The difficulties faced by first-year students in mathematics are, according to experience, due to algebraic gaps from secondary school. To avoid typical mistakes and to address such gaps, the author of the proven textbook "Mathematics for Universities of Applied Sciences" offers this study book as a targeted training course. With a reasonable time investment and through self-study, the reader is provided with a successful entry point and is guided to connect with mathematics lectures. For those areas of school mathematics where particularly many errors are typically made, the first-year student will find test tasks here. If these test tasks can be solved correctly, there is no need to repeat the relevant chapter. Otherwise, the student should read the explanations carefully and then practice the relevant exercises.