Introductory Modern Algebra

This insightful book combines the history, pedagogy, and popularization of algebra to present a unified discussion of the subject. Classical Algebra provides a complete and contemporary perspective on classical polynomial algebra through the exploration of how it was developed and how it exists today. With a focus on prominent areas such as the numerical solutions of equations, the systematic study of equations, and Galois theory, this book facilitates a thorough understanding of algebra and illustrates how the concepts of modern algebra originally developed from classical algebraic precursors. This book successfully ties together the disconnect between classical and modern algebraand provides readers with answers to many fascinating questions that typically go unexamined, including: What is algebra about? How did it arise? What uses does it have? How did it develop? What problems and issues have occurred in its history? How were these problems and issues resolved? The author answers these questions and more, shedding light on a rich history of the subject—from ancient and medieval times to the present. Structured as eleven «lessons» that are intended to give the reader further insight on classical algebra, each chapter contains thought-provoking problems and stimulating questions, for which complete answers are provided in an appendix. Complemented with a mixture of historical remarks and analyses of polynomial equations throughout, Classical Algebra: Its Nature, Origins, and Uses is an excellent book for mathematics courses at the undergraduate level. It also serves as a valuable resource to anyone with a general interest in mathematics.

LINEAR ALGEBRA EXPLORE A COMPREHENSIVE INTRODUCTORY TEXT IN LINEAR ALGEBRA WITH COMPELLING SUPPLEMENTARY MATERIALS, INCLUDING A COMPANION WEBSITE AND SOLUTIONS MANUALS Linear Algebra delivers a fulsome exploration of the central concepts in linear algebra, including multidimensional spaces, linear transformations, matrices, matrix algebra, determinants, vector spaces, subspaces, linear independence, basis, inner products, and eigenvectors. While the text provides challenging problems that engage readers in the mathematical theory of linear algebra, it is written in an accessible and simple-to-grasp fashion appropriate for junior undergraduate students.An emphasis on logic, set theory, and functions exists throughout the book, and these topics are introduced early to provide students with a foundation from which to attack the rest of the material in the text. Linear Algebra includes accompanying material in the form of a companion website that features solutions manuals for students and instructors. Finally, the concluding chapter in the book includes discussions of advanced topics like generalized eigenvectors, Schur’s Lemma, Jordan canonical form, and quadratic forms. Readers will also benefit from the inclusion of:A thorough introduction to logic and set theory, as well as descriptions of functions and linear transformationsAn exploration of Euclidean spaces and linear transformations between Euclidean spaces, including vectors, vector algebra, orthogonality, the standard matrix, Gauss-Jordan elimination, inverses, and determinantsDiscussions of abstract vector spaces, including subspaces, linear independence, dimension, and change of basisA treatment on defining geometries on vector spaces, including the Gram-Schmidt processPerfect for undergraduate students taking their first course in the subject matter, Linear Algebra will also earn a place in the libraries of researchers in computer science or statistics seeking an accessible and practical foundation in linear algebra.

Praise for the Third Edition "This volume is ground-breaking in terms of mathematical texts in that it does not teach from a detached perspective, but instead, looks to show students that competent mathematicians bring an intuitive understanding to the subject rather than just a master of applications."  –  Electric Review Learn foundational and advanced topics in linear algebra with this concise and approachable resource A comprehensive introduction, Linear Algebra: Ideas and Applications, Fifth Edition provides a discussion of the theory and applications of linear algebra that blends abstract and computational concepts. With a focus on the development of mathematical intuition, the book emphasizes the need to understand both the applications of a particular technique and the mathematical ideas underlying the technique.  The book introduces each new concept in the context of explicit numerical examples, which allows the abstract concepts to grow organically out of the necessity to solve specific problems. The intuitive discussions are consistently followed by rigorous statements of results and proofs. Linear Algebra: Ideas and Applications, Fifth Edition also features: A new application section on section on Google’s Page Rank Algorithm. A new application section on pricing long term health insurance at a Continuing Care Retirement Community (CCRC). Many other illuminating applications of linear algebra with self-study questions for additional study. End-of-chapter summaries and sections with true-false questions to aid readers with further comprehension of the presented material Numerous computer exercises throughout using MATLAB® code Linear Algebra: Ideas and Applications, Fifth Edition is an excellent undergraduate-level textbook for one or two semester undergraduate courses in mathematics, science, computer science, and engineering. With an emphasis on intuition development, the book is also an ideal self-study reference.

