E-Books → Elementary Linear Algebra

Published by: voska89 on 29-12-2023, 05:00 | 0

Free Download Elementary Linear Algebra
English | 2012 | ISBN: 9780988557208 | 953 Pages | PDF (True) | 5 MB
This is an e-textbook for a first course in linear algebra. The topics covered include: Linear Systems, The Vector Space R^n, Matrix Algebra, Determinants, Abstract Vector Spaces, Linear Transformations, Eigenvalues and Eigenvectors, and Orthogonality in R^n. It introduces linear transformations in R^n quite early and uses them to motivate the addition and multiplication of matrices. In addition to the usual theory there are several sections devoted to applications such as Markov chain models, age structured population models, Leontief imput-output models, error-correcting codes, linear recurrence relations, systems of differential equations, and the characterization of real quadratic curves and real quadratic surfaces. We also obtain the canonical forms for real 2 x 2 and 3 x 3 matrices. The book is rigorous in its treatment of the theory and all important results are proved. What separates this book from print treatments of linear algebra and other e-textbooks is the use of the digital environment to create a pedagogical product that supports student understanding. Specifically, without limitations of length we can regularly spiral back to important concepts and algorithms. Thus, each section begins with a subsection, "What you need to know" reviewing definitions and contains a short quiz with links to solutions. Also to facilitate student understanding, which depends on mastery of over 100 concepts, nearly every instance of a fundamental term is linked back to its definition. Likewise, in proofs, citation of previous results (lemmas, theorems, corollaries) are linked to their original statements and proofs. Also in each section there is a subsection. How to do it, where we describe the specific algorithms students will need to enact when assigned exercises. Further, in addition to a large selection of exercises, each section contains numerous challenge exercises (problems) which require knowledge of the theorems and the application of mathematical reasoning.

E-Books → Commutative Algebra

Published by: voska89 on 29-12-2023, 03:41 | 0

Free Download Commutative Algebra
English | 2023 | ISBN: 1470471272 | 392 Pages | PDF | 4 MB
This book provides an introduction to classical methods in commutative algebra and their applications to number theory, algebraic geometry, and computational algebra. The use of number theory as a motivating theme throughout the book provides a rich and interesting context for the material covered. In addition, many results are reinterpreted from a geometric perspective, providing further insight and motivation for the study of commutative algebra. The content covers the classical theory of Noetherian rings, including primary decomposition and dimension theory, topological methods such as completions, computational techniques, local methods and multiplicity theory, as well as some topics of a more arithmetic nature, including the theory of Dedekind rings, lattice embeddings, and Witt vectors. Homological methods appear in the author's sequel, Homological Methods in Commutative Algebra.

E-Books → Applied Linear Algebra and Matrix Methods

Published by: voska89 on 29-12-2023, 02:19 | 0

Free Download Applied Linear Algebra and Matrix Methods
English | 2023 | ISBN: 3031395611 | 321 Pages | PDF EPUB (True) | 21 MB
This textbook is designed for a first course in linear algebra for undergraduate students from a wide range of quantitative and data driven fields. By focusing on applications and implementation, students will be prepared to go on to apply the power of linear algebra in their own discipline. With an ever-increasing need to understand and solve real problems, this text aims to provide a growing and diverse group of students with an applied linear algebra toolkit they can use to successfully grapple with the complex world and the challenging problems that lie ahead. Applications such as least squares problems, information retrieval, linear regression, Markov processes, finding connections in networks, and more, are introduced on a small scale as early as possible and then explored in more generality as projects. Additionally, the book draws on the geometry of vectors and matrices as the basis for the mathematics, with the concept of orthogonality taking center stage. Important matrix factorizations as well as the concepts of eigenvalues and eigenvectors emerge organically from the interplay between matrix computations and geometry.

E-Books → Algebra Without Borders – Classical and Constructive Nonassociative Algebraic Structures

Published by: voska89 on 29-12-2023, 02:03 | 0

E-Books → Algebra Gruppen – Ringe – Körper – Zahlen

Published by: voska89 on 29-12-2023, 02:03 | 0

Free Download Algebra: Gruppen - Ringe - Körper - Zahlen
Deutsch | 2023 | ISBN: 3662672421 | 246 Seiten | PDF (True) | 5.3 MB
Im Zentrum stehen die algebraischen Strukturen der Gruppen, Ringe und Körper und ihre Bedeutung für das Lösen von Gleichungen, die Galoistheorie und die algebraische Zahlentheorie. Diese Anwendungen helfen auch dabei, das Dickicht an Begriffen und Abstraktionen in der modernen Algebra zu lichten.