Bücher von Steven Roman

This book is about object-oriented programming and how it is implemented in Microsoft Visual Basic. Accordingly, the book has two separate, but inter- twined, goals. The first is to describe the general concepts of object orientation and the second is to describe how to do object-oriented programming in Visual Basic. I intend this to be a short, no-nonsense book that can be read through once and then easily referred to at later times. (Long stories about a mythical company and its programming problems are seldom interesting the first time through, let alone the second, third or fourth times!) To read this book, you need only a minimal acquaintance with Visual Basic. In particular, I assume you can construct a simple Visual Basic program and have some rudimentary knowledge of fundamental programming tech- niques. This book does not teach Visual Basic - it teaches you how to pro- gram Visual Basic in an object-oriented way. The issue here is not how much Visual Basic you already know - it is that you want to learn about object- oriented programming techniques. With regard to the first goal of the book, it is my feeling that a discussion of the underlying concepts of object orientation Oust what is an object, a class, encapsulation, abstraction, and so on) is essential in order to take full advan- tage of any object-oriented language. Simply put, it will help you understand what you are doing if you know why you are doing it.

This book is a thorough introduction to linear algebra, for the graduate or advanced undergraduate student. Prerequisites are limited to a knowledge of the basic properties of matrices and determinants. However, since we cover the basics of vector spaces and linear transformations rather rapidly, a prior course in linear algebra (even at the sophomore level), along with a certain measure of "e;mathematical maturity,"e; is highly desirable. Chapter 0 contains a summary of certain topics in modern algebra that are required for the sequel. This chapter should be skimmed quickly and then used primarily as a reference. Chapters 1-3 contain a discussion of the basic properties of vector spaces and linear transformations. Chapter 4 is devoted to a discussion of modules, emphasizing a comparison between the properties of modules and those of vector spaces. Chapter 5 provides more on modules. The main goals of this chapter are to prove that any two bases of a free module have the same cardinality and to introduce noetherian modules. However, the instructor may simply skim over this chapter, omitting all proofs. Chapter 6 is devoted to the theory of modules over a principal ideal domain, establishing the cyclic decomposition theorem for finitely generated modules. This theorem is the key to the structure theorems for finite dimensional linear operators, discussed in Chapters 7 and 8. Chapter 9 is devoted to real and complex inner product spaces.

Intended for graduate courses or for independent study, this book presents the basic theory of fields. The first part begins with a discussion of polynomials over a ring, the division algorithm, irreducibility, field extensions, and embeddings. The second part is devoted to Galois theory. The third part of the book treats the theory of binomials. The book concludes with a chapter on families of binomials - the Kummer theory.

It then proceeds to a discussion of modules, emphasizing a comparison with vector spaces, and presents a thorough discussion of inner product spaces, eigenvalues, eigenvectors, and finite dimensional spectral theory, culminating in the finite dimensional spectral theorem for normal operators.

The remaining three chapters deal with coding theory: communication channels, decoding in the presence of errors, the general theory of linear codes, and such specific codes as Hamming codes, the simplex codes, and many others.

The first chapter of the book introduces the definitions of category and functor and discusses diagrams,duality, initial and terminal objects, special types of morphisms, and some special types of categories,particularly comma categories and hom-set categories.

This textbook provides an introduction to the Catalan numbers and their remarkable properties, along with their various applications in combinatorics.

Written for readers who are not computer or electrical engineers, this book is for those who want enough information to make intelligent buying or upgrading decisions, maximize their productivity, and become less dependant on others for help.

Fundamentals of Group Theory provides a comprehensive account of the basic theory of groups. Group Theory is a timely and fundamental addition to literature in the study of groups.

This user-friendly book is intended to be a thorough introduction to the subject of ordered sets and lattices, with an emphasis on the latter. The presentation is lucid and the book contains a plethora of exercises, examples, and illustrations.

Completely rewritten for its second edition, this book concentrates on discrete derivative pricing models, culminating in a thorough derivation of the Black-Scholes option pricing formulas as a limiting case of the Cox-Ross-Rubinstein discrete model.