Formation of professional identity among junior students of a technical university through solving applied problems of cryptography and steganography by means of the disciplines of mathematical analysis, linear algebra and analytic geometry

Abstract

The article addresses the issue of forming professional identity among lower-year students at technical universities pursuing degrees in information security. This occurs in a context dominated by fundamental mathematical training that is frequently perceived as abstract and disconnected from future professional practice. The integration of applied problems from cryptography and steganography into the curricula of mathematical analysis and linear algebra with analytic geometry is substantiated. Within these courses, the Hill cipher, matrix operations in finite fields, affine transformations, Fourier series, discrete cosine transforms, and modular arithmetic illustrate the direct relevance of the mathematical apparatus to information security methods. This didactic approach simultaneously develops the cognitive, value-motivational, and conative components of professional identity. It helps overcome motivational deficits and facilitates the transition from academic to professional thinking. Comparative analysis of the results from a two-year experiment involving experimental and control groups of students demonstrates a marked positive trend in the experimental group. The growth in indicators across all identity components more than doubles the values observed in the control group. An inversion of the motivational profile occurs, with intrinsic motivation and cognitive activity becoming dominant. There is also significant improvement in practical skills and overall academic performance, while the level of theoretical knowledge remains unchanged. The identified correlations between professional identity, motivation, and academic achievement confirm the cumulative effect of systematically incorporating professionally oriented tasks. These tasks serve as a catalyst for mastering fundamental material and promote early professional self determination in information security. The article’s materials highlight the high relevance of the proposed model for the design of mathematics courses in technical education.