A major aspect of mathematical training and its benefit to society is the ability to use logic to solve problems. The American Mathematics Competitions have been given for more than fifty years to millions of students. This book considers the basic ideas behind the solutions to the majority of these problems, and presents examples and exercises from past exams to illustrate the concepts. Anyone preparing for the Mathematical Olympiads will find many useful ideas here, but people generally interested in logical problem solving should also find the problems and their solutions stimulating. The book can be used either for self-study or as topic-oriented material and samples of problems for practice exams. Useful reading for anyone who enjoys solving mathematical problems, and equally valuable for educators or parents who have children with mathematical interest and ability.

Differential geometry arguably offers the smoothest transition from the standard university mathematics sequence of the first four semesters in calculus, linear algebra, and differential equations to the higher levels of abstraction and proof encountered at the upper division by mathematics majors. Today it is possible to describe differential geometry as "the study of structures on the tangent space," and this text develops this point of view. This book, unlike other introductory texts in differential geometry, develops the architecture necessary to introduce symplectic and contact geometry alongside its Riemannian cousin. The main goal of this book is to bring the undergraduate student who already has a solid foundation in the standard mathematics curriculum into contact with the beauty of higher mathematics. In particular, the presentation here emphasizes the consequences of a definition and the careful use of examples and constructions in order to explore those consequences.

The First Steps in Algebra by G. A. Wentworth: In this foundational textbook, G. A. Wentworth introduces readers to the basic principles and concepts of algebra. "The First Steps in Algebra" serves as an essential resource for students beginning their journey into the world of algebra, providing clear explanations and numerous examples to help build a solid mathematical foundation. Key Aspects of the Book "The First Steps in Algebra": Introduction to Algebra: Wentworth's book provides a gentle introduction to algebraic concepts, making it accessible to students new to the subject. Step-by-Step Learning: The book follows a structured approach, guiding learners through progressively more complex topics in algebra. Problem-Solving Skills: "The First Steps in Algebra" encourages students to develop their problem-solving skills and apply algebraic techniques to real-world scenarios. G. A. Wentworth was an American mathematician and educator born in 1857. He authored several influential mathematics textbooks, including "The First Steps in Algebra," which played a significant role in shaping the way algebra is taught in schools. Wentworth's dedication to mathematical education has had a lasting impact on countless students and teachers.

Take it step-by-step for algebra success! The quickest route to learning a subject is through a solid grounding in the basics. So what you won’t find in Easy Algebra Step-by-Step is a lot of endless drills. Instead, you get a clear explanation that breaks down complex concepts into easy-to-understand steps, followed by highly focused exercises that are linked to core skills--enabling learners to grasp when and how to apply those techniques. This book features: Large step-by-step charts breaking down each step within a process and showing clear connections between topics and annotations to clarify difficulties Stay-in-step panels show how to cope with variations to the core steps Step-it-up exercises link practice to the core steps already presented Missteps and stumbles highlight common errors to avoid You can master algebra as long as you take it Step-by-Step!