Elementary mathematics. Part 1

The textbook is intended for repetition and systematization of student knowledge in preparation for exams and olympiads in mathematics. Aimed at applicants to those higher educational institutions where it is required to demonstrate a high level of knowledge in mathematics - both in theory and in practice of solving problems. Part 1 of the book includes the following sections: “The Theory of Real Numbers”, “Numerical Equalities and Inequalities. Abbreviated multiplication formulas. Known algebraic inequalities", "Algebraic equations and inequalities". The book contains all the necessary definitions, formulations and proofs of properties and theorems. Particular attention in the manual is paid to the analysis of various techniques and methods for solving problems (Part 1 includes more than 450 problems with solutions from variants of examination tasks at Lomonosov Moscow State University, MEPhI, MIPT, Bauman MSTU, MTUSI, HSE, Plekhanov Russian Economic Academy, Financial Academy and other universities), as well as about 625 problems for independent solution (with answers and solutions). Much attention is paid to problems with non-standard approaches to solution. The book includes a lot of additional and reference material that expands the student’s mathematical horizons.

The manual is recommended for high school students, students of preparatory departments and courses for preparing for Olympiads (at the level of Lomonosov Moscow State University) and the Unified State Exam (in the most difficult its parts), as well as teachers teaching elementary mathematics courses.

Published by decision of the Editorial and Publishing Council of Lomonosov Moscow State University. You can also purchase in our online store Part 2. Systems of equations and inequalities. Text problems. Sequences. Progression. Elements of set theory