Standard Algebra
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| Author | : Bruno Nachtergaele |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 209 |
| Release | : 2015-11-30 |
| Genre | : Mathematics |
| ISBN | : 9814723797 |
This is an introductory textbook designed for undergraduate mathematics majors with an emphasis on abstraction and in particular, the concept of proofs in the setting of linear algebra. Typically such a student would have taken calculus, though the only prerequisite is suitable mathematical grounding. The purpose of this book is to bridge the gap between the more conceptual and computational oriented undergraduate classes to the more abstract oriented classes. The book begins with systems of linear equations and complex numbers, then relates these to the abstract notion of linear maps on finite-dimensional vector spaces, and covers diagonalization, eigenspaces, determinants, and the Spectral Theorem. Each chapter concludes with both proof-writing and computational exercises.
| Author | : Charles C Pinter |
| Publisher | : Courier Corporation |
| Total Pages | : 402 |
| Release | : 2010-01-14 |
| Genre | : Mathematics |
| ISBN | : 0486474178 |
Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.
| Author | : John Hunter |
| Publisher | : |
| Total Pages | : 116 |
| Release | : 1872 |
| Genre | : |
| ISBN | : |
| Author | : Serge Lang |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 380 |
| Release | : 2013-06-29 |
| Genre | : Mathematics |
| ISBN | : 1475768982 |
The companion title, Linear Algebra, has sold over 8,000 copies The writing style is very accessible The material can be covered easily in a one-year or one-term course Includes Noah Snyder's proof of the Mason-Stothers polynomial abc theorem New material included on product structure for matrices including descriptions of the conjugation representation of the diagonal group
| Author | : Sheldon Axler |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 276 |
| Release | : 1997-07-18 |
| Genre | : Mathematics |
| ISBN | : 9780387982595 |
This text for a second course in linear algebra, aimed at math majors and graduates, adopts a novel approach by banishing determinants to the end of the book and focusing on understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presents - without having defined determinants - a clean proof that every linear operator on a finite-dimensional complex vector space has an eigenvalue. The book starts by discussing vector spaces, linear independence, span, basics, and dimension. Students are introduced to inner-product spaces in the first half of the book and shortly thereafter to the finite- dimensional spectral theorem. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. This second edition features new chapters on diagonal matrices, on linear functionals and adjoints, and on the spectral theorem; some sections, such as those on self-adjoint and normal operators, have been entirely rewritten; and hundreds of minor improvements have been made throughout the text.
| Author | : Paolo Aluffi |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 713 |
| Release | : 2021-11-09 |
| Genre | : Education |
| ISBN | : 147046571X |
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.
| Author | : |
| Publisher | : |
| Total Pages | : 92 |
| Release | : 1872 |
| Genre | : |
| ISBN | : |
| Author | : Nathaniel Max Rock |
| Publisher | : Team Rock Press |
| Total Pages | : 412 |
| Release | : 2005-08 |
| Genre | : Education |
| ISBN | : 097493920X |
Standards-Driven Power Algebra I is a textbook and classroom supplement for students, parents, teachers and administrators who need to perform in a standards-based environment. This book is from the official Standards-Driven Series (Standards-Driven and Power Algebra I are trademarks of Nathaniel Max Rock). The book features 412 pages of hands-on standards-driven study guide material on how to understand and retain Algebra I. Standards-Driven means that the book takes a standard-by-standard approach to curriculum. Each of the 25 Algebra I standards are covered one-at-a-time. Full explanations with step-by-step instructions are provided. Worksheets for each standard are provided with explanations. 25-question multiple choice quizzes are provided for each standard. Seven, full-length, 100 problem comprehensive final exams are included with answer keys. Newly revised and classroom tested. Author Nathaniel Max Rock is an engineer by training with a Masters Degree in business. He brings years of life-learning and math-learning experiences to this work which is used as a supplemental text in his high school Algebra I classes. If you are struggling in a "standards-based" Algebra I class, then you need this book! (E-Book ISBN#0-9749392-1-8 (ISBN13#978-0-9749392-1-6))
| Author | : M. Hazewinkel |
| Publisher | : Elsevier |
| Total Pages | : 899 |
| Release | : 2000-04-06 |
| Genre | : Mathematics |
| ISBN | : 0080532969 |
| Author | : Saunders Mac Lane |
| Publisher | : American Mathematical Society |
| Total Pages | : 650 |
| Release | : 2023-10-10 |
| Genre | : Mathematics |
| ISBN | : 147047476X |
This book presents modern algebra from first principles and is accessible to undergraduates or graduates. It combines standard materials and necessary algebraic manipulations with general concepts that clarify meaning and importance. This conceptual approach to algebra starts with a description of algebraic structures by means of axioms chosen to suit the examples, for instance, axioms for groups, rings, fields, lattices, and vector spaces. This axiomatic approach—emphasized by Hilbert and developed in Germany by Noether, Artin, Van der Waerden, et al., in the 1920s—was popularized for the graduate level in the 1940s and 1950s to some degree by the authors' publication of A Survey of Modern Algebra. The present book presents the developments from that time to the first printing of this book. This third edition includes corrections made by the authors.
