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Basic Algebra II: Second Edition
by Nathan JacobsonA classic text and standard reference for a generation, this volume and its companion are the work of an expert algebraist who taught at Yale for more than three decades. Nathan Jacobson's books possess a conceptual and theoretical orientation; in addition to their value as classroom texts, they serve as valuable references.Volume II comprises all of the subjects usually covered in a first-year graduate course in algebra. Topics include categories, universal algebra, modules, basic structure theory of rings, classical representation theory of finite groups, elements of homological algebra with applications, commutative ideal theory, and formally real fields. In addition to the immediate introduction and constant use of categories and functors, it revisits many topics from Volume I with greater depth and sophistication. Exercises appear throughout the text, along with insightful, carefully explained proofs.
Basic Algebraic Geometry 1: Varieties in Projective Space (Springer Study Edition Ser.)
by Miles Reid Igor R. ShafarevichShafarevich's Basic Algebraic Geometry has been a classic and universally used introduction to the subject since its first appearance over 40 years ago. As the translator writes in a prefatory note, ``For all [advanced undergraduate and beginning graduate] students, and for the many specialists in other branches of math who need a liberal education in algebraic geometry, Shafarevich's book is a must.'' The third edition, in addition to some minor corrections, now offers a new treatment of the Riemann--Roch theorem for curves, including a proof from first principles. Shafarevich's book is an attractive and accessible introduction to algebraic geometry, suitable for beginning students and nonspecialists, and the new edition is set to remain a popular introduction to the field.
Basic Algebraic Geometry 2: Schemes and Complex Manifolds
by Miles Reid Igor R. ShafarevichShafarevich's Basic Algebraic Geometry has been a classic and universally used introduction to the subject since its first appearance over 40 years ago. As the translator writes in a prefatory note, ``For all [advanced undergraduate and beginning graduate] students, and for the many specialists in other branches of math who need a liberal education in algebraic geometry, Shafarevich's book is a must.'' The second volume is in two parts: Book II is a gentle cultural introduction to scheme theory, with the first aim of putting abstract algebraic varieties on a firm foundation; a second aim is to introduce Hilbert schemes and moduli spaces, that serve as parameter spaces for other geometric constructions. Book III discusses complex manifolds and their relation with algebraic varieties, Kähler geometry and Hodge theory. The final section raises an important problem in uniformising higher dimensional varieties that has been widely studied as the ``Shafarevich conjecture''. The style of Basic Algebraic Geometry 2 and its minimal prerequisites make it to a large extent independent of Basic Algebraic Geometry 1, and accessible to beginning graduate students in mathematics and in theoretical physics.
Basic Algebraic Topology
by Anant R. ShastriBuilding on rudimentary knowledge of real analysis, point-set topology, and basic algebra, Basic Algebraic Topology provides plenty of material for a two-semester course in algebraic topology. The book first introduces the necessary fundamental concepts, such as relative homotopy, fibrations and cofibrations, category theory, cell complexes, and si
Basic Algebraic Topology and its Applications
by Mahima Ranjan AdhikariThis book provides an accessible introduction to algebraic topology, a field at the intersection of topology, geometry and algebra, together with its applications. Moreover, it covers several related topics that are in fact important in the overall scheme of algebraic topology. Comprising eighteen chapters and two appendices, the book integrates various concepts of algebraic topology, supported by examples, exercises, applications and historical notes. Primarily intended as a textbook, the book offers a valuable resource for undergraduate, postgraduate and advanced mathematics students alike. Focusing more on the geometric than on algebraic aspects of the subject, as well as its natural development, the book conveys the basic language of modern algebraic topology by exploring homotopy, homology and cohomology theories, and examines a variety of spaces: spheres, projective spaces, classical groups and their quotient spaces, function spaces, polyhedra, topological groups, Lie groups and cell complexes, etc. The book studies a variety of maps, which are continuous functions between spaces. It also reveals the importance of algebraic topology in contemporary mathematics, theoretical physics, computer science, chemistry, economics, and the biological and medical sciences, and encourages students to engage in further study.
