{"id":17798,"date":"2020-09-05T12:00:00","date_gmt":"2020-09-05T10:00:00","guid":{"rendered":"https:\/\/newsite.finki.ukim.mk\/announcements\/informacija-za-podgotvitelna-nastava-po-matematika-i-programiranje\/"},"modified":"2020-09-05T12:00:00","modified_gmt":"2020-09-05T10:00:00","slug":"informacija-za-podgotvitelna-nastava-po-matematika-i-programiranje","status":"publish","type":"announcement","link":"https:\/\/finki.ukim.mk\/en\/announcements\/informacija-za-podgotvitelna-nastava-po-matematika-i-programiranje\/","title":{"rendered":"\u0418\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u0458\u0430 \u0437\u0430 \u043f\u043e\u0434\u0433\u043e\u0442\u0432\u0438\u0442\u0435\u043b\u043d\u0430 \u043d\u0430\u0441\u0442\u0430\u0432\u0430 \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u0438\u0440\u0430\u045a\u0435"},"content":{"rendered":"

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\u041f\u0440\u0435\u0434\u0432\u0438\u0434\u0435\u043d\u043e \u0435 \u0434\u043d\u0435\u0432\u043d\u043e \u0434\u0430 \u0441\u0435 \u0440\u0435\u0430\u043b\u0438\u0437\u0438\u0440\u0430\u0430\u0442 \u043f\u043e 6 \u0447\u0430\u0441\u0430 \u043d\u0430\u0441\u0442\u0430\u0432\u0430 \u0438 \u0432\u0435\u0436\u0431\u0438 \u0432\u043e \u0433\u0440\u0443\u043f\u0438 \u043e\u0434 \u043f\u043e 18 \u0434\u043e 32 \u0441\u0442\u0443\u0434\u0435\u043d\u0442\u0438. \u041d\u0430\u0441\u0442\u0430\u0432\u0430\u0442\u0430 \u045c\u0435 \u0441\u0435 \u0440\u0435\u0430\u043b\u0438\u0437\u0438\u0440\u0430 \u0441\u043e \u043f\u043e\u0447\u0435\u0442\u043e\u043a \u043e\u0434 9 \u0447\u0430\u0441\u043e\u0442 \u0438 \u0441\u043e \u043f\u043e\u0433\u043e\u043b\u0435\u043c\u0430 \u043f\u0430\u0443\u0437\u0430 \u043f\u043e\u043c\u0435\u0453\u0443 \u043f\u0440\u0432\u0438\u043e\u0442 \u0438 \u0432\u0442\u043e\u0440\u0438\u043e\u0442 \u0431\u043b\u043e\u043a \u043e\u0434 3 \u0447\u0430\u0441\u0430, \u0437\u0430 \u0434\u0430 \u0441\u0435 \u043e\u0432\u043e\u0437\u043c\u043e\u0436\u0438 \u0432\u0440\u0435\u043c\u0435 \u0438 \u0437\u0430 \u0434\u043e\u043f\u043e\u043b\u043d\u0438\u0442\u0435\u043b\u043d\u043e \u0441\u0430\u043c\u043e\u0441\u0442\u043e\u0458\u043d\u043e \u0432\u0435\u0436\u0431\u0430\u045a\u0435 \u043d\u0430 \u0438\u0437\u0443\u0447\u0435\u043d\u0438\u0442\u0435 \u043a\u043e\u043d\u0446\u0435\u043f\u0442\u0438, \u0441\u043e \u0448\u0442\u043e \u045c\u0435 \u0431\u0438\u0434\u0435 \u043e\u0431\u0435\u0437\u0431\u0435\u0434\u0435\u043d\u0430 \u0438 \u0441\u043e\u043e\u0434\u0432\u0435\u0442\u043d\u0430 \u043f\u043b\u0430\u0442\u0444\u043e\u0440\u043c\u0430 \u0437\u0430 \u0434\u0430\u043b\u0435\u0447\u0438\u043d\u0441\u043a\u043e \u0443\u0447\u0435\u045a\u0435. \u041d\u0430\u0441\u0442\u0430\u0432\u0430\u0442\u0430 \u045c\u0435 \u0441\u0435 \u0438\u0437\u0432\u0435\u0434\u0443\u0432\u0430 \u043e\u043d\u043b\u0430\u0458\u043d.<\/p>\n

