Invitation to Mathematics Jacobs Konrad

Jacobs Konrad :
Aperçu :
https://books.google.fr/books?id=Mgajuf62voQC&pg=PA250&lpg=PA250&dq=Invitation+to+Mathematics++Jacobs+Konrad&source=bl&ots=Mpbjr3_3In&sig=Gx1Rf5Nufmt82yIbohOSYMLOxao&hl=fr&sa=X&ei=Ln78VIr-NJPhasXjgqgO&ved=0CFIQ6AEwCQ#v=onepage&q=Invitation%20to%20Mathematics%20%20Jacobs%20Konrad&f=false
Paperback: 247 pages
Publisher: Princeton University Press (November 30, 1991)
Language: English
ISBN-10: 0691025282
ISBN-13: 978-0691025285
Product Dimensions: 6 x 0.6 x 9 inches
Shipping Weight: 1.1 poundsPaperback: 247 pages
Publisher: Princeton University Press (November 30, 1991)
Language: English
ISBN-10: 0691025282
ISBN-13: 978-0691025285
Product Dimensions: 6 x 0.6 x 9 inches
Shipping Weight: 1.1 pounds
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Review
"This is a wonderful book ... [which] provides an informal introduction to mathematical thinking.... This book is the latest in the succession of books designed to introduce mathematical ideas to the general public."--The Times Higher Education Supplement

"Should be read by all teachers of mathematics and mathematics educators."--The Mathematics Teacher
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The author divides his subject into algebra, analysis, and geometry. Each of the three areas could be further subdivided, and could easily generate books in their own right. The author sets himself an ambitious goal; presenting mathematics as a unified subject. That is good, as many recent trends in math tend to fragment and subdivide into sub-specialties, making it hard for readers to get started if they are not already specialists. The author K. Jacobs succeeds admirably in teaching the fundamentals, and at the same time introduce newcomers to mathematical thinking. Ideas are traced thru time, the Greeks, the nineteenth century, and up to active and current trends in math such as game theory, optimization, and dynamical systems...Of the sciences, math stands out in the way some central ideas and tools are timeless. Key math ideas from our first mathematical experiences, perhaps early in life, often have more permanence this way. While the fads do change in math, there are some landmarks that remain, and which inspire generations. And they are as useful now as they were at their inception, the fundamentals of numbers, of geometry, of calculus and differential equations, and more.
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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.

Konrad Jacobs