Building bridges between classical results and contemporary nonstandard problems, this highly relevant work embraces important topics in analysis and algebra from a problem-solving perspective. The book is structured to assist the reader in formulating and proving conjectures, as well as devising solutions to important mathematical problems by making connections between various concepts and ideas from different areas of mathematics. Instructors and motivated mathematics students from high school juniors to college seniors will find the work a useful resource in calculus, linear and abstract algebra, analysis and differential equations. Students with an interest in mathematics competitions must have this book in their personal libraries.

The authors learned a lot of mathematics from the problems encountered in various Romanian national contests. This is something that stayed with them for the entire of their careers. One of the goals of the book is to make the exposition of the material more interesting, at least for the beginners in Olympiad mathematics. Here and there they left unanswered questions related to the problems presented in the hopes that the reader will accept and even enjoy these challenges. The problems in the book were selected from the 1975 to 1986 Romanian Team Selection Tests. The problems are not only accompanied by their solutions, but also many have more than one solution and comments in order to make them clearer or to get connections to other problems.

The main areas covered are: telescoping sums and products in algebra and trigonometry the use of complex numbers and de Moivre's Formula Abel's summation formula mathematical induction combinatorial identities multiplicative functions and the use of Mobius function. The theory is presented together with rich examples. At the end, you are invited to solve problems from a list of 125 questions divided into three levels.