\u041a\u0443\u0440\u0441\u043e\u0442 \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u045c\u0435 \u0441\u0435 \u0440\u0435\u0430\u043b\u0438\u0437\u0438\u0440\u0430 \u0432\u043e \u0442\u0435\u043a\u043e\u0442 \u043d\u0430 6 \u0434\u0435\u043d\u0430 (40 \u0447\u0430\u0441\u0430), \u0434\u043e\u0434\u0435\u043a\u0430 \u043a\u0443\u0440\u0441\u043e\u0442 \u043f\u043e \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u0438\u0440\u0430\u045a\u0435 \u045c\u0435 \u0441\u0435 \u0440\u0435\u0430\u043b\u0438\u0437\u0438\u0440\u0430 \u0432\u043e \u0442\u0435\u043a\u043e\u0442 \u043d\u0430 5 \u0434\u0435\u043d\u0430 (20 \u0447\u0430\u0441\u0430). \u0426\u0435\u043d\u0430\u0442\u0430 \u0437\u0430 \u0441\u043b\u0435\u0434\u0435\u045a\u0435 \u043d\u0430 \u043a\u0443\u0440\u0441\u043e\u0442 \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438\u0437\u043d\u0435\u0441\u0443\u0432\u0430 4000 \u0434\u0435\u043d\u0430\u0440\u0438. \u0426\u0435\u043d\u0430\u0442\u0430 \u0437\u0430 \u0441\u043b\u0435\u0434\u0435\u045a\u0435 \u043d\u0430 \u043a\u0443\u0440\u0441\u043e\u0442 \u043f\u043e \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u0438\u0440\u0430\u045a\u0435 \u0435 2000 \u0434\u0435\u043d\u0430\u0440\u0438.<\/p>\n

\u0421\u0442\u0443\u0434\u0435\u043d\u0442\u0438\u0442\u0435 \u043a\u043e\u0438 \u043f\u043b\u0430\u043d\u0438\u0440\u0430\u0430\u0442 \u0434\u0430 \u0441\u043b\u0435\u0434\u0430\u0442 \u043d\u0435\u043a\u043e\u0458 \u043e\u0434 \u043a\u0443\u0440\u0441\u0435\u0432\u0438\u0442\u0435 (\u0438\u043b\u0438 \u0434\u0432\u0430\u0442\u0430) \u0442\u0440\u0435\u0431\u0430 \u0434\u0430 \u0441\u0435 \u043f\u0440\u0438\u0458\u0430\u0432\u0430\u0442 \u043d\u0430\u0458\u0434\u043e\u0446\u043d\u0430 \u0434\u043e \u0447\u0435\u0442\u0432\u0440\u0442\u043e\u043a, 10.9.2020 \u0434\u043e 16 \u0447\u0430\u0441\u043e\u0442 \u043f\u0440\u0435\u043a\u0443 \u043f\u043e\u043f\u043e\u043b\u043d\u0443\u0432\u0430\u045a\u0435 \u043d\u0430 \u0441\u043b\u0435\u0434\u043d\u0430\u0432\u0430 form<\/a><\/p>\n

Further information about the preparatory classes is available at the following email address: podgotvitelna@finki.ukim.mk<\/a>.<\/p>\n

\u0421\u0438\u0442\u0435 \u0441\u0442\u0443\u0434\u0435\u043d\u0442\u0438 \u043a\u043e\u0438 \u0441\u0435 \u043f\u0440\u0438\u0458\u0430\u0432\u0438\u043b\u0435 \u0437\u0430 \u0441\u043b\u0435\u0434\u0435\u045a\u0435 \u043d\u0430 \u043d\u0430\u0441\u0442\u0430\u0432\u0430\u0442\u0430 \u0432\u043e \u043f\u0440\u0435\u0434\u0432\u0438\u0434\u0435\u043d\u0438\u043e\u0442 \u0440\u043e\u043a, \u045c\u0435 \u0431\u0438\u0434\u0430\u0442 \u0438\u0437\u0432\u0435\u0441\u0442\u0435\u043d\u0438 \u043d\u0430\u0458\u0434\u043e\u0446\u043d\u0430 \u0434\u043e \u043f\u0435\u0442\u043e\u043a, 11.9.2020 \u0434\u043e 15 \u0447\u0430\u0441\u043e\u0442 \u0441\u043e \u043f\u043e\u0440\u0430\u043a\u0430 \u043d\u0430 \u0435-\u0430\u0434\u0440\u0435\u0441\u0430\u0442\u0430 \u043a\u043e\u0458\u0430 \u0458\u0430 \u0432\u043d\u0435\u043b\u0435 \u0432\u043e \u043f\u0440\u0438\u0458\u0430\u0432\u0430\u0442\u0430, \u0434\u0430\u043b\u0438 \u0441\u0435 \u0430\u043a\u0442\u0438\u0432\u0438\u0440\u0430\u043d\u0438 \u0433\u0440\u0443\u043f\u0438\u0442\u0435 \u0438 \u0434\u0430\u043b\u0438 \u043d\u0430\u0441\u0442\u0430\u0432\u0430\u0442\u0430 \u045c\u0435 \u0437\u0430\u043f\u043e\u0447\u043d\u0435.<\/p>\n

