High School Curriculum for Mathematics and Computer Science Specialization

1. Algorithms

   • Algorithm concept, characteristics
   • Data, variables, expressions, operations
   • Basic structures: linear, alternative, repetitive
   • Algorithm description, pseudocode representation



2. Basic Elements of a Programming Language (Pascal or C, optional)

   • Language vocabulary
   • Constants, identifiers
   • Data type concept. Arithmetic, logical, relational operators
   • Defining data types
   • Variables. Variable declaration
   • Program structure. Comments
   • Expressions. Assignment statement
   • Data input/output
   • Control structures: compound statement, alternative and repetitive structures



3. Predefined Subprograms

   • Subprograms. Parameter passing mechanisms
   • Predefined procedures and functions



4. Structured Data Types

   • Array type
   • Character string type: operators, predefined procedures and functions for reading, displaying, concatenation, search, extraction, insertion, deletion
   • Record type



5. Text Files

   • Text files. Access types
   • Predefined procedures and functions for text files



6. Elementary Algorithms

   • Problems involving digits of a number
   • Divisibility. Prime numbers. Euclid's algorithm
   • Fibonacci sequence
   • Finding minimum/maximum
   • Sorting methods: bubble sort, selection sort
   • Merge sort
   • Search methods: sequential search, binary search
   • Analysis of algorithm complexity considering execution efficiency criteria and memory usage



7. User-Defined Subprograms

   • Procedures and functions: declaration and invocation, formal parameters and actual parameters, value parameters, reference parameters, global variables and local variables, scope
   • Modular design of problem solving



8. Recursion

   • Recursive procedures and functions



9. Backtracking Method

   • Generation problems



10. Generation of Combinatorial Elements

    • Permutations, arrangements, combinations
    • Cartesian product, subsets



11. Graphs

    • Undirected graphs: terminology (node/vertex, edge, adjacency, incidence, degree, path, elementary path, cycle, elementary cycle, length, subgraph, partial graph), properties (connected, connected component, complete graph), memory representation methods (adjacency matrix, adjacency list)
    • Trees: terminology (node, edge, root, descendant, direct descendant/child, ancestor, direct ancestor/parent, siblings, leaf node), memory representation methods (adjacency matrix, parent array)