Basic Analysis I: Functions of a Real Variable
by James K. PetersonBasic Analysis I: Functions of a Real Variable is designed for students who have completed the usual calculus and ordinary differential equation sequence and a basic course in linear algebra. This is a critical course in the use of abstraction, but is just first volume in a sequence of courses which prepare students to become practicing scientists. This book is written with the aim of balancing the theory and abstraction with clear explanations and arguments, so that students who are from a variety of different areas can follow this text and use it profitably for self-study. It can also be used as a supplementary text for anyone whose work requires that they begin to assimilate more abstract mathematical concepts as part of their professional growth. Features Can be used as a traditional textbook as well as for self-study Suitable for undergraduate mathematics students, or for those in other disciplines requiring a solid grounding in abstraction Emphasises learning how to understand the consequences of assumptions using a variety of tools to provide the proofs of propositions
Basic Analysis II: A Modern Calculus in Many Variables
by James K. PetersonBasic Analysis II: A Modern Calculus in Many Variables focuses on differentiation in Rn and important concepts about mappings from Rn to Rm, such as the inverse and implicit function theorem and change of variable formulae for multidimensional integration. These topics converge nicely with many other important applied and theoretical areas which are no longer covered in mathematical science curricula. Although it follows on from the preceding volume, this is a self-contained book, accessible to undergraduates with a minimal grounding in analysis. Features Can be used as a traditional textbook as well as for self-study Suitable for undergraduates in mathematics and associated disciplines Emphasises learning how to understand the consequences of assumptions using a variety of tools to provide the proofs of propositions
Basic Analysis III: Mappings on Infinite Dimensional Spaces
by James K. PetersonBasic Analysis III: Mappings on Infinite Dimensional Spaces is intended as a first course in abstract linear analysis. This textbook cover metric spaces, normed linear spaces and inner product spaces, along with many other deeper abstract ideas such a completeness, operators and dual spaces. These topics act as an important tool in the development of a mathematically trained scientist. Feature: Can be used as a traditional textbook as well as for self-study Suitable for undergraduates in mathematics and associated disciplines Emphasizes learning how to understand the consequences of assumptions using a variety of tools to provide the proofs of propositions
Basic Analysis IV: Measure Theory and Integration
by James K. PetersonBasic Analysis IV: Measure Theory and Integration introduces students to concepts from measure theory and continues their training in the abstract way of looking at the world. This is a most important skill to have when your life's work will involve quantitative modeling to gain insight into the real world. This text generalizes the notion of integration to a very abstract setting in a variety of ways. We generalize the notion of the length of an interval to the measure of a set and learn how to construct the usual ideas from integration using measures. We discuss carefully the many notions of convergence that measure theory provides. Features • Can be used as a traditional textbook as well as for self-study • Suitable for advanced students in mathematics and associated disciplines• Emphasises learning how to understand the consequences of assumptions using a variety of tools to provide the proofs of propositions
Basic Analysis V: Functional Analysis and Topology
by James K. PetersonBasic Analysis V: Functional Analysis and Topology introduces graduate students in science to concepts from topology and functional analysis, both linear and nonlinear. It is the fifth book in a series designed to train interested readers how to think properly using mathematical abstractions, and how to use the tools of mathematical analysis in applications. It is important to realize that the most difficult part of applying mathematical reasoning to a new problem domain is choosing the underlying mathematical framework to use on the problem. Once that choice is made, we have many tools we can use to solve the problem. However, a different choice would open up avenues of analysis from a different, perhaps more productive, perspective. In this volume, the nature of these critical choices is discussed using applications involving the immune system and cognition. Features Develops a proof of the Jordan Canonical form to show some basic ideas in algebraic topology Provides a thorough treatment of topological spaces, finishing with the Krein–Milman theorem Discusses topological degree theory (Brouwer, Leray–Schauder, and Coincidence) Carefully develops manifolds and functions on manifolds ending with Riemannian metrics Suitable for advanced students in mathematics and associated disciplines Can be used as a traditional textbook as well as for self-study Author James K. Peterson is an Emeritus Professor at the School of Mathematical and Statistical Sciences, Clemson University. He tries hard to build interesting models of complex phenomena using a blend of mathematics, computation, and science. To this end, he has written four books on how to teach such things to biologists and cognitive scientists. These books grew out of his Calculus for Biologists courses offered to the biology majors from 2007 to 2015. He has taught the analysis courses since he started teaching both at Clemson and at his previous post at Michigan Technological University. In between, he spent time as a senior engineer in various aerospace firms and even did a short stint in a software development company. The problems he was exposed to were very hard, and not amenable to solution using just one approach. Using tools from many branches of mathematics, from many types of computational languages, and from first-principles analysis of natural phenomena was absolutely essential to make progress. In both mathematical and applied areas, students often need to use advanced mathematics tools they have not learned properly. So, he has recently written a series of five books on mathematical analysis to help researchers with the problem of learning new things after they have earned their degrees and are practicing scientists. Along the way, he has also written papers in immunology, cognitive science, and neural network technology, in addition to having grants from the NSF, NASA, and the US Army. He also likes to paint, build furniture, and write stories.