Brief outlines of the material covered in the preparatory mathematics and programming classes are provided below.<\/p>\n

The mathematics curriculum covers significant portions of the material studied in elementary and secondary education.<\/p>\n

Description of the topics to be covered:<\/p>\n

Topic 1: Basic Number Sets; Algebraic and Rational Expressions
\nBasic 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. Intact rational expressions, monomials, polynomials, operations, factorization, LCM and GCD. Fractional rational expressions: definition and operations.<\/p>\n

Topic 2: Linear Functions, Linear Equations and Inequalities; Systems of Linear Equations
\nLinear 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.<\/p>\n

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.<\/p>\n

Topic 4: Logarithmic Functions. Trigonometric Functions
Logarithmic function, rules for logarithms, relations between logarithms with different bases. Trigonometry: trigonometric functions of an acute angle, relations among trigonometric functions of the same angle, values of trigonometric functions for some angles, solving a right triangle, definitions of the trigonometric functions (sine, cosine, tangent and cotangent) from an arbitrary angle, value of the trigonometric functions for some angles.<\/p>\n

Topic 5: Mathematical Logic
\nExpressions. 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.<\/p>\n

Topic 6: Sets; Combinatorics
\nSets. Subsets and set equality. Operations on sets. Induction.
\nCombinatorics: combinations, permutations, variations. Binomial formula.<\/p>\n

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

Topic 1: Algorithms and Programming
\nAn introduction to algorithms. Reviewing simple algorithms and developing example algorithms. Ways to master algorithmic concepts. Tools for beginner programming.<\/p>\n

Topic 2: Integrated Development Environments. Code::Blocks
\nProgramming. Elements of programming environments: compiler, linker, debugger, libraries of standard functions. Code::Blocks: installation, description of the environment's appearance: main window, workspace. Creating a new project and adding a source file to the project. Building and running a project.<\/p>\n

Topic 3: Introduction to the C programming language
\nSyntax of C: alphabet, keywords, special symbols, and comments. Preprocessor and header files. Including a file with the include directive. Data types in C: basic (char, int, float, double). Expressions and statements in C. Variables and their declaration. Structure of programs in C. Operators in C: arithmetic, assignment, increment and decrement (prefix, postfix), relational, and logical operators. Input\/output operations: printf and scanf. Examples of simple C programs.<\/p>\n

Topic 4: Sequential Structure. Writing simple programs
\nSequential structure, a block of statements. Empty statement. Writing simple C programs.<\/p>\n

Topic 5: Control Structures. Selection Statements
\nControl statements: selection statements, repetition statements, and jump statements. Selection statements: if, if-else, and switch. Nested if statements. Examples of C programs using selection statements.<\/p>\n

Topic 6: Loop Statements
\nThe while statement\u2014implementation of the while-do control structure. Examples of using the while statement. The do-while statement\u2014implementation of the repeat-until control structure. Examples of using the do-while statement. The for statement\u2014implementation of the for-to-step control structure. Examples of using the for statement. Jump statements: break and continue.<\/p>\n

Topic 7: One-Dimensional Array
\nArrays as data structures. Declaring an array. Accessing an array element \u2013 element indices. Initializing an array. Examples of C programs using arrays.<\/p>\n

Topic 8*: Text Strings
\nRepresentation of character strings in C. Visual representation of memory occupied by a character string. Assigning a value to a character string. Reading and displaying character strings. Extracting a character from a character string. Modifying a part of a character string. Iterating through a string and determining its length. Some useful C functions for working with strings: strlen(), strcpy(), strcat(), and strcmp(). Examples of C programs using strings. <\/p>\n

(* will be partially implemented, depending on the students' achievements in previous topics)<\/p>","protected":false},"featured_media":15124,"template":"","class_list":["post-17798","announcement","type-announcement","status-publish","has-post-thumbnail","hentry"],"_links":{"self":[{"href":"https:\/\/finki.ukim.mk\/en\/wp-json\/wp\/v2\/announcement\/17798","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/finki.ukim.mk\/en\/wp-json\/wp\/v2\/announcement"}],"about":[{"href":"https:\/\/finki.ukim.mk\/en\/wp-json\/wp\/v2\/types\/announcement"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/finki.ukim.mk\/en\/wp-json\/wp\/v2\/media\/15124"}],"wp:attachment":[{"href":"https:\/\/finki.ukim.mk\/en\/wp-json\/wp\/v2\/media?parent=17798"}],"curies":[{"name":"WordPress","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}