Each undergraduate course of algebra begins with basic notions and results concerning groups, rings, modules and linear algebra. That is, it begins with simple notions and simple results. Our intention was to provide a collection of exercises which cover only the easy part of ring theory, what we have named the "Basics of Ring Theory." This seems to be the part each student or beginner in ring theory (or even algebra) should know - but surely trying to solve as many of these exercises as possible independently. As difficult (or impossible) as this may seem, we have made every effort to avoid...

The book Complex Analysis through Examples and Exercises has come out from the lectures and exercises that the author held mostly for mathematician and physists . The book is an attempt to present the rat her involved subject of complex analysis through an active approach by the reader. Thus this book is a complex combination of theory and examples. Complex analysis is involved in all branches of mathematics. It often happens that the complex analysis is the shortest path for solving a problem in real circum stances. We are using the (Cauchy) integral approach and the (Weierstrass) power se...

It became more and more usual, from, say, the 1970s, for each book on Module Theory, to point out and prove some (but in no more than 15 to 20 pages) generalizations to (mostly modular) lattices. This was justified by the nowadays widely accepted perception that the structure of a module over a ring is best understood in terms of the lattice struc- ture of its submodule lattice. Citing Louis H. Rowen "this important example (the lattice of all the submodules of a module) is the raison d'etre for the study of lattice theory by ring theorists." Indeed, many module-theoretic results can be...

This book, in some sense, began to be written by the first author in 1983, when optional lectures on Abelian groups were held at the Fac- ulty of Mathematics and Computer Science, 'Babes-Bolyai' University in Cluj-Napoca, Romania. From 1992, these lectures were extended to a twosemester electivecourse on abelian groups for undergraduate stu- dents, followed by a twosemester course on the same topic for graduate students in Algebra. All the other authors attended these two years of lectures and are now Assistants to the Chair of Algebra of this Fac- ulty. The first draft of this collection,...

The understanding of results and notions for a student in mathematics requires solving ex ercises. The exercises are also meant to test the reader's understanding of the text material, and to enhance the skill in doing calculations. This book is written with these three things in mind. It is a collection of more than 450 exercises in Functional Analysis, meant to help a student understand much better the basic facts which are usually presented in an introductory course in Functional Analysis. Another goal of this book is to help the reader to understand the richness of ideas and techniques...

Over the past decade there has been an increasing demand for suitable material in the area of mathematical modelling as applied to science, engineering, business and management. Recent developments in computer technology and related software have provided the necessary tools of increasing power and sophistication which have significant implications for the use and role of mathematical modelling in the above disciplines. In the past, traditional methods have relied heavily on expensive experimentation and the building of scaled models, but now a more flexible and cost effective approach is...

In my early years I was constituted in the exacting imperatives of philosophical analysis. That stern face is present in the composition of the Newton essays chosen here for republication. It is my hope that potential readers will be patient with the old Adam of analysis, and seize the portrait of Newton's intellec- tual world presented in these essays. It is gratifying for me to acknowledge the encouragement of Robert Butts and John Nicholas of the University of Western Ontario, intellectual comrades in arms. It was at Western that I began my intellectual journey, and many of the present...

This volume covers in detail both the fundamental and practical properties of interstitial intermetallic materials, materials which are useful as hydrogen storage materials, as rechargeable hydrogen electrodes in batteries, and as new potential hard permanent magnetic materials. Various techniques, such as magnetic, diffraction, thermodynamic and spectral methods for studying these materials are covered in detail at a tutorial level. The synthetic methods used to obtain these new materials are also covered in detail.

Molecular Physics and Hypersonic Flows bridges the gap between the fluid dynamics and molecular physics communities, emphasizing the role played by elementary processes in hypersonic flows. In particular, the work is primarily dedicated to filling the gap between microscopic and macroscopic treatments of the source terms to be inserted in the fluid dynamics codes.
The first part of the book describes the molecular dynamics of elementary processes both in the gas phase and in the interaction with surfaces by using quantum mechanical and phenomenological approaches. A second...