Basic and Advanced Bayesian Structural Equation Modeling
by Xin-Yuan Song Sik-Yum LeeThis book provides clear instructions to researchers on how to apply Structural Equation Models (SEMs) for analyzing the inter relationships between observed and latent variables.Basic and Advanced Bayesian Structural Equation Modeling introduces basic and advanced SEMs for analyzing various kinds of complex data, such as ordered and unordered categorical data, multilevel data, mixture data, longitudinal data, highly non-normal data, as well as some of their combinations. In addition, Bayesian semiparametric SEMs to capture the true distribution of explanatory latent variables are introduced, whilst SEM with a nonparametric structural equation to assess unspecified functional relationships among latent variables are also explored.Statistical methodologies are developed using the Bayesian approach giving reliable results for small samples and allowing the use of prior information leading to better statistical results. Estimates of the parameters and model comparison statistics are obtained via powerful Markov Chain Monte Carlo methods in statistical computing.Introduces the Bayesian approach to SEMs, including discussion on the selection of prior distributions, and data augmentation.Demonstrates how to utilize the recent powerful tools in statistical computing including, but not limited to, the Gibbs sampler, the Metropolis-Hasting algorithm, and path sampling for producing various statistical results such as Bayesian estimates and Bayesian model comparison statistics in the analysis of basic and advanced SEMs.Discusses the Bayes factor, Deviance Information Criterion (DIC), and $L_\nu$-measure for Bayesian model comparison.Introduces a number of important generalizations of SEMs, including multilevel and mixture SEMs, latent curve models and longitudinal SEMs, semiparametric SEMs and those with various types of discrete data, and nonparametric structural equations.Illustrates how to use the freely available software WinBUGS to produce the results.Provides numerous real examples for illustrating the theoretical concepts and computational procedures that are presented throughout the book.Researchers and advanced level students in statistics, biostatistics, public health, business, education, psychology and social science will benefit from this book.
Basic Applied Bioinformatics
by Mir Asif Iquebal Ratan Kumar Choudhary Chandra Sekhar MukhopadhyayAn accessible guide that introduces students in all areas of life sciences to bioinformatics Basic Applied Bioinformatics provides a practical guidance in bioinformatics and helps students to optimize parameters for data analysis and then to draw accurate conclusions from the results. In addition to parameter optimization, the text will also familiarize students with relevant terminology. Basic Applied Bioinformatics is written as an accessible guide for graduate students studying bioinformatics, biotechnology, and other related sub-disciplines of the life sciences. This accessible text outlines the basics of bioinformatics, including pertinent information such as downloading molecular sequences (nucleotide and protein) from databases; BLAST analyses; primer designing and its quality checking, multiple sequence alignment (global and local using freely available software); phylogenetic tree construction (using UPGMA, NJ, MP, ME, FM algorithm and MEGA7 suite), prediction of protein structures and genome annotation, RNASeq data analyses and identification of differentially expressed genes and similar advanced bioinformatics analyses. The authors Chandra Sekhar Mukhopadhyay, Ratan Kumar Choudhary, and Mir Asif Iquebal are noted experts in the field and have come together to provide an updated information on bioinformatics. Salient features of this book includes: Accessible and updated information on bioinformatics tools A practical step-by-step approach to molecular-data analyses Information pertinent to study a variety of disciplines including biotechnology, zoology, bioinformatics and other related fields Worked examples, glossary terms, problems and solutions Basic Applied Bioinformatics gives students studying bioinformatics, agricultural biotechnology, animal biotechnology, medical biotechnology, microbial biotechnology, and zoology an updated introduction to the growing field of bioinformatics.
