The importance of mathematical preparation for studying higher mathematics and physics in higher education institutions

The article examines the fundamental importance of sound mathematical preparation for the successful study of higher mathematics and physics courses by students of higher education institutions. The key aspects of the relationship between basic mathematical knowledge and the complexity of higher mathematics and physical disciplines are analyzed. The impact of weak basic preparation on academic success is considered and methods for improving learning efficiency are proposed. In the modern educational space where exact sciences are beginning to play a key role in the training of qualified specialists in engineering, technical, computer and natural sciences, the problem of insufficient basic mathematical training is becoming increasingly relevant. Often, students, entering higher education institutions, demonstrate gaps in knowledge of elementary algebra, trigonometry, geometry and the basics of analysis, which creates significant obstacles to consolidating complex academic concepts. The article analyzes key aspects of the relationship between strong school mathematical knowledge and the ability of students to effectively master the material of higher mathematics, which includes differential and integral calculus, linear algebra, differential equations, etc. Special attention is paid to the influence of this knowledge on the understanding and application of physical laws, the latter physics is largely based on the mathematical apparatus. Typical difficulties that students encounter due to weak basic training are studied, such as problems with algebraic transformations, working with fractions, trigonometric functions, and the logic of mathematical proofs. The study also covers the negative consequences of insufficient training, including a decrease in academic performance, student demotivation, difficulties in adapting to the intensive pace of higher education, and, in some cases, expulsion. Based on the analysis of Ukrainian and foreign scientific sources, as well as general teaching experience, effective methods and practical recommendations are proposed to improve the effectiveness of learning and overcome existing gaps. Among them are the introduction of diagnostic testing, the organization of remedial courses, strengthening individual work with students, the use of interdisciplinary connections, and the formation of sustainable motivation to study the exact sciences. The article emphasizes the need for a systematic approach to solving this problem at all levels of the educational process in order to ensure high quality training of future specialists