Set linear algebras, introduced by the authors in this book, are the most generalized form of linear algebras. These structures make use of very few algebraic operations and are easily accessible to non-mathematicians as well. The dominance of computers in everyday life calls for a paradigm shift in the concepts of linear algebra. The authors believe that set linear algebra will cater to that need.
The main aim of this book is to present a completely algebraic approach to the Enriques' classification of smooth projective surfaces defined over an algebraically closed field of arbitrary characteristic. This algebraic approach is one of the novelties of this book among the other modern textbooks devoted to this subject. Two chapters on surface singularities are also included. The book can be useful as a textbook for a graduate course on surfaces, for researchers or graduate students in algebraic geometry, as well as those mathematicians working in algebraic geometry or related fields.
Elementary Number Theory: A Problem Oriented Approach
This book is designed so that it may be used in several ways : it can be used for self study, as a guide for tutorially directed work, or as a supplementary text or source of problems for an ordinary first or second course in number theory. The aim of the book is similar to that of Aufgaben und Lehrsatze aus der Analysis by Polya and Szego. ... The book is written by hand in calligraphy by Gregory Maskarinec. A unique presentation.
IN this book we have sought to give an account of a department of mathematics which is now generally regarded as fundamental. A list of the men to whom the successive advances of the subject are due, includes, with few exceptions, the names of the greatest French and German mathematicians of the century, from Cauchy and Gauss onward. And in line with these advances lie the chief fields of mathematical activity at the present day.
Our first knowledge of differential geometry usually comes from the study of the curves and surfaces in $I!!R^3$ that arise in calculus. Here we learn about line and surface integrals, divergence and curl, and the various forms of Stokes' Theorem. If we are fortunate, we may encounter curvature and such things as the Serret-Frenet formulas. With just the basic tools from multivariable calculus, plus a little knowledge of linear algebra, it is possible to begin a much richer and rewarding study of differential geometry, which is what is presented in this book.
