This highly readable volume on optimization in function spaces is based on author Amol Sasane's lecture notes, which he developed over several years while teaching a course for third-year undergraduat
Designed for undergraduate math majors, this rigorous and rewarding treatment covers the usual topics of first-year calculus: limits, derivatives, integrals, and infinite series. Prerequisites are a s
A precise, self-contained treatment of Galois theory, this Dover Aurora original features detailed proofs and complete solutions to exercises. The approach advances from introductory material to exten
In this original text, prolific mathematics author Steven G. Krantz addresses conformal geometry, a subject that has occupied him for four decades and for which he helped to develop some of the modern
In addition to serving as an introduction to the basics of point-set topology, this text bridges the gap between the elementary calculus sequence and higher-level mathematics courses. A versatile, ori
Mathematical induction ? along with its equivalents, complete induction and well-ordering, and its immediate consequence, the pigeonhole principle ? are essential proof techniques. Every mathematician
Posing the question "What exactly is a number?" a distinguished German mathematician presents this intriguing and accessible survey. Albrecht Beutelspracher ? founder of the renowned
This well-written and engaging volume introduces knot theory, an area of growing interest in contemporary math teaching. The hands-on approach features many exercises to be completed by readers and re
This thorough, rigorous course on the theory of differentiable manifolds requires a strong background in undergraduate mathematics, including multivariable calculus, linear algebra, elementary abstrac
Derived from courses the author taught at Harvard and Johns Hopkins, this original book introduces the concepts of category theory ? categories, functors, natural transformations, the Yoneda lemma, li
