This book is an outgrowth of a collection of sixty-two problems offered in the The American Mathematical Monthly (AMM) the author has worked over the last two decades. Each selected problem has a central theme, contains gems of sophisticated ideas connected to important current research, and opens new vistas in the understanding of mathematics. The AMM problem section provides one of the most challenging and interesting problem sections among the various journals and online sources currently available. The published problems and solutions have become a treasure trove rife with mathematical gems. The author presents either his published solution in the AMM or an alternative solution to the published one to present and develop problem-solving techniques. A rich glossary of important theorems and formulas is included for easy reference. The reader may regard this book as a starter set for AMM problems, providing a jumping of point to new ideas, and extending their personal lexicon of problems and solutions. This collection is intended to encourage the reader to move away from routine exercises toward creative solutions, as well as offering the reader a systematic illustration of how to organize the transition from problem solving to exploring, investigating and discovering new results.

A conceptually clear induction to fundamental analysis theorems, a tutorial for creative approaches for solving problems, a collection of modern challenging problems, a pathway to undergraduate research—all these desires gave life to the pages here. This book exposes students to stimulating and enlightening proofs and hard problems of classical analysis mainly published in The American Mathematical Monthly. The author presents proofs as a form of exploration rather than just a manipulation of symbols. Drawing on the papers from the Mathematical Association of America's journals, numerous conceptually clear proofs are offered. Each proof provides either a novel presentation of a familiar theorem or a lively discussion of a single issue, sometimes with multiple derivations. The book collects and presents problems to promote creative techniques for problem-solving and undergraduate research and offers instructors an opportunity to assign these problems as projects. This book provides a wealth of opportunities for these projects. Each problem is selected for its natural charm—the connection with an authentic mathematical experience, its origination from the ingenious work of professionals, develops well-shaped results of broader interest.

Tired of seeing the same careers foisted upon women in TV, movies and magazines? Chemical engineer Stephanie Espy, a graduate of MIT, UC Berkeley and Emory University, tells the stories of 44 inspiring women in STEM to show girls and young women around the world a new set of women heroes to look up to.The statistics for women in Science, Technology, Engineering and Mathematics (STEM) careers are just plain sad. In recent years, fewer than 20% of college graduates in engineering and computer science were women. While stereotypes pervade about women in these fields, the truth is that most girls have never even heard of these careers and are not aware of the wide range of options that exist.In STEM Gems, you and your daughter, niece, neighbor, friend or student will discover: The stories of 44 inspiring women in diverse STEM fields and how they made it; The challenges these incredible women faced in pursuit of their dreams; The tremendous accomplishments these Gems have achieved in their respective STEM fields; Advice on how to pursue science, technology, engineering and mathematics careers; Actionable steps girls and young women can take right now to set themselves up for success; What girls and young women can expect in a promising STEM career, and much, much more!Through the powerful stories of the STEM Gems in this book, girls and young women will have their pick of current role models of various ages, ethnicities and job types. And through the eight chapters that outline actionable steps, girls and young women will learn what they can do right now, today, to set themselves up for success and to create their own unique paths. STEM Gems is relatable, encouraging and inspiring, demonstrating the limitless possibilities for the next generation of women.

Contains more than 100 different ideas, methods and techniques that anyone should be able to use in graphics programming, ranging from basic geometry to specific algorithms in fields like anti-aliased line drawing, texture mapping, splines and polygon rendering.

A guide to the identification, structure, and uses of precious and semi-precious stones, novelty stones, agates, and crystals.

This book is a comprehensive guide to utilizing and creating Ruby Gems. Coverage provides an enormous code library that will help developers improve their projects. It details 34 of the best and most useful Gems, including ones to speed up web applications, process credit card payments, produce PDF documents, read and update RSS feeds, and acquire real-time shipping prices from FedEx and UPS. Each of these also comes complete with actual use cases and code examples that readers can immediately use in their own projects. In addition, the book describes how readers can package and distribute their own Ruby Gems.