Selected Exercises In Algebra
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Author | : Rocco Chirivì |
Publisher | : Springer Nature |
Total Pages | : 252 |
Release | : 2020-01-29 |
Genre | : Mathematics |
ISBN | : 303036156X |
This book, the first of two volumes, contains over 250 selected exercises in Algebra which have featured as exam questions for the Arithmetic course taught by the authors at the University of Pisa. Each exercise is presented together with one or more solutions, carefully written with consistent language and notation. A distinguishing feature of this book is the fact that each exercise is unique and requires some creative thinking in order to be solved. The themes covered in this volume are: mathematical induction, combinatorics, modular arithmetic, Abelian groups, commutative rings, polynomials, field extensions, finite fields. The book includes a detailed section recalling relevant theory which can be used as a reference for study and revision. A list of preliminary exercises introduces the main techniques to be applied in solving the proposed exam questions. This volume is aimed at first year students in Mathematics and Computer Science.
Author | : Rocco Chirivì |
Publisher | : Springer Nature |
Total Pages | : 301 |
Release | : 2022-11-28 |
Genre | : Mathematics |
ISBN | : 3031126513 |
This book, the second of two volumes, contains approximately 350 exercises in Algebra which have featured exam questions for the Algebraic Structure and Algebra I courses taught by the authors at the University of Pisa. Each exercise is presented together with one or more solutions, carefully written with consistent language and notation. A distinguishing feature of this book is the fact that each exercise is unique and requires some creative thinking to be solved. The themes covered in this volume are: group theory and Sylow theorems, commutative rings with an emphasis on unique factorisation, Gaussian integers, field extensions and Galois theory. The book includes a detailed section recalling relevant theory that can be used as a reference for study and revision. A list of preliminary exercises introduces the main techniques to be applied in solving the proposed exam questions. This volume is aimed at second year students in Mathematics and Computer science.
Author | : Alexandra I. Kostrikin |
Publisher | : CRC Press |
Total Pages | : 480 |
Release | : 1996-02-09 |
Genre | : Mathematics |
ISBN | : 9782884490306 |
This book is a collection of exercises for courses in higher algebra, linear algebra and geometry. It is helpful for postgraduate students in checking the solutions and answers to the exercises.
Author | : Rocco Chirivì |
Publisher | : |
Total Pages | : 0 |
Release | : 2022 |
Genre | : |
ISBN | : 9783031126529 |
This book, the second of two volumes, contains approximately 350 exercises in Algebra which have featured exam questions for the Algebraic Structure and Algebra I courses taught by the authors at the University of Pisa. Each exercise is presented together with one or more solutions, carefully written with consistent language and notation. A distinguishing feature of this book is the fact that each exercise is unique and requires some creative thinking to be solved. The themes covered in this volume are: group theory and Sylow theorems, commutative rings with an emphasis on unique factorisation, Gaussian integers, field extensions and Galois theory. The book includes a detailed section recalling relevant theory that can be used as a reference for study and revision. A list of preliminary exercises introduces the main techniques to be applied in solving the proposed exam questions. This volume is aimed at second year students in Mathematics and Computer science.
Author | : Clifford Bergman |
Publisher | : CRC Press |
Total Pages | : 324 |
Release | : 2011-09-20 |
Genre | : Computers |
ISBN | : 1439851298 |
Starting with the most basic notions, Universal Algebra: Fundamentals and Selected Topics introduces all the key elements needed to read and understand current research in this field. Based on the author’s two-semester course, the text prepares students for research work by providing a solid grounding in the fundamental constructions and concepts of universal algebra and by introducing a variety of recent research topics. The first part of the book focuses on core components, including subalgebras, congruences, lattices, direct and subdirect products, isomorphism theorems, a clone of operations, terms, free algebras, Birkhoff’s theorem, and standard Maltsev conditions. The second part covers topics that demonstrate the power and breadth of the subject. The author discusses the consequences of Jónsson’s lemma, finitely and nonfinitely based algebras, definable principal congruences, and the work of Foster and Pixley on primal and quasiprimal algebras. He also includes a proof of Murskiĭ’s theorem on primal algebras and presents McKenzie’s characterization of directly representable varieties, which clearly shows the power of the universal algebraic toolbox. The last chapter covers the rudiments of tame congruence theory. Throughout the text, a series of examples illustrates concepts as they are introduced and helps students understand how universal algebra sheds light on topics they have already studied, such as Abelian groups and commutative rings. Suitable for newcomers to the field, the book also includes carefully selected exercises that reinforce the concepts and push students to a deeper understanding of the theorems and techniques.
Author | : Mạnh Hà Nguyẽ̂n |
Publisher | : |
Total Pages | : 330 |
Release | : 198? |
Genre | : Algebra |
ISBN | : |
Author | : Thomas Simpson |
Publisher | : |
Total Pages | : 352 |
Release | : 1752 |
Genre | : Mathematics |
ISBN | : |
Author | : T.Y. Lam |
Publisher | : Springer Science & Business Media |
Total Pages | : 427 |
Release | : 2009-12-08 |
Genre | : Mathematics |
ISBN | : 0387488995 |
This volume offers a compendium of exercises of varying degree of difficulty in the theory of modules and rings. It is the companion volume to GTM 189. All exercises are solved in full detail. Each section begins with an introduction giving the general background and the theoretical basis for the problems that follow.
Author | : Anthony G. Petrello |
Publisher | : |
Total Pages | : 123 |
Release | : 1978 |
Genre | : Algebra |
ISBN | : |
Author | : Stephen Boyd |
Publisher | : Cambridge University Press |
Total Pages | : 477 |
Release | : 2018-06-07 |
Genre | : Business & Economics |
ISBN | : 1316518965 |
A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.