Kenneth Hoffman Bücher

Exploring the complex evolution of America, this book delves into the nation's journey from its founding ideals of freedom to the challenges posed by socialism and bondage. It presents America as a work in progress, examining the tensions and contradictions that have shaped its identity. Through this lens, the narrative reflects on the ongoing struggle between liberty and control, inviting readers to consider the implications for the future of the American experiment.

Developed for an introductory course in mathematical analysis at MIT, this text focuses on concepts, principles, and methods. Its introductions to real and complex analysis are closely formulated, and they constitute a natural introduction to complex function theory. Starting with an overview of the real number system, the text presents results for subsets and functions related to Euclidean space of n dimensions. It offers a rigorous review of the fundamentals of calculus, emphasizing power series expansions and introducing the theory of complex-analytic functions. Subsequent chapters cover sequences of functions, normed linear spaces, and the Lebesgue interval. They discuss most of the basic properties of integral and measure, including a brief look at orthogonal expansions. A chapter on differentiable mappings addresses implicit and inverse function theorems and the change of variable theorem. Exercises appear throughout the book, and extensive supplementary material includes a Bibliography, List of Symbols, Index, and an Appendix with background in elementary set theory.