Algebra

Este libro es fruto de un Descubrimiento a Nivel Mundial en Matemáticas, en el Campo de la Factorización (Algebra), realizado en Santa Cruz, en la ciudad de "CAMIRI", Capital Petrolera de BOLIVIA. El objetivo principal de este Libro, es presentar un nuevo método de Factorización: "El Método Alfa". Actualmente hay 14 métodos de Factorización, que se enseñan en los Colegios de Secundaria. El Método ALFA, puede fácilmente reemplazar a 10 (diez) de los 14 (catorce). En su parte principal nos muestra en detalle, las Reglas Básicas del "Método Alfa" y hace una análisis comparativo de los actuales métodos de Factorización vs. El Método Alfa. Este nuevo Método ALFA, NOS PERMITE: (1).- "Predecir" si un ejercicio se puede o no Factorizar "sin resolverlo el Ejercicio". (2).- Encontrar el resultado "ya NO por tanteo", sino por "simple comparación" (3).- Les ofrece una nueva forma de verificar los resultados (propias del AUTOR), por simple suma y resta. (4).- Trabaja los 4 términos INDEPENDIENTE de los SIGNOS. (5).- Nos ofrece la "Secuencia ALFA" (Propia del AUTOR), que permite al final, la ubicación correcta de los 4 términos obtenidos, que son el RESULTADO de la FACTORIZACION. Este libro cuenta con una serie de Ejemplos ilustrativos y Ejercicios para practicar. Además de una serie de Trabajos Prácticos "tipo Examen" que facilitan la labor del profesor dentro y fuera de las aulas. ¿Es muy importante hacer resaltar que el "Método ALFA", puede ser fácilmente enseñado por los Profesores y Catedráticos, a todos los alumnos (as) de Colegios Secundarios, Pre-Universitarios y de la Universidad. Al final de Libro presenta una serie de Documentos y Certificados que avalan la LARGA trayectoria del Método ALFA desde su DESCUBRIMIENTO, hace mas de 30 años (1992)

This book gives a comprehensive introduction to Universal Algebraic Logic. The three main themes are (i) universal logic and the question of what logic is, (ii) duality theories between the world of logics and the world of algebra, and (iii) Tarskian algebraic logic proper including algebras of relations of various ranks, cylindric algebras, relation algebras, polyadic algebras and other kinds of algebras of logic. One of the strengths of our approach is that it is directly applicable to a wide range of logics including not only propositional logics but also e.g. classical first order logic and other quantifier logics. Following the Tarskian tradition, besides the connections between logic and algebra, related logical connections with geometry and eventually spacetime geometry leading up to relativity are also part of the perspective of the book. Besides Tarskian algebraizations of logics, category theoretical perspectives are also touched upon. This book, apart from being a monograph containing state of the art results in algebraic logic, can be used as the basis for a number of different courses intended for both novices and more experienced students of logic, mathematics, or philosophy. For instance, the first two chapters can be used in their own right as a crash course in Universal Algebra.

This book offers an original introduction to the representation theory of algebras, suitable for beginning researchers in algebra. It includes many results and techniques not usually covered in introductory books, some of which appear here for the first time in book form. The exposition employs methods from linear algebra (spectral methods and quadratic forms), as well as categorical and homological methods (module categories, Galois coverings, Hochschild cohomology) to present classical aspects of ring theory under new light. This includes topics such as rings with several objects, the Harada-Sai lemma, chain conditions, and Auslander-Reiten theory. Noteworthy and significant results covered in the book include the Brauer-Thrall conjectures, Drozd's theorem, and criteria to distinguish tame from wild algebras. This text may serve as the basis for a second graduate course in algebra or as an introduction to research in the field of representation theory of algebras. The originality of the exposition and the wealth of topics covered also make it a valuable resource for more established researchers.

