Some aspects of programming education are examined in this work. It is emphasised, based on the entertainment value, the most appropriate examples are chosen to demonstrate the different language constructions and data structures. Such an example is the demonstrated algorithm for solving the widespread nowadays "Sudoku" puzzle. This is made, because of the connection with the term set and putting it into practice in the programming. Using the so built program there are solved some combinatorial problems, connected to the Sudoku matrices.
A mathematical model, describing some different weaving structures, is made in this article. The terms self-mirror and rotation-stable weaving structure are initiated here. There are used the properties and operations in the set of the binary matrices and an equivalence relation in this set. Some combinatorial problems about finding the cardinal number and the elements of the factor set according to this relation is discussed. We propose an algorithm, which solves these problems. The presentation of an arbitrary binary matrix using sequence of nonnegative integers is discussed. It is shown that the presentation of binary matrices using ordered n-tuples of natural numbers makes the algorithms faster and saves a lot of memory. Implementing these ideas a computer program, which receives all of the examined objects, is created. In the paper we use object-oriented programming using the syntax and the semantic of C++ programming language. Some advantages in the use of bitwise operations are shown. The results we have received are used to describe the topology of the different weaving structures.
The paper presents a formal model for generation of personalized learning paths. The paths consist of self-modifying learning activities suitable for the achievement of course goals. The course goals (as defined by the teacher) are a list of functions/predicates with specific slots and include obligatory activities required for the automatized construction of learning paths. Further, the problems related to automatized learning path construction are identified and solved with the use of an original approach. The approach includes (but is not limited to): introduction of different points of view (aspects) for learning objects; automatized gathering/accumulation of metadata for learning activities; generation of personalized learning paths using set of student achievements, etc.
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