Basic Biostatistics: Statistics for Public Health Practice
by B. Burt GerstmanBasic Biostatistics is a concise, introductory text that covers biostatistical principles and focuses on the common types of data encountered in public health and biomedical fields. The text puts equal emphasis on exploratory and confirmatory statistical methods. Sampling, exploratory data analysis, estimation, hypothesis testing, and power and precision are covered through detailed, illustrative examples. The book is organized into three parts: Part I addresses basic concepts and techniques; Part II covers analytic techniques for quantitative response variables; and Part III covers techniques for categorical responses. The Second Edition offers many new exercises as well as an all new chapter on "Poisson Random Variables and the Analysis of Rates." With language, examples, and exercises that are accessible to students with modest mathematical backgrounds, this is the perfect introductory biostatistics text for undergraduates and graduates in various fields of public health. Features: Illustrative, relevant examples and exercises incorporated throughout the book. Answers to odd-numbered exercises provided in the back of the book. (Instructors may requests answers to even-numbered exercises from the publisher. Chapters are intentionally brief and limited in scope to allow for flexibility in the order of coverage. Equal attention is given to manual calculations as well as the use of statistical software
Basic Business Math: A Life-Skills Approach
by Richard P. TruchonTrust Crisp to take the misery out of math! This easy book covers whole numbers, fractions, decimals, percentages, simple equations, and percentage formulas with examples of: commissions, markups and markdowns, discounts, sales tax, simple and compound interest, and installment loans. Practice with bar, line and circle graphs, follow with just a touch of statistics-averages, medians, modes, etc. Answers included. It simply makes math work for anyone!
Basic Business Statistics
by Mark L. Berenson David M. Levine Timothy C. Krehbiel David F. StephanBerenson shows readers how statistics is used in each functional area of business. Basic Business Statistics shows the relevance of statistics by familiarizing readers with the statistical applications used in the business world, providing clear instructions for using statistical applications, and offering ample opportunities for practice. The twelfth edition has built on the application emphasis and provides enhanced coverage of statistics.
Basic Business Statistics: Concepts and Applications
by Mark L. Berenson David M. Levine Kathryn A. SzabatStatistics is essential for all business majors and this text helps students see the role statistics will play in their own careers by providing examples drawn from all functional areas of business. Guided by principles set by major statistical and business science associations (ASA and DSI), plus the authors' diverse teaching experiences, the Thirteenth Edition of Berenson/Levine/Szabat's Basic Business Statistics continues to innovate and improve the way this course is taught to all students.
Basic Calculus of Planetary Orbits and Interplanetary Flight: The Missions of the Voyagers, Cassini, and Juno
by Alexander J. HahnIntended for a one- or two-semester course, this text applies basic, one-variable calculus to analyze the motion both of planets in their orbits as well as interplanetary spacecraft in their trajectories. The remarkable spacecraft missions to the inner and outermost reaches of our solar system have been one of the greatest success stories of modern human history. Much of the underlying mathematical story is presented alongside the astonishing images and extensive data that NASA’s Voyager, NEAR-Shoemaker, Cassini, and Juno missions have sent back to us. First and second year college students in mathematics, engineering, or science, and those seeking an enriching independent study, will experience the mathematical language and methods of single variable calculus within their application to relevant conceptual and strategic aspects of the navigation of a spacecraft. The reader is expected to have taken one or two semesters of the basic calculus of derivatives, integrals, and the role that limits play. Additional prerequisites include knowledge of coordinate plane geometry, basic trigonometry, functions and graphs, including trig, inverse, exponential, and log functions. The discussions begin with the rich history of humanity’s efforts to understand the universe from the Greeks, to Newton and the Scientific Revolution, to Hubble and galaxies, to NASA and the space missions. The calculus of polar functions that plays a central mathematical role is presented in a self-contained way in complete detail. Each of the six chapters is followed by an extensive problem set that deals with and also expands on the concerns of the chapter. The instructor has the flexibility to engage them with greater or lesser intensity. “I have been an aerospace engineer for 39 years and honestly, it would be hard for me to overstate how valuable I believe this book will be to numerous scientific and engineering disciplines and in particular to the future of aerospace engineering … This book is perfectly crafted to motivate, educate, and prepare the scientists and engineers who wish to reach for the sky and beyond.” —Dr. Mario Zoccoli, Aerospace Engineer, NASA and Lockheed Martin
