An Excursion through Elementary Mathematics, Volume III pdf 安东尼奥·卡米尼亚·穆尼兹·内托
Explore the depths of elementary mathematics with "An Excursion through Elementary Mathematics, Volume III: Discrete Mathematics and Polynomial Algebra," authored by Antonio Caminha Muniz Neto. This book offers a thorough and detailed examination of topics commonly featured in Mathematical Olympiads worldwide. It builds on high school mathematics and serves as an excellent preparatory resource for first-semester undergraduate courses.
The third and final volume of this series delves into a range of subjects, including Counting, Generating Functions, Graph Theory, Number Theory, Complex Numbers, Polynomials, and more. Unlike other books in this field that often present a collection of questions or problem-solving tips, this volume begins with fundamental theoretical principles, striking a balance between being overly general and excessively axiomatic.
The book's approach includes discussing examples and problems only when they effectively demonstrate theoretical applications. Detailed proofs of propositions are provided, followed by their application to Olympic-level problems. Additionally, the book covers some of the most challenging problems from National and International Mathematics Olympiads and explores many essential theorems relevant to the topics.
An extensive Appendix is included, offering hints or complete solutions for all difficult problems, making this book a valuable resource for anyone interested in deepening their understanding of elementary mathematics at an advanced level.