Abstract Algebra

In the same way the subject evolved historically, Ronald Solomon lets the abstract concepts emerge gradually from less abstract problems about geometry, polynomials, numbers, and more. Solomon also strongly emphasizes the connections between algebra and other areas of mathematics -- analysis (the infinitesimal calculus) and geometry. Readers will see that the various areas of mathematics are not hermetically sealed off from each other and that most of the truly important achievements in mathematics have been the product of a fruitful interaction of different areas. Using this book, readers will gain a true understanding of the subject while being creative mathematically as opposed to simply imitating template problems.