Building bridges between classical results and contemporary nonstandard problems, this highly relevant work embraces important topics in analysis and algebra from a problem-solving perspective. The book is structured to assist the reader in formulating and proving conjectures, as well as devising solutions to important mathematical problems by making connections between various concepts and ideas from different areas of mathematics. Instructors and motivated mathematics students from high school juniors to college seniors will find the work a useful resource in calculus, linear and abstract algebra, analysis and differential equations. Students with an interest in mathematics competitions must have this book in their personal libraries.
This book takes familiar ideas and extends them to a rich variety of problems. The intended audience is the ambitious high school or college student. The topics covered span algebra, geometry, number theory, and even a few elements of mathematical analysis. Each chapter explores specific themes and ideas that underlie the aforementioned subject areas. The ""landscapes"" presented provide a ""view"" into areas that are not typically encountered in great depth in standard coursework but nonetheless have profound implications.
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