Invitation to Mathematics

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.