The tenth edition of Mathematical Ideas is the best ever! We have continued with the features and pedagogy that have made this book so successful over the years and at the same time, we've spent a considerable amount of time to incorporate fresh data, new photos, and new content (by way of a new chapter on trigonometry). We have tried to reflect the needs of our users-both long-time readers and those new to the Math Ideas way of teaching liberal arts math. We hope you'll be pleased with the results.Like its predecessors, this edition has been designed with a variety of students in mind. It is well-suited for several courses, including the aforementioned liberal arts audience, survey courses in mathematics, and mathematics for prospective and in-service elementary and middle school teachers. Ample topics are included for a two-term course, yet the variety of topics and flexibility of sequence make the text suitable for shorter courses as well. Our main objectives continue to be to provide comprehensive coverage of topics, appropriate organization, clear exposition, an abundance of examples, and well-planned exercise sets with numerous applications.Chapter Openers Each chapter opens with an application related to the chapter topic. These help students see the relevance of mathematics they are about to learn. Margin Notes This popular feature has become a hallmark of this text and has been retained, updated, and added to where appropriate. Interspersed throughout the text, they deal with various subjects such as lives of mathematicians, historical vignettes, stamp and coin reproductions, anecdotes, newspaper and magazine articles, and current research in mathematics. They are designed to show students that math can be fun and interesting. We hope that users continue to enjoy the margin notes as much as we enjoy researching and composing them. Varied Exercise Sets We continue to present a variety of exercises including drill, conceptual, and applied problems. We continue to use graphs, tables, and charts when appropriate. Most sections include a few challenging exercises that require students to extend the ideas presented in the section. To address the issue of writing across the curriculum, most exercise sets include some exercises that require the student to answer by writing a few sentences. For Further Thought These entries encourage students to discuss among themselves their reasoning processes to gain a deeper understanding of key mathematical concepts by taking what they've just learned one step further. Examples Numerous, carefully written examples illustrate the concepts and skills introduced and give students step-by-step directions to help solve similar problems. Problem Solving Special paragraphs labeled "problem solving" relate the discussion of problem-solving strategies to techniques learned earlier in the chapter. Collaborative Investigations In response to instructor requests, we continue to address the issue of cooperative learning in the end-of-chapter feature "Collaborative Investigation." These exercises can be done in small groups or with the whole class and are designed to promote communication about mathematics topics. Chapter Tests Each chapter concludes with a chapter test so students can check their mastery of the material. The answers are provided at the back of the text.