Problems in Mathematics

The book is intended for college undergraduates majoring in Mathematics. It contains more than three thousand mathematics problems and covers each topic taught at school. The problems were contributed by 120 of the higher schools of the USSR and all the universities. The book is divided into four parts: Algebra and Trigonometry, Fundamentals of Analysis, Geometry and Vector Algebra, and the Problems and Questions Set during Oral Examinations. The authors believe that this material will help the readers to systematize their knowledge in the principal divisions of mathematics. In writing the book, the authors have used their experience of examining students in mathematics at higher schools and the preparation of television courses designed to help students revise their knowledge for the entrance examinations to higher educational establishments. To make it easier for readers to grasp the material, some of the sections have been supplemented with explanatory text. The problems are all answered and some have additional hints or complete solutions. The authors hope that this book will help those who want to enter the various types of higher school, aid the teachers, and be of use to all those who want to deepen and systematize their knowledge of mathematics.