Abstract
<jats:p>The article analyzes the significance and place of the academic discipline “Linear Algebra” in the structure of training bachelors of higher education in specialty A4.04 Secondary Education (Mathematics). The research characterizes the content and experience of studying the course “Linear Algebra” in the process of training bachelors in specialty A4.04 Secondary Education (Mathematics) at the Rivne State University of the Humanities. The article determines the content, goal, objectives of the course, and the expected results of studying the academic discipline. “Linear Algebra” is a separate academic discipline for the professional training of bachelors of higher education in specialty A4.04 Secondary Education (Mathematics) in the process of mastering mathematical competencies. The course is one of the mandatory components of the educational and professional program for training future mathematics teachers in specialty A4.04 Secondary Education (Mathematics). It is studied in the first year of study and initiates the process of mastering mathematical disciplines by students, creates the prerequisites for studying other subjects of the mathematical cycle. Linear algebra introduces the concepts of abstract algebraic structures (groups, rings, fields), which are studied later in the courses “Algebra and Number Theory”, “Number Systems”, and “General Algebra”. The article emphasizes the fact that when studying linear algebra, it is necessary to take into account the realities of modern life, in particular, the use of information and communication technologies and artificial intelligence by students in the learning process. These tools allow intensifying, accelerating, and better mastering the material. It is suggested that students pay special attention to theoretical and logical connections, concepts, theorems, and patterns that form the foundation of the discipline as part of science. For example, the application of the principles of isomorphism and homomorphism is an important means of scientific research and is essential for understanding the structure and essence of various systems. This approach allows solving problems by building mathematical models. Moreover, the same homomorphic (isomorphic) image, for example, a mathematical formula, is used to solve a whole class (set) of problems.</jats:p>