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Concrete Abstract Algebra: From Numbers to Gröbner Bases epub download

by Niels Lauritzen


Nice book on applications of abstract algebra (cryptography, Groebner bases, et.  . Based on this part, the work seems a veritable little gem and lives up to its aptly chosen title, striking a rare balance between theory and application

Nice book on applications of abstract algebra (cryptography, Groebner bases, et. A little thin on some topics. Based on this part, the work seems a veritable little gem and lives up to its aptly chosen title, striking a rare balance between theory and application. The work is clearly aimed at delivering a course at the intersection of mathematics and computer science, targeted at reaching the relevant applications timely through a judicially frugal exposition, as well as motivating abstract concepts with interesting examples, and, for this purpose, I highly recommend it.

Lauritzen does a great job of motivating the concepts covered. A special feature is that Gr"obner bases do not appear as an isolated example. 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. The text is very readable, and the well-chosen exercises help the reader understand the material. I highly recommend this book as a text for teaching abstract algebra. They are fully integrated as a subject that can be successfully taught in an undergraduate context.

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Concrete Abstract Algebra book . Start by marking Concrete Abstract Algebra: From Numbers to Gr�bner Bases as Want to Read: Want to Read savin. ant to Read. Concrete Abstract Algebra develops the theory of abstract algebra from numbers to Gr"obner bases, while takin in all the usual material of a traditional introductory course.

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Concrete Abstract Algebra develops the theory of abstract algebra from .

Concrete Abstract Algebra develops the theory of abstract algebra from numbers to Gr"obner bases, while takin in all the usual material of a traditional introductory course. 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.

Download PDF book format. Personal Name: Lauritzen, Niels, 1964-. Publication, Distribution, et. Cambridge, UK ; New York. Choose file format of this book to download: pdf chm txt rtf doc. Download this format book. Concrete abstract algebra : from numbers to Grobner bases Niels Lauritzen. Book's title: Concrete abstract algebra : from numbers to Grobner bases Niels Lauritzen. Library of Congress Control Number: 2003051248.

The reduced Groebner basis is here applied to offer a closed form solution to the three-dimensional intersection problem vital in Photogrammetry and Computer . Concrete Abstract Algebra: From Numbers to Gr?bner Bases.

The reduced Groebner basis is here applied to offer a closed form solution to the three-dimensional intersection problem vital in Photogrammetry and Computer vision. From the observations of type horizontal directions Ti and vertical directions Bi, with i 1, 2, 3, we demonstrate that the three nonlinear system of equations can be decomposed to three quartic polynomials, i. e. polynomials of degree four, whose roots can be obtained with the help of solve command in Matlab software. Buchberger algorithm applied to planar lateration and intersection problems.

Syllabus: The book has five chapters: 1. Numbers, 2. Groups, 3. Rings, 4. Polynomials, 5. Grobner Bases. I intend to cover almost all of the material in all five chapters. Grobner bases will definitely be covered. However, I will exclude some of the number-theoretic topics (factoring algorithms, quadratic reciprocity). Grading: There will be two midterms and one final exam.

Concrete Abstract Algebra develops the theory of abstract algebra from numbers to Gr"obner bases, while takin in all the usual material of a traditional introductory course. 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. A special feature is that Gr"obner bases do not appear as an isolated example. They are fully integrated as a subject that can be successfully taught in an undergraduate context. Lauritzen's approach to teaching abstract algebra is based on an extensive use of examples, applications, and exercises. The basic philosophy is that inspiring, non-trivial applications and examples give motivation and ease the learning of abstract concepts. This book is built on several years of experienced teaching introductory abstract algebra at Aarhus, where the emphasis on concrete and inspiring examples has improved student performance significantly.

Concrete Abstract Algebra: From Numbers to Gröbner Bases epub download

ISBN13: 978-0521534109

ISBN: 0521534100

Author: Niels Lauritzen

Category: Math and Science

Subcategory: Mathematics

Language: English

Publisher: Cambridge University Press; 1 edition (October 20, 2003)

Pages: 256 pages

ePUB size: 1438 kb

FB2 size: 1497 kb

Rating: 4.9

Votes: 939

Other