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A Book of Set Theory
Accessible approach to set theory for upper-level undergraduates poses rigorous but simple arguments. Topics include classes and sets, functions, natural and cardinal numbers, arithmetic of ordinal numbers, and more. 1971 edition with new material by author.
Theory of Lattice-Ordered Groups
Provides a thorough discussion of the orderability of a group. The book details the major developments in the theory of lattice-ordered groups, delineating standard approaches to structural and permutation representations. A radically new presentation of the theory of varieties of lattice-ordered groups is offered.;This work is intended for pure and applied mathematicians and algebraists interested in topics such as group, order, number and lattice theory, universal algebra, and representation theory; and upper-level undergraduate and graduate students in these disciplines.;College or university bookstores may order five or more copies at a special student price which is available from Marcel Dekker Inc, upon request.
Finite Difference Methods for Nonlinear Evolution Equations
Nonlinear evolution equations are widely used to describe nonlinear phenomena in natural and social sciences. However, they are usually quite difficult to solve in most instances. This book introduces the finite difference methods for solving nonlinear evolution equations. The main numerical analysis tool is the energy method. This book covers the difference methods for the initial-boundary value problems of twelve nonlinear partial differential equations. They are Fisher equation, Burgers' equation, regularized long-wave equation, Korteweg-de Vries equation, Camassa-Holm equation, Schrödinger equation, Kuramoto-Tsuzuki equation, Zakharov equation, Ginzburg-Landau equation, Cahn-Hilliard equation, epitaxial growth model and phase field crystal model. This book is a monograph for the graduate students and science researchers majoring in computational mathematics and applied mathematics. It will be also useful to all researchers in related disciplines.
Stable Modules and the D(2)-Problem
This 2003 book is concerned with two fundamental problems in low-dimensional topology. Firstly, the D(2)-problem, which asks whether cohomology detects dimension, and secondly the realization problem, which asks whether every algebraic 2-complex is geometrically realizable. The author shows that for a large class of fundamental groups these problems are equivalent. Moreover, in the case of finite groups, Professor Johnson develops general methods and gives complete solutions in a number of cases. In particular, he presents a complete treatment of Yoneda extension theory from the viewpoint of derived objects and proves that for groups of period four, two-dimensional homotopy types are parametrized by isomorphism classes of projective modules. This book is carefully written with an eye on the wider context and as such is suitable for graduate students wanting to learn low-dimensional homotopy theory as well as established researchers in the field.
A Generalized Taylor's Formula for Functions of Several Variables and Certain of its Applications
The classical Taylor's formula of advanced calculus is generalized, extending the notion of the differentiability class Cm, with applications to maxima and minima and to sufficiency of jets.
Structures for Semantics
Formalization plays an important role in semantics. Doing semantics and following the literature requires considerable technical sophistica tion and acquaintance with quite advanced mathematical techniques and structures. But semantics isn't mathematics. These techniques and structures are tools that help us build semantic theories. Our real aim is to understand semantic phenomena and we need the technique to make our understanding of these phenomena precise. The problems in semantics are most often too hard and slippery, to completely trust our informal understanding of them. This should not be taken as an attack on informal reasoning in semantics. On the contrary, in my view, very often the essential insight in a diagnosis of what is going on in a certain semantic phenomenon takes place at the informal level. It is very easy, however, to be misled into thinking that a certain informal insight provides a satisfying analysis of a certain problem; it will often turn out that there is a fundamental unclarity about what the informal insight actually is. Formalization helps to sharpen those insights and put them to the test.
