This book is an ideal text for an advanced course in the theory of complex functions. The author successfully enables the reader to experience function theory personally and to participate in the work of the creative mathematician. Unlike the first volume, it contains numerous glimpses of the function theory of several complex variables emphasizing how autonomous this discipline has become. Covered are Weierstrass' product theorem, Mittag-Leffler's theorem, the Riemann mapping theorem, and Runge's theorems on approximations of analytic functions.
Hidden Harmonies: The Lives and Times of the Pythagorean Theorem
A squared plus b squared equals c squared. It sounds simple, doesn't it? Yet this familiar expression is a gateway into the riotous garden of mathematics, and sends us on a journey of exploration in the company of two inspired guides, acclaimed authors Robert and Ellen Kaplan. With wit, verve, and clarity, they trace the life of the Pythagorean theorem, from ancient Babylon to the present, visiting along the way Leonardo da Vinci, Albert Einstein, President James Garfield, and the Freemasons-not to mention the elusive Pythagoras himself, who almost certainly did not make the statement that bears his name.
God's Equation: Einstein, Relativity, and the Expanding Universe
Are we on the verge of solving the riddle of creation using Einstein's ""greatest blunder""? In a work that is at once lucid, exhilarating and profound, renowned mathematician Dr. Amir Aczel, critically acclaimed author of Fermat's Last Theorem, takes us into the heart of science's greatest mystery.
This is the text for a two-semester multivariable calculus course. The setting is n-dimensional Euclidean space, with the material on differentiation culminating in the Inverse Function Theorem and its consequences, and the material on integration culminating in the Generalized Fundamental Theorem of Integral Calculus (often called Stokes's Theorem) and some of its consequences in turn. The prerequisite is a proof-based course in one-variable calculus.
Introduction to the Theory of GroupsAnyone who has studied "abstract algebra" and linear algebra as an undergraduate can understand this book. This edition has been completely revised and reorganized, without however losing any of the clarity of presentation that was the hallmark of the previous editions. The first six chapters provide ample material for a first course: beginning with the basic properties of groups and homomorphisms, topics covered include Lagrange's theorem, the Noether isomorphism theorems, symmetric groups, G-sets, the Sylow theorems, finite Abelian groups, the Krull-Schmidt theorem, solvable and nilpotent groups, and the Jordan-Holder theorem.
