### Summary and Info

Based on a well-received course designed for philosophy students, this book is an informal introduction to mathematical thinking. The work will be rewarding not only for philosophers concerned with mathematical questions but also for serious amateur mathematicians with an interest in the "frontiers" as well as the foundations of mathematics. In what might be termed a sampler of the discipline, Konrad Jacobs discusses an unusually wide range of topics, including such items of contemporary interest as knot theory, optimization theory, and dynamical systems. Using Euclidean geometry and algebra to introduce the mathematical mode of thought, the author then turns to recent developments. In the process he offers what he calls a "Smithsonian of mathematical showpieces": the five Platonic Solids, the Mbius Strip, the Cantor Discontinuum, the Peano Curve, Reidemeister's Knot Table, the plane ornaments, Alexander's Horned Sphere, and Antoine's Necklace. The treatments of geometry and algebra are followed by a chapter on induction and one on optimization, game theory, and mathematical economics. The chapter on topology includes a discussion of topological spaces and continuous mappings, curves and knots, Euler's polyhedral formula for surfaces, and the fundamental group. The last chapter deals with dynamics and contains material on the Game of Life, circle rotation, Smale's "horseshoe," and stability and instability, among other topics This book is about writing in the professional mathematical environment. There are few people equal to this task, yet Steven Krantz is one who qualifies. While the book is nominally about writing, it's also about how to function in the mathematical profession. Those who are familiar with Krantz's writing will recognize his lively, inimitable style. In this volume, he addresses these nuts-and-bolts issues: syntax, grammar, structure, and style; mathematical exposition; use of the computer and T[subscript E]X; E-mail etiquette; and all aspects of publishing a journal article.Krantz's frank and straightforward approach makes this particularly suitable as a textbook. He does not avoid difficult topics. His intent is to demonstrate to the reader how to successfully operate within the profession. He outlines how to write grant proposals that are persuasive and compelling, how to write a letter of recommendation describing the research abilities of a candidate for promotion or tenure, and what a dean is looking for in a letter of recommendation. He further addresses some basic issues such as writing a book proposal to a publisher or applying for a job. Read more... The basics -- Topics specific to the writing of mathematics -- Exposition -- Other types of writing -- Books -- The modern writing environment -- Closing thoughts

### More About the Author

Steven George Krantz (born February 3, 1951) is an American scholar, mathematician, and writer. He has authored numerous research papers and several books, and edited journals such as the Notices of the American Mathematical Society and The Journal of Geometric Analysis.

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