Real and complex polynomials. Theorems and problemsReal and complex polynomials. Theorems and problems

The book contains about a thousand tasks that can be used in the study of algebra in both regular and specialized physics and mathematics classes and in preparation for the Unified State Exam and other exams and mathematical Olympiads up to the highest level. It can serve as an addition to the well-known problem books used in secondary and higher school.

It contains collections of problems on the main topics studied at school: algebraic and trigonometric equations and systems, solving algebraic and trigonometric inequalities, proving inequalities, complex numbers. The issues that go beyond the scope of the school curriculum, but accessible to the understanding of schoolchildren, are considered. The necessary theoretical information is presented in the form of task cycles.

The book contains both easy and difficult problems that were offered at mathematical Olympiads at one time or contain non-trivial facts from theory that go beyond the scope of the program. Some tasks are left without instructions and solutions, teachers can use them for training exams and Olympiads.

The book is of interest to both schoolchildren and students, teachers and all lovers of mathematics.