"Mathematics: Training manual for practical and independent work for students of the 2nd year in the specialty 43" is an indispensable assistant for second year students , who master the basics of mathematical analysis and applied mathematical methods as part of their professional training. The author’s team created this manual in order to make the study of mathematics not only understandable, but also fascinating, helping students to consolidate theoretical knowledge through practical tasks and independent work. This textbook is a comprehensive collection, which contains a variety of exercises, tasks and practical tasks aimed at developing analytical thinking, logic and skills for solving specific mathematical problems. The book details key topics of the course, such as differential and integral calculus, function theory, analytical geometry, as well as the foundations of mathematical logic and discrete mathematics, making it a universal tool for securing knowledge throughout the course spectrum. An intriguing feature of this manual is the combination of theoretical material with practical tasks that stimulate independent thinking and allow students not only to understand, but also to apply the knowledge gained in real situations. Each exercise is accompanied by detailed comments and recommendations, which is especially important for those who are just beginning their journey in the complex but fascinating field of mathematics. This approach contributes to the development of analytical skills, the ability to work with mathematical models and prepare for future professional challenges. This manual is ideal for students studying in specialty 43, as well as those who are interested in applied mathematics, engineering sciences and technical disciplines. It can be an excellent help for students seeking to improve their academic performance, as well as for teachers looking for effective materials for practical training and independent work. The age category of readers is from 17 years and older, since the book is designed for students who have already mastered basic mathematical concepts and are looking for ways to study the subject in depth. A special advantage of this manual is its structured approach to learning. The author's team, including experienced teachers and methodologists, has created material that not only helps to understand complex mathematical concepts, but also motivates to independently search for solutions. The book focuses on developing critical thinking skills, working with graphs, analyzing functions and solving applied problems, which makes it especially relevant for future engineers, technologists and information technology specialists. The style of presentation in the book is clear and accessible, which is especially important for students facing mathematics for the first time or experiencing difficulties in mastering it. At the same time, the authors do not avoid the use of modern methods of presentation of material, including diagrams, illustrations and examples from real practice, which makes learning more lively and interesting. If you are looking for a tutorial that will not only help you understand mathematics, but also teach you how to apply it in practice, "Mathematics: Training manual for practical and independent work for students of the 2nd year in the specialty 43" will become your reliable companion on the way to professional success This book deserves the attention of those who value a systematic approach, want to develop analytical abilities and are ready for new challenges in the field of science and technology. Do not miss the opportunity to make your learning process more efficient and exciting by discovering the richness of the mathematical world through the pages of this unique manual.