Brief, clear, and well written, this introductory treatment bridges the gap between traditional and modern algebra. Includes exercises with complete solutions. The only prerequisite is high school-level algebra. 1959 edition.
Functional analysis arose from traditional topics of calculus and integral and differential equations. This accessible text by an internationally renowned teacher and author starts with problems in numerical analysis and shows how they lead naturally to the concepts of functional analysis. Suitable for advanced undergraduates and graduate students, this book provides coherent explanations for complex concepts. Topics include Banach and Hilbert spaces, contraction mappings and other criteria for convergence, differentiation and integration in Banach spaces, the Kantorovich test for convergence of an iteration, and Rall's ideas of polynomial and quadratic operators. Numerous examples appear throughout the text.
"Recommended with confidence" by The Times Literary Supplement, this lively survey starts with arithmetic and algebra and gradually proceeds to trigonometry and calculus. The author, who is internationally renowned for his innovative teaching methods, offers insights into the pleasures of mathematics that will appeal to readers of all backgrounds. 1943 edition.
A noted educator's account of some of the more stimulating and surprising branches of mathematics, this volume profiles the mathematical mind and the aims of mathematics. Five introductory chapters offer conceptual groundwork, and subsequent chapters present lucid, accessible explorations of non-Euclidean geometry, matrices, determinants, group theory, and related topics. 1955 edition.