Praise for the Third Edition “This volume is ground-breaking in terms of mathematical texts in that it does not teach from a detached perspective, but instead, looks to show students that competent mathematicians bring an intuitive understanding to the subject rather than just a master of applications.” – Electric Review A comprehensive introduction, Linear Algebra: Ideas and Applications, Fourth Edition provides a discussion of the theory and applications of linear algebra that blends abstract and computational concepts. With a focus on the development of mathematical intuition, the book emphasizes the need to understand both the applications of a particular technique and the mathematical ideas underlying the technique. The book introduces each new concept in the context of an explicit numerical example, which allows the abstract concepts to grow organically out of the necessity to solve specific problems. The intuitive discussions are consistently followed by rigorous statements of results and proofs. Linear Algebra: Ideas and Applications, Fourth Edition also features: Two new and independent sections on the rapidly developing subject of wavelets A thoroughly updated section on electrical circuit theory Illuminating applications of linear algebra with self-study questions for additional study End-of-chapter summaries and sections with true-false questions to aid readers with further comprehension of the presented material Numerous computer exercises throughout using MATLAB® code Linear Algebra: Ideas and Applications, Fourth Edition is an excellent undergraduate-level textbook for one or two semester courses for students majoring in mathematics, science, computer science, and engineering. With an emphasis on intuition development, the book is also an ideal self-study reference.

Maintaining the same accessible and hands-on presentation, Introductory Biostatistics, Second Edition continues to provide an organized introduction to basic statistical concepts commonly applied in research across the health sciences. With plenty of real-world examples, the new edition provides a practical, modern approach to the statistical topics found in the biomedical and public health fields. Beginning with an overview of descriptive statistics in the health sciences, the book delivers topical coverage of probability models, parameter estimation, and hypothesis testing. Subsequently, the book focuses on more advanced topics with coverage of regression analysis, logistic regression, methods for count data, analysis of survival data, and designs for clinical trials. This extensive update of Introductory Biostatistics, Second Edition includes: • A new chapter on the use of higher order Analysis of Variance (ANOVA) in factorial and block designs • A new chapter on testing and inference methods for repeatedly measured outcomes including continuous, binary, and count outcomes • R incorporated throughout along with SAS®, allowing readers to replicate results from presented examples with either software • Multiple additional exercises, with partial solutions available to aid comprehension of crucial concepts • Notes on Computations sections to provide further guidance on the use of software • A related website that hosts the large data sets presented throughout the book Introductory Biostatistics, Second Edition is an excellent textbook for upper-undergraduate and graduate students in introductory biostatistics courses. The book is also an ideal reference for applied statisticians working in the fields of public health, nursing, dentistry, and medicine.

Accessible, succinct, and including numerous student-friendly features, this introductory textbook offers an exceptional foundation to the field for those who are coming to it for the first time. Provides an ideal first course book in phonology, written by a renowned phonologist Developed and tested in the classroom through years of experience and use Emphasizes analysis of phonological data, placing this in its scientific context, and explains the relevant methodology Guides students through the larger questions of what phonological patterns reveal about language Includes numerous course-friendly features, including multi-part exercises and annotated suggestions for further reading at the end of each chapter

Compact but comprehensive, this textbook presents the essential concepts of electronic circuit theory. As well as covering classical linear theory involving resistance, capacitance and inductance it treats practical nonlinear circuits containing components such as operational amplifiers, Zener diodes and exponential diodes. The book’s straightforward approach highlights the similarity between the equations describing direct current (DC), alternating current (AC) and small-signal nonlinear behaviour, thus making the analysis of these circuits easier to comprehend. Introductory Circuits explains: the laws and analysis of DC circuits including those containing controlled sources; AC circuits, focusing on complex currents and voltages, and with extension to frequency domain performance; opamp circuits, including their use in amplifiers and switches; change behaviour within circuits, whether intentional (small-signal performance) or caused by unwanted changes in components. In addition to worked examples within the text a number of problems for student solution are provided at the end of each chapter, ranging in difficulty from the simple to the more challenging. Most solutions for these problems are provided in the book, while others can be found on the accompanying website. Introductory Circuits is designed for first year undergraduate mechanical, biomedical, materials, chemical and civil engineering students who are taking short electrical engineering courses and find other texts on the subject too content-heavy for their needs. With its clear structure and consistent treatment of resistive, reactive and small-signal operation, this volume is also a great supporting text for mainstream electrical engineering students.

