid format, meaning that classes will be held on the Faculty premises and will also be available online via Microsoft Teams.

For the course in mathematics , a total of 40 hours is planned for the period од 15.9.2025 to 20.9.2025 година, while the course in programming will comprise 20 hours, during the period from 22.9.2025 година до 26.9.2025 година. The fee for attending the course in mathematics is MKD 5,000. The fee for attending the course in programming е MKD 3,000.

Студентите кои планираат да следат некој од курсевите (или двата) треба да се пријават најдоцна до сабота, 13.09.2025 до крајот на денот преку пополнување на following form.

Further information about the preparatory classes is available at the following email address: podgotvitelna@finki.ukim.mk

All students who register for the classes by the stated deadline ќе бидат известени најдоцна до сабота, 13.09.2025 година by a message sent to the email address entered in their application, informing them whether the groups have been formed and whether the classes will commence.

B. How to Apply

In order to attend the preparatory course, you must submit a payment receipt for the appropriate amount.

– 3000 denars for preparatory programming instruction (if you are only taking programming)

– 5000 denars for preparatory math classes (if you are only taking math)

– 8000 denars for preparatory instruction in programming and mathematics (if you have selected both courses)

The payment slip (available here) should contain the following information:

Inquiry purpose: preparatory course in programming/mathematics/programming and mathematics (depending on which course you will be taking)

Recipient title: RM Budget – UKIМ – Faculty of Informatics and Computer Engineering, Skopje

Recipient's bank: NBRM

Recipient's account: 100000000063095

account of a budget user: 1600161700 788 13

Income code and program: 723012 41

Payment slip (слика или документ за електронско плаќање) потребно е да ја испратите на podgotvitelna@finki.ukim.mkнајдоцна до 16.9.2025 (вторник) до 9ч (наутро) ако имате избрано математика или и двата курса, или до 20.9.2025 година ако имате избрано само програмирање.

For any questions, you can write to us at podgotvitelna@finki.ukim.mk.

V. Brief Summaries of Material for Preparatory Instruction

Brief outlines of the material covered in the preparatory mathematics and programming classes are provided below.

Details of the Mathematics Course

The mathematics classes cover significant portions of the material taught in primary and secondary education that are required in order to follow first-year mathematics courses more easily across all study programmes.

Description of the topics to be covered:

Topic 1: Basic Number Sets; Algebraic and Rational Expressions
- Basic number sets. Natural numbers: review of operations and laws, prime and coprime numbers, divisibility. Number systems, decimal and binary number systems. Integers: review of operations, ordering. Rational numbers: review of operations with fractions, decimal numbers, infinite decimal numbers. Real numbers: concept, geometric representation, ordering. Algebraic and rational expressions: exponents on natural numbers, operations with powers. Integral rational expressions: monomials, polynomials, operations, factoring, LCM and GCD. Fractional rational expressions: definition and operations.
Topic 2: Linear Functions, Linear Equations and Inequalities; Systems of Linear Equations
- Linear functions, linear equations and inequalities. Cartesian coordinate system in the plane. Real-valued functions: domain and range. Linear functions, behaviour and graphs. Linear equations in one unknown: solution, discussion and application. Linear inequalities in one unknown. Systems of linear equations: systems of two linear equations in two unknowns and equivalence. Methods for solving systems of two linear equations in two unknowns. Solving systems of linear inequalities in one unknown. Absolute value of a real number. Equations and inequalities involving absolute values.
Topic 3: Quadratic Equations and Inequalities; Powers and Roots
- Quadratic Equations: solving a complete quadratic equation, solving an incomplete quadratic equation, discussing the solutions of a complete quadratic equation. Quadratic Function (properties and graph) and a quadratic inequality with one unknown. Powers and Roots: a power with an integer exponent, a root (concept, expanding and contracting), taking roots of products and quotients, exponentiating and rooting a root, normal form of a root, irrational expressions. Rationalizing the denominator of a fraction. A power with a rational exponent.
Topic 4: Exponential and Logarithmic Functions; Trigonometric Functions
- Exponential functions: definition, graphs and properties. Logarithmic functions, logarithm rules and relationships between logarithms with different bases. Trigonometry: trigonometric functions of an acute angle; relationships between the trigonometric functions of the same angle; values of trigonometric functions for selected angles; solving right-angled triangles; definitions of the trigonometric functions (sine, cosine, tangent and cotangent) of an arbitrary angle; values of the trigonometric functions of an arbitrary angle.
Topic 5: Mathematical Logic
- Expressions. Operations with expressions and truth tables. Expression formulas and tautologies. Translating sentences from natural language into logical expression formulas. Expression functions: concept and solution of an expression function. Quantifiers. Axioms, theorems, proofs. Proving simple mathematical problems.
Topic 6: Sets; Combinatorics
- Sets. Subsets and equality of sets. Operations on sets. Induction. Combinatorics: combinations, permutations and variations. Binomial theorem.

Details of the Programming Course

The programming classes cover significant portions of the material taught in secondary education and also include methods for mastering algorithmic concepts more easily.

Topic 1: Algorithms and Programming; Integrated Development Environments
- The concept of an algorithm. Simple algorithms and the development of sample algorithms. Elements of programming environments: compiler, linker, debugger and standard-function libraries. Working with an integrated development environment: installation and an overview of the environment, including the main window and workspace. Creating a new project and adding a source file to the project. Building and running a project.
Topic 2: Introduction to the C++ Programming Language
- C++ syntax: alphabet, words, special symbols and comments. Quantities and data. Basic data types (char, int, float, double, bool). Expressions and statements in C++. Variables and their declaration. Structure of C++ programs. Operators in C++: arithmetic, assignment, increment and decrement (prefix and postfix), relational and logical operators. Input and output. Examples of simple C++ programs.
Topic 3: Sequential Structure; Developing Simple Programs
- Sequential structure and blocks of statements. Empty statement. Development of simple C++ programs.
Topic 4: Control Structures; Selection Statements
- Control statements: selection statements, iteration statements and jump statements. Selection statements: if, if-else and switch. Nesting if statements. Examples of C++ programs using selection statements.
Topic 5: Iteration Statements
- The while statement—implementation of the while-do control structure. Examples of using the while statement. The do-while statement—implementation of the repeat-until control structure. Examples of using the do-while statement. The for statement—implementation of the for-to-step control structure. Examples of using the for statement. Jump statements: break and continue.
Topic 6: One-Dimensional Arrays
- Низите како податочни структури. Декларирање на низа. Пристап до елемент на низа – индекси на елементи. Иницијализација на низа. Примери на C++ програми со примена на низи.

We wish you a successful teaching.