Training Manual . - M. : Education, 1989. — 352 s. The main purpose of this book is to prepare students for continuing education in higher education institutions, increasing the level of general mathematical training .. The elective is built as an in-depth study of the issues provided by the program of the main course . Deepening is implemented on the basis of teaching methods and techniques for solving mathematical problems . Converting Numerical and Algebraic Expressions. Some practical recommendations . Variable replacement. Conditional equality . Tasks. Equations and systems of equations . Rational equations resulting from transformations to linear and square. Irrational Equations . The appearance of extra roots . On the concept of permissible values of the unknown . Replacing the unknown. Finding the rational roots of a polynomial with integer coefficients. Multiplication by factors. Systems of Equations . Equations containing absolute values. Tasks. Inequality. Transforming Inequalities . Inequalities containing absolute values. Tasks. Text Tasks. Selection of unknowns . Compiling equations (limitations). Several non-standard tasks. How to do without equations . Tasks. Square tri-member. The existence of the roots of the quadratic equation. Signs of Roots . The location of the roots of the square three-member . Reciprocal arrangement of the roots of two square three-member. Equations, inequalities and systems with parameter. Equations, inequalities and systems with parameter. Graphic Interpretations . Tasks for maximum-minimum. Proof of Inequality . Tasks. Numbers and Numerical Sequences. Natural and integers. Solving equations in integers. Rational, Irrational and Real Numbers . The method of complete mathematical induction . Numerical Sequences. Sequence summation. Complex numbers. Tasks. Planimetry. Construction of the drawing. Identification of characteristic features of a given configuration. Challenges . Geometric methods of solving problems . Analytical Methods . Coordinate Method. Vector method. Tasks. Answers, directions, solutions. Approximate distribution of classes by topic (minimum level).