Selection Tests in Algebra for Mathematical Olympiads (Problem Books in Mathematics)

This book compiles thoughtfully curated selection tests proposed to IMO (International Mathematical Olympiad) teams across many countries. Offering a blend of original solutions and adaptations by the author, this work is chronologically organized, featuring problems from 1968 to 2024, and provides a unique insight into the evolution of this mathematical contest.

The work starts with a section containing key theories and examples, serving as a quick reference guide. The main inequalities and functional equations are covered, along with topics on mathematical induction and polynomials. This is followed by the problems themselves, covering equations and systems of equations, inequalities, functional equations and inequalities, mathematical induction, and polynomials. A meticulously crafted index helps the reader navigate through the topics with ease. References are provided for further reading and self-study.

Besides serving as an invaluable preparation tool for both aspiring students and those passionate about mathematics alike, this book also complements 'Selection Tests in Number Theory for Mathematical Olympiads,' from the same author, available at Springer.

Corneliu Mănescu-Avram is a graduate of the Faculty of Mathematics at the University of Bucharest, Romania. In 2010, he obtained the QTS (Qualified Teacher Status) certification. He is an active problem solver and contributor to numerous mathematical journals, including Mathematical Reflections, Crux Mathematicorum, Pi Mu Epsilon Journal, Pentagonal Kappe Mathematical Journal, Mathematical Excalibur, School Science and Mathematics, Mathematical Recreations (in Romanian), and Mathematical Review from Timișoara (in Romanian). Manescu-Avram has worked as a computer programmer and a high school teacher of mathematics, computer science, and astronomy. He has also authored 'Selection Tests in Number Theory for Mathematical Olympiads,' published by Springer. Although retired, he remains actively engaged in mathematical pursuits.