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Lectures on Algebra
This book is a timely survey of much of the algebra developed during the last several centuries including its applications to algebraic geometry and its potential use in geometric modeling.The present volume makes an ideal textbook for an abstract algebra course, while the forthcoming sequel, Lectures on Algebra II, will serve as a textbook for a linear algebra course. The author''s fondness for algebraic geometry shows up in both volumes, and his recent preoccupation with the applications of group theory to the calculation of Galois groups is evident in the second volume which contains more local rings and more algebraic geometry. Both books are based on the author''s lectures at Purdue University over the last few years.
Algebra: Chapter 0
Algebra: Chapter 0 is a self-contained introduction to the main topics of algebra, suitable for a first sequence on the subject at the beginning graduate or upper undergraduate level. The primary distinguishing feature of the book, compared to standard textbooks in algebra, is the early introduction of categories, used as a unifying theme in the presentation of the main topics. A second feature consists of an emphasis on homological algebra: basic notions on complexes are presented as soon as modules have been introduced, and an extensive last chapter on homological algebra can form the basis for a follow-up introductory course on the subject. Approximately 1,000 exercises both provide adequate practice to consolidate the understanding of the main body of the text and offer the opportunity to explore many other topics, including applications to number theory and algebraic geometry. This will allow instructors to adapt the textbook to their specific choice of topics and provide the independent reader with a richer exposure to algebra. Many exercises include substantial hints, and navigation of the topics is facilitated by an extensive index and by hundreds of cross-references.
Advanced Algebra
Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Advanced Algebra includes chapters on modern algebra which treat various topics in commutative and noncommutative algebra and provide introductions to the theory of associative algebras, homological algebras, algebraic number theory, and algebraic geometry. Many examples and hundreds of problems are included, along with hints or complete solutions for most of the problems. Together the two books give the reader a global view of algebra and its role in mathematics as a whole.
A Tour of Representation Theory
Offers an introduction to four different flavours of representation theory: representations of algebras, groups, Lie algebras, and Hopf algebras. A separate part of the book is devoted to each of these areas and they are all treated in sufficient depth to enable the reader to pursue research in representation theory.
Handbook of Atmospheric Electrodynamics
The participation of such diverse scientific and technical disciplines as meteorology, astronomy, atmospheric electricity, ionospheric and magnetospheric physics, electromagnetic wave propagation, and radio techniques in the research of atmospherics means that results are published in scientific papers widely spread throughout the literature. This Handbook collects the latest knowledge on atmospherics and presents it in two volumes. Each chapter is written by an expert in his or her field. Topics include the physics of thunderclouds, thunder, global atmospheric electric currents, biological aspects of sferics, and various space techniques for detecting lightning within our own atmosphere as well as in the atmospheres of other planets. Up-to-date applications and methodology are detailed. Volumes I and II offer a comprehensive discussion that together will serve as an important resource for practitioners, professionals, and students alike.
Concepts In Particle Physics: A Concise Introduction To The Standard Model
The 2013 discovery of the Higgs boson posed a challenge to both physics undergraduates and their instructors. Since particle physics is seldom taught at the undergraduate level, the question 'what is the Higgs and why does its discovery matter?' is a common question among undergraduates. Equally, answering this question is a problem for physics instructors.This book is an attempt to put the key concepts of particle physics together in an appealing way, and yet give enough extra tidbits for students seriously considering graduate studies in particle physics. It starts with some recapitulation of relativity and quantum mechanics, and then builds on it to give both conceptual ideas regarding the Standard Model of particle physics as well as technical details. It is presented in an informal lecture style, and includes 'remarks' sections where extra material, history, or technical details are presented for the interested student. The last lecture presents an assessment of the open questions, and where the future might take us.
Mathematical Modelling of Physical Systems
Comprehensive and thorough, this monograph emphasizes the main role differential geometry and convex analysis play in the understanding of physical, chemical, and mechanical notions. Central focus is placed on specifying the agreement between the functional framework and its physical necessity and on making clear the intrinsic character of physical elements, independent from specific charts or frames. The book is divided into four sections, covering thermostructure, classical mechanics, fluid mechanics modelling, and behavior laws. An extensive appendix provides notations and definitions as well as brief explanation of integral manifolds, symplectic structure, and contact structure. Plenty of examples are provided throughout the book, and reviews of basic principles in differential geometry and convex analysis are presented as needed. This book is a useful resource for graduate students and researchers in the field.
geoENV II — Geostatistics for Environmental Applications
This book contains selected contributions from the geoENV98 - the Second European Conference on Geostatistics for Environmental Sciences, held in Valencia, Spain in November 1998. This second book of the geoENV series illustrates the developments on geostatistics as applied to the environmental sciences which have occurred during the past two years. It also presents practical applications which will be of interest to both researchers and practitioners. The book starts with three keynote papers on ecology, climatology and soil science, followed by forty-three contributions. The contents of the book are eminently practical. The objective of the editors was to compile a set of papers in which t...
Differential Topology
The main subjects of the Siegen Topology Symposium are reflected in this collection of 16 research and expository papers. They center around differential topology and, more specifically, around linking phenomena in 3, 4 and higher dimensions, tangent fields, immersions and other vector bundle morphisms. Manifold categories, K-theory and group actions are also discussed.
