Concrete Abstract Algebra: From Numbers to Gröbner Bases
| Author | : | |
| Rating | : | 4.49 (908 Votes) |
| Asin | : | 0521826799 |
| Format Type | : | paperback |
| Number of Pages | : | 256 Pages |
| Publish Date | : | 2013-02-23 |
| Language | : | English |
DESCRIPTION:
The basic philosophy is that inspiring, non-trivial applications and examples give motivation and ease the learning of abstract concepts. A special feature is that Gr"obner bases do not appear as an isolated example. In addition, there is a rich supply of topics such as cryptography, factoring algorithms for integers, quadratic residues, finite fields, factoring algorithms for polynomials, and systems of non-linear equations. Lauritzen's approach to teaching abstract algebra is based on an extensive use of examples, applications, and exercises. They are fully integrated as a subject that can be successfully taught in an undergraduate context. This book is built on several years of experienced teaching introductory abstract algebra at Aarhus,
Annoyingly Informal I have a love-hate relationship with this book. Lauritzen writes in a semi-informal manner which makes this a lot less dry than other math books, but at the same time, certain details which should be laid out explicitly are not always done so. For example, the definition of a ring appears in bold letters and is set apart from the rest of the text, whereas the definition of a. Four Stars Nice book on applications of abstract algebra (cryptography, Groebner bases, etc.) A little thin on some topics. Well-written.
"Lauritzen does a great job of motivating the concepts covered. The title of the book seems to be contradictory, but after reading the book, you will really have the feeling that Lauritzen achieved his goal: to concretize the abstract without losing rigor and depth. If you are looking for a solid introduction to the topic of abstract algebra, this is the book for you." Computing Reviews . I highly recommend this book as a text for teaching abstract algebra. The text is very readable, and the well-chosen exercises help the reader understand the material