Ellina Grigorieva Livres

Through engaging problems, this book illustrates essential reasoning methods for learning number theory. Each technique is accompanied by problems, detailed hints, and solutions, enabling readers to systematically and creatively tackle a variety of abstract challenges. New solutions often require innovative applications of earlier concepts rather than mere memorization. Questions allow for experimental numeric validation or visual interpretation, fostering both deductive and intuitive thinking. The first chapter introduces simple topics like even and odd numbers, divisibility, and prime numbers, guiding readers to solve complex, Olympiad-style problems. It also addresses perfect, amicable, and figurate numbers and introduces congruence. The subsequent chapter covers the Euclidean algorithm, representations of integers in various bases, continued fractions, quadratic irrationalities, and the Lagrange Theorem, concluding with different proof methods. The third chapter focuses on Diophantine equations, including techniques for solving Fermat’s equations and factorization methods. Chapter Four explores Pythagorean triples and quadruples, linking them to geometry and algebra. It also discusses Waring’s problem and quadratic residues, along with intriguing word problems. Appendices offer a historical overview of number theory from ancient civilizations to modern developments. This book serves as a self-study guide or supplementary t

Featuring over 160 challenging problems, this resource serves as an effective self-study guide for mathematics competitions and enhances problem-solving abilities in plane geometry and the history of mathematics. Each problem is accompanied by hints and comprehensive solutions, making it suitable for both students and enthusiasts looking to deepen their understanding and skills in mathematical concepts.

Focusing on nonstandard mathematical problems, this book encourages readers to develop insight and synthesize various mathematical concepts rather than relying solely on standard methods. Authored by a skilled female mathematician, it aims to enhance mental activity and mathematical proficiency, making it an excellent resource for those preparing for mathematics Olympiads.

This book aims to dispel the mystery and fear experienced by students surrounding sequences, series, convergence, and their applications. The author, an accomplished female mathematician, achieves this by taking a problem solving approach, starting with fascinating problems and solving them step by step with clear explanations and illuminating diagrams. The reader will find the problems interesting, unusual, and fun, yet solved with the rigor expected in a competition. Some problems are taken directly from mathematics competitions, with the name and year of the exam provided for reference. Proof techniques are emphasized, with a variety of methods presented. The text aims to expand the mind of the reader by often presenting multiple ways to attack the same problem, as well as drawing connections with different fields of mathematics. Intuitive and visual arguments are presented alongside technical proofs to provide a well-rounded methodology. With nearly 300 problems including hints, answers, and solutions, Methods of Solving Sequences and Series Problems is an ideal resource for those learning calculus, preparing for mathematics competitions, or just looking for a worthwhile challenge. It can also be used by faculty who are looking for interesting and insightful problems that are not commonly found in other textbooks.

This book aims to dispel the mystery and fear experienced by students surrounding sequences, series, convergence, and their applications. The author, an accomplished female mathematician, achieves this by taking a problem solving approach, starting with fascinating problems and solving them step by step with clear explanations and illuminating diagrams. The reader will find the problems interesting, unusual, and fun, yet solved with the rigor expected in a competition. Some problems are taken directly from mathematics competitions, with the name and year of the exam provided for reference. Proof techniques are emphasized, with a variety of methods presented. The text aims to expand the mind of the reader by often presenting multiple ways to attack the same problem, as well as drawing connections with different fields of mathematics. Intuitive and visual arguments are presented alongside technical proofs to provide a well-rounded methodology. With nearly 300 problems including hints, answers, and solutions, Methods of Solving Sequences and Series Problems is an ideal resource for those learning calculus, preparing for mathematics competitions, or just looking for a worthwhile challenge. It can also be used by faculty who are looking for interesting and insightful problems that are not commonly found in other textbooks.