This book, which is bosed on Polya's method of problem solving, aids students in their transition from calculus (or precolculus) to higher-level mathematics. The book begins by providing a great deal of guidance on how to approach definitions, examples, and theorems in mathematics. It ends by providing projects for independent study.
Students will follow Pôlyo's four-step process: learn ta understand the problem; devise a plan to solve the problem; carry out that plan; and look bock and check what the results told them. Special emphosis is placed on rending corefully and writing well. The outhors have included a wide voriety of examples, exercises with solutions, problems, and over 40 illustrations, chusen ta emphosize these goals. Historical connections are made throughout the text, and students are encouroged to use the rather extensive bibliogrophy ta begin making connections of their own. While standard texts in this ares prepore students for future courses in algebra, this book also includes chapters on sequences, convergence, and metric spaces for those wanting ta bridge the gap between the standard course in calculus and one in onalysis.