Basic Category Theory
by Tom LeinsterAt the heart of this short introduction to category theory is the idea of a universal property, important throughout mathematics. After an introductory chapter giving the basic definitions, separate chapters explain three ways of expressing universal properties: via adjoint functors, representable functors, and limits. A final chapter ties all three together. The book is suitable for use in courses or for independent study. Assuming relatively little mathematical background, it is ideal for beginning graduate students or advanced undergraduates learning category theory for the first time. For each new categorical concept, a generous supply of examples is provided, taken from different parts of mathematics. At points where the leap in abstraction is particularly great (such as the Yoneda lemma), the reader will find careful and extensive explanations. Copious exercises are included.
Basic College Mathematics
by Jamie Blair Jennifer Crawford Jeffrey Slater John TobeyThe Tobey/Slater/Blair/Crawford series builds essential skills one at a time by breaking the mathematics down into manageable pieces. This practical "building block" organization makes it easy for students to understand each topic and gain confidence as they move through each section. Students will find many opportunities to check and reinforce their understanding of concepts throughout the text. With this revision, the author team has added a new Math Coach feature that provides students with an office hour experience by helping them to avoid commonly made mistakes. With Tobey/Slater/Blair/Crawford, students have a tutor, a study companion, and now a coach, with them every step of the way.
Basic College Mathematics: An Applied Approach (Eighth Edition)
by Joanne S. Lockwood Vernon C. Barker Richard N. AufmannWith its complete, interactive, objective-based approach, Basic College Mathematics is the best-seller in this market. The Eighth Edition provides mathematically sound and comprehensive coverage of the topics considered essential in a basic college math course. Furthermore, the Instructor's Annotated Edition features a comprehensive selection of instructor support material. The Aufmann Interactive Method is incorporated throughout the text, ensuring that students interact with and master the concepts as they are presented. This approach is especially important in the context of rapidly growing distance-learning and self-paced laboratory situations.
Basic College Mathematics
by Elayn Martin-GayElayn Martin-Gay firmly believes that every student can succeed, and her developmental math textbooks and video resources are motivated by this belief. Basic College Mathematics, Fourth Edition was written to help readers effectively make the transition from arithmetic to algebra. The new edition offers new resources like the Student Organizer and now includes Student Resources in the back of the book to help students on their quest for success.
Basic College Mathematics
by Julie Miller Molly O'Neill Nancy HydeGet Better Results with high quality digital content and an easy to use platform! NEW Media Update edition! The Miller/O’Neill/Hyde text paperback series has aligned with a new online homework platform – Connect Math Hosted by ALEKS Corp. Based on a comprehensive market development process involving full-time and adjunct math faculty, Connect Math Hosted by ALEKS was built to excel in two areas: quality content and ease of use. A team of instructors and subject matter experts created the stepped out solutions for each algorithmic question, pulled from exercises in the text, to follow the exact methodology and language of the text in order to remain consistent across print and digital materials. The workflow is intuitive so that instructors can deliver assignments, quizzes, and tests easily online. Online study assets are specifically tied to the textbook. Connect Math Hosted by ALEKS also combines an online homework manager with an artificial-intelligent, diagnostic assessment to gauge the students’ current knowledge. With Connect Math Hosted by ALEKS Plus, students have 24/7 online access to an integrated, media-rich eBook . Also new for this edition is the addition of Basic College Mathematics in ALEKS 360!
