An Excursion through Elementary Mathematics, Volume I pdf 安东尼奥·卡米尼亚·穆尼兹·内托
Discover the fundamentals of elementary mathematics with "An Excursion through Elementary Mathematics, Volume I: Real Numbers and Functions," authored by Antonio Caminha Muniz Neto. This book provides a thorough and detailed exploration of mathematics topics commonly featured in Mathematical Olympiads across the globe. It builds on high school mathematics and serves as an excellent resource for preparing for a first-semester undergraduate course.
In this first volume, readers will delve into Real Numbers, Functions, Real Analysis, Systems of Equations, Limits, Derivatives, and much more. Unlike other publications that often present a collection of questions or problem-solving tips, this book begins with basic theoretical principles, ensuring it is neither too general nor overly axiomatic.
The approach taken in this book includes discussing examples and problems only when they effectively illustrate theoretical applications. Detailed proofs of propositions are provided, followed by their application to Olympic-level problems. The book also addresses some of the most challenging problems from National and International Mathematics Olympiads and explores many essential theorems relevant to the covered topics.
To enhance its utility, the book includes an extensive Appendix offering hints or complete solutions for all difficult problems, making it a valuable resource for those looking to deepen their understanding of elementary mathematics at an advanced level.