Gegen Angst vor Mathematik hilft Verstehen. Dieses Buch setzt nur elementare Schulkenntnisse voraus und entwickelt die Mathematik schrittweise und systematisch von der Bruchrechnung über die Differenzial- und Integralrechnung sowie die Lineare Algebra bis zur Funktionalanalysis. Dabei werden Sie vom Vertrauten zum Neuen geführt. Neben vielen Anwendungsbeispielen aus den Ingenieurwissenschaften finden Sie zu jedem Teil des Buchs zahlreiche Aufgaben (mit Lösungen im elektronischen Zusatzmaterial).Mit der hier vorliegenden vierten Auflage wurde der Text grundlegend überarbeitet, es wurden neue Anwendungsbeispiele aufgenommen, und das Gesamtwerk ¿Mathematik verstehen und anwenden¿ wurde aufgrund des Umfangs in zwei Bände aufgeteilt. Dieser erste Band wird durch einen zweiten ergänzt, in dem weiterführende Themen wie die Vektoranalysis, Differenzialgleichungen und die Fourier-Analysis behandelt werden. Außerdem beinhaltet der zweite Band eine Einführung in die Wahrscheinlichkeitsrechnung und Statistik.Zielgruppe sind Studierende der Ingenieur- und Naturwissenschaften an Fachhochschulen und Universitäten. Trotz der verständlichen Darstellung für ein Bachelor-Studium geht die mathematische Exaktheit nicht verloren. Hintergrundinformationen und Beweise ergänzen die sehr umfangreiche Stoffauswahl und bieten Anknüpfungspunkte für ein Masterstudium. Daneben erleichtern sie auch den Einstieg in Spezialvorlesungen der Mathematik wie beispielsweise die Numerik, die Funktionalanalysis und insbesondere die Fourier-Analysis.Stimmen zur ersten Auflage:¿Sowohl mathematisch exakt als auch äußerst anschaulich. Eine echte Bereicherung der großen Auswahl an Büchern zum Thema Ingenieurmathematik.¿Prof. Dr. Andreas Gessinger, Rheinische Fachhochschule Köln¿Der Spagat zwischen Verständlichkeit und mathematischer Tiefe ist hervorragend gelungen. Eine breite Palette von praxisorientierten Beispielen wirkt motivationsfördernd.¿Prof. Dr. Helga Tecklenburg, Hochschule für Technik, Wirtschaft und Kultur Leipzig

This book gathers, in a beautifully structured way, recent findings on chain conditions in commutative algebra that were previously only available in papers. The majority of chapters are self-contained, and all include detailed proofs, a wealth of examples and solved exercises, and a complete reference list. The topics covered include S-Noetherian, S-Artinian, Nonnil-Noetherian, and Strongly Hopfian properties on commutative rings and their transfer to extensions such as polynomial and power series rings, and more. Though primarily intended for readers with a background in commutative rings, modules, polynomials and power series extension rings, the book can also be used as a reference guide to support graduate-level algebra courses, or as a starting point for further research.

He [Kronecker] was, in fact, attempting to describe and to initiate a new branch of mathematics, which would contain both number theory and alge- braic geometry as special cases.-Andre Weil [62] This book is about mathematics, not the history or philosophy of mathemat- ics. Still, history and philosophy were prominent among my motives for writing it, and historical and philosophical issues will be major factors in determining whether it wins acceptance. Most mathematicians prefer constructive methods. Given two proofs of the same statement, one constructive and the other not, most will prefer the constructive proof. The real philosophical disagreement over the role of con- structions in mathematics is between those-the majority-who believe that to exclude from mathematics all statements that cannot be proved construc- tively would omit far too much, and those of us who believe, on the contrary, that the most interesting parts of mathematics can be dealt with construc- tively, and that the greater rigor and precision of mathematics done in that way adds immensely to its value.