Basic Complex Analysis
by Jerrold E. Marsden Michael J. HoffmanBasic Complex Analysis skillfully combines a clear exposition of core theory with a rich variety of applications. Designed for undergraduates in mathematics, the physical sciences, and engineering who have completed two years of calculus and are taking complex analysis for the first time...
Basic Computational Techniques For Data Analysis: An Exploration in MS-Excel
by D. Narayana Sharad RanjanThis book will help readers acquire knowledge and equip them in handling various statistical and financial computations using MS Excel. The book is designed to equip students to navigate through MS Excel spreadsheets to compute various statistical and financial measures for use in data analysis. Basic Computational Techniques for Data Analysis illustrates the concepts used in economic and financial decision-making in business as well as in day-to-day life, thus enhancing a deeper understanding of the concepts from both theoretical and practical perspectives. After going through the textbook, readers will be able to ascertain the inbuilt capabilities in MS Excel and comprehend basic computations in statistics and finance. This book is essential as a supportive companion for students of economics, commerce, management and social science subjects in general. Key Features: • Provides an in-depth and clear understanding of various data analysis techniques • Systemic and stepwise explanation of financial and statistical concepts using MS Excel functions • Prior knowledge of statistics, finance and MS-Excel functions not required to understand the concepts • Simplistic clarification of topics such as Future Value of Money, Loan Amortization and Investment Decision Criteria
Basic Computational Techniques for Data Analysis: An Exploration in MS Excel
by D Narayana Sharad Ranjan Nupur TyagiThis book is designed to equip students to navigate through MS Excel and basic data computation methods, which are essential tools in research or professional settings and in classrooms. It illustrates the concepts used in research and data analysis and economic and financial decision-making in business and in daily life. The book will help students acquire knowledge and develop skills in statistical techniques and financial analysis using MS Excel. With illustrations and examples, it will help the readers to: • Visualize, present, and analyze data through MS Excel spreadsheets and tables and create personal or business spreadsheets • Learn how to work with spreadsheets, use formulae, and perform calculations and analysis • Create tables including Pivot Tables • Become familiar with basic statistical and financial measures • Design creative spread sheets and communicate effectively in business using spreadsheets and data analysis This revised and updated second edition will be an essential resource for students of economics, commerce, management, and other social science subjects, and will be useful to those studying econometrics, financial technology, basic computational techniques, data analysis, and applied economics. Content The book is developed through three phases, with each phase standing on its own as well as providing a foundation for the next. In the first phase, Excel is introduced for the students to learn entry of data, manipulation of data, carrying out operations and develop presentations. The second phase introduces basic statistical measures of data summarisation and analysis, following which these are illustrated in Excel spreadsheets with the techniques introduced in the first phase. In addition, a few advanced tools of statistical analysis are introduced and illustrated in Excel. The third phase introduces financial measures of common use, their general computation and working them out in Excel. The book intends to illustrate the concepts used in economic and financial decision-making in business and in daily life; it helps demonstrate a deeper understanding from both theoretical and practical perspectives. An effort has been made to make the book student-friendly by using simple language and giving a number of illustrations in each chapter, solved in such a simple manner that they can be easily understood by the students. Practical questions have been included at the end of each chapter so that the students can independently solve them and test their understanding of the concepts and computations introduced in the chapter. Outcome At the end, students will be able to describe what a spreadsheet is and what Excel’s capabilities are and can work with elements that make up the structure of a worksheet. They will be able to work with spreadsheets and enter data in Excel, use formulae and calculations, and create tables, charts and pivot tables. They will be familiar with basic statistical and financial measures of general use. They will be able to do basic computations in statistics and finance in Excel. Students will acquire the capacity to create personal and/or business spreadsheets following current professional and/or industry standards. Their potential for critical thinking to design and create spreadsheets and communicate in a business setting using spreadsheet vocabulary will be enhanced. In the digital age, students necessarily need to know data, data sources and how to ‘dirty’ their hands with data. There can be no substitute to ‘talking through numbers’. The book introduces students to a variety of Indian and International data sources and teaches them how to import data-be it social, economic, financial and so on-to the Excel sheet. Once they master it, the data world is there for them to conquer! The educational background required for the student to understand the text is some basic English and Mathematics of school-leaving level. Some fl air for numbers will be an asse