Overview
- Collection of 250 exercises and preliminary exercises
- The notes on the relevant theory provide the reader with a readily available, comprehensive reference
- The proposed exercises and carefully drafted solutions are organized by topic
Part of the book series: UNITEXT (UNITEXT, volume 119)
Part of the book sub series: La Matematica per il 3+2 (UNITEXTMAT)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (3 chapters)
Keywords
About this book
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.
Reviews
“This book is filled with rich exercises with detailed historical notes mirroring Arithmetic and Algebra. … This book can be used for both the professor who needs a reservoir of problems for homework or projects and for the student who wishes to tackle more exercises for drill and practice. The book left me thinking that the more you practice and know, the better.” (MAA Reviews, April 12, 2020)
Authors and Affiliations
About the authors
Rocco Chirivì obtained a degree in Mathematics from the University of Pisa in 1995; he earned his Diploma di Licenza from the Scuola Normale of Pisa in 1997, followed by his Diploma di Perfezionamento in 2000. He was a researcher in Algebra at the University of Pisa from 2002 to 2012 and has since been working as a researcher at the University of Salento. His main research focus is Representation Theory, at the intersection between Algebra, Combinatorics and the geometry of varieties related to group actions.
Ilaria Del Corso attended the Corso di Perfezionamento at the Scuola Normale from 1990 to 1992 and has been an associate professor in Algebra at the University of Pisa since 2001. She has extensive teaching experience in Algebra and Algebraic Number Theory. Her research in Algebraic Number Theory concerns number fields and local fields, focusing in particular on the study of ramification and on the Galois module structure of certain field extensions.
Roberto Dvornicich, having been a student at the Scuola Normale of Pisa, obtained a degree in Mathematics from the University of Pisa in 1972 and later attended the Corso di Perfezionamento at the Scuola Normale. He has been a full professor in Algebra at the University of Pisa since 1990. His main research interests lie within Algebraic Number Theory (arithmetic properties of number fields and local fields) and in Diophantine Analysis (algebraic equations over the integers or some number field).
Bibliographic Information
Book Title: Selected Exercises in Algebra
Book Subtitle: Volume 1
Authors: Rocco Chirivì, Ilaria Del Corso, Roberto Dvornicich
Translated by: Alessandra Caraceni
Series Title: UNITEXT
DOI: https://doi.org/10.1007/978-3-030-36156-3
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2020
Softcover ISBN: 978-3-030-36155-6Published: 30 January 2020
eBook ISBN: 978-3-030-36156-3Published: 29 January 2020
Series ISSN: 2038-5714
Series E-ISSN: 2532-3318
Edition Number: 1
Number of Pages: XVI, 240
Number of Illustrations: 27 b/w illustrations
Topics: Group Theory and Generalizations, Combinatorics, Number Theory, Discrete Optimization, General Algebraic Systems