In this age of increasing human domination of the Earth's biological and physical resources, a basic understanding of ecology is more important than ever. Students need a textbook that introduces them to the basic principles of ecological science, one that is relevant to today's world, and one that does not overwhelm them with detail and jargon. Peter Cotgreave and Irwin Forseth have designed this book to meet the needs of these students, by providing a basic synthesis of how individual organisms interact with their physical environment, and with each other, to generate the complex ecosystems we see around us. The unifying theme of the book is biodiversity-its patterns, causes, and the growing worldwide threats to it. Basic ecological principles are illustrated using clearly described examples from the current ecological literature. This approach makes the book valuable to all students studying ecology. Examples have been chosen carefully to represent as wide a range of ecosystems (terrestrial and aquatic, northern and southern hemisphere) and life forms (animal, plant and microbe) as possible. Particular attention is paid to consequences of global change on organisms, populations, ecological communities and ecosystems. The end result is a text that presents a readable and persuasive picture of how the Earth's natural systems function, and how that functioning may change over the coming century. Features include: · strong coverage of applied and evolutionary ecology · applications of ecology to the real world · a question-orientated approach · the only comprehensive treatment of ecology written for the introductory student · an emphasis on definitions of key words and phrases · an integration of experimental, observational and theoretical material · examples drawn from all over the world and a wide variety of organisms · a logical structure, building from the response of individual organisms to physical factors, through population growth and population interactions, to community structure and ecosystem function · suggested further reading lists for each chapter · boxes to explain key concepts in more depth · dedicated textsite featuring additional information and teaching aids www.blackwellpublishing.com/cotgreave Peter Cotgreave is an animal ecologist who has worked for the University of Oxford and the Zoological Society of London. His research interests centre on abundance and rarity within animal communities. Irwin Forseth is a plant physiological ecologist who has taught introductory ecology and plant ecology at the University of Maryland since 1982. His research focuses on plant responses to the environment. The authors have studied organisms as diverse as green plants, insects and mammals in habitats from deserts to tropical rainforests. They have worked in ecological research and education in Africa, Asia, North and South America, Europe and the Caribbean.

This book concerns the use of dioid algebra as (max, +) algebra to treat the synchronization of tasks expressed by the maximum of the ends of the tasks conditioning the beginning of another task – a criterion of linear programming. A classical example is the departure time of a train which should wait for the arrival of other trains in order to allow for the changeover of passengers. The content focuses on the modeling of a class of dynamic systems usually called “discrete event systems” where the timing of the events is crucial. Events are viewed as sudden changes in a process which is, essentially, a man-made system, such as automated manufacturing lines or transportation systems. Its main advantage is its formalism which allows us to clearly describe complex notions and the possibilities to transpose theoretical results between dioids and practical applications.

Explore the main algebraic structures and number systems that play a central role across the field of mathematics Algebra and number theory are two powerful branches of modern mathematics at the forefront of current mathematical research, and each plays an increasingly significant role in different branches of mathematics, from geometry and topology to computing and communications. Based on the authors' extensive experience within the field, Algebra and Number Theory has an innovative approach that integrates three disciplines—linear algebra, abstract algebra, and number theory—into one comprehensive and fluid presentation, facilitating a deeper understanding of the topic and improving readers' retention of the main concepts. The book begins with an introduction to the elements of set theory. Next, the authors discuss matrices, determinants, and elements of field theory, including preliminary information related to integers and complex numbers. Subsequent chapters explore key ideas relating to linear algebra such as vector spaces, linear mapping, and bilinear forms. The book explores the development of the main ideas of algebraic structures and concludes with applications of algebraic ideas to number theory. Interesting applications are provided throughout to demonstrate the relevance of the discussed concepts. In addition, chapter exercises allow readers to test their comprehension of the presented material. Algebra and Number Theory is an excellent book for courses on linear algebra, abstract algebra, and number theory at the upper-undergraduate level. It is also a valuable reference for researchers working in different fields of mathematics, computer science, and engineering as well as for individuals preparing for a career in mathematics education.