Here we present a nearly complete treatment of the Grand Universe of linear and weakly nonlinear regression models within the first 8 chapters. Our point of view is both an algebraic view as well as a stochastic one. For example, there is an equivalent lemma between a best, linear uniformly unbiased estimation (BLUUE) in a Gauss-Markov model and a least squares solution (LESS) in a system of linear equations. While BLUUE is a stochastic regression model, LESS is an algebraic solution. In the first six chapters we concentrate on underdetermined and overdeterimined linear systems as well as systems with a datum defect. We review estimators/algebraic solutions of type MINOLESS, BLIMBE, BLUMBE, BLUUE, BIQUE, BLE, BIQUE and Total Least Squares. The highlight is the simultaneous determination of the first moment and the second central moment of a probability distribution in an inhomogeneous multilinear estimation by the so called E-D correspondence as well as its Bayes design. In addition, we discuss continuous networks versus discrete networks, use of Grassmann-Pluecker coordinates, criterion matrices of type Taylor-Karman as well as FUZZY sets. Chapter seven is a speciality in the treatment of an overdetermined system of nonlinear equations on curved manifolds. The von Mises-Fisher distribution is characteristic for circular or (hyper) spherical data. Our last chapter eight is devoted to probabilistic regression, the special Gauss-Markov model with random effects leading to estimators of type BLIP and VIP including Bayesian estimation. The fifth problem of algebraic regression, the system of conditional equations of homogeneous and inhomogeneous type, is formulated. An analogue is the inhomogeneous general linear Gauss-Markov model with fixed and random effects, also called mixed model. Collocation is an example. Another speciality is our sixth problem of probabilistic regression, the model "e;errors-in-variable"e;, also called Total Least Squares, namely SIMEX and SYMEX developed by Carroll-Cook-Stefanski-Polzehl-Zwanzig. Another speciality is the treatment of the three-dimensional datum transformation and its relation to the Procrustes Algorithm. The sixth problem of generalized algebraic regression is the system of conditional equations with unknowns, also called Gauss-Helmert model. A new method of an algebraic solution technique, the concept of Groebner Basis and Multipolynomial Resultant is finally presented, illustrating polynomial nonlinear equations. A great part of the work is presented in four Appendices. Appendix A is a treatment, of tensor algebra, namely linear algebra, matrix algebra and multilinear algebra. Appendix B is devoted to sampling distributions and their use in terms of confidence intervals and confidence regions. Appendix C reviews the elementary notions of statistics, namely random events and stochastic processes. Appendix D introduces the basics of Groebner basis algebra, its careful definition, the Buchberger Algorithm, especially the C. F. Gauss combinatorial algorithm Throughout we give numerous examples and present various test computations. Our reference list includes more than 3000 references, books and papers. This book is a source of knowledge and inspiration not only for geodesists and mathematicians, but also for engineers in general, as well as natural scientists and economists. Inference on effects which result in observations via linear and nonlinear functions is a general task in science. The authors provide a comprehensive in-depth treatise on the analysis and solution of such problems. I wish all readers of this brilliant encyclopaedic book this pleasure and much benefit. Prof. Dr. Harro WalkInstitute of Stochastics and Applications, Universitat Stuttgart, Germany.

FREE PERSONAL ASSISTANT IS INCLUDED with your purchase. If you have questions with any problems in the book, please go to readablemath.wixsite.com/2020 and click "Ask Fred".A FREE WORKBOOK if you need extra practice. Please go to readablemath.wixsite.com/2020 to request a copy.PERFECT MATERIALS to supplement your child's learning.EXCEPTIONAL for inspiring your child to GET AHEAD and EXCEL in math.GREAT for helping students who struggled in math CLARIFY and REVIEW CONCEPTS.Contains ESSENTIAL lessons for building a STRONG FOUNDATION in math, so your child can succeed in ALGEBRA I, ALGEBRA II, PRE-CALCULUS/TRIGONOMETRY, CALCULUS and BEYOND.For a fraction of the price, your child is guaranteed to learn more from this book than a traditional textbook, as it is full of COMPUTATIONAL TRICKS and IDEAS.It is a MUST-HAVE for all students who want to DEVELOP the CONFIDENCE and ability to perform mathematical tasks at a HIGH LEVEL.I have over 24 years of tutoring experience. I tutor students from 1st grade to college. My past students include those from MIT, U-Penn, UC Berkeley, and more.In addition to having a DOUBLE-MAJOR in Math and Computer Science as an undergrad, I have a MASTER degree from UCLA.

Die Aufgabensammlung enthalt Aufgaben mit vollstandig durchgerechneten Losungen zu den Themen Analysis und lineare Algebra, wie sie im Kompendium Hohere Mathematik"e; dargestellt sind. Das Spektrum reicht von Aufgaben zur reinen Rechentechnik bis hin zu Anwendungsaufgaben, bei denen zunachst eine geeignete Modellierung gesucht ist, um dann die entsprechenden Techniken anwenden zu konnen. Ferner enthalt der Band speziell ausgewiesene Aufgaben, wie sie in Klausuren an Fachhochschulen oder Berufsakademien vorkommen konnen.

This proceedings volume gathers selected, revised papers presented at the 51st Southeastern International Conference on Combinatorics, Graph Theory and Computing (SEICCGTC 2020), held at Florida Atlantic University in Boca Raton, USA, on March 9-13, 2020. The SEICCGTC is broadly considered to be a trendsetter for other conferences around the world - many of the ideas and themes first discussed at it have subsequently been explored at other conferences and symposia.The conference has been held annually since 1970, in Baton Rouge, Louisiana and Boca Raton, Florida. Over the years, it has grown to become the major annual conference in its fields, and plays a major role in disseminating results and in fostering collaborative work.This volume is intended for the community of pure and applied mathematicians, in academia, industry and government, working in combinatorics and graph theory, as well as related areas of computer science and the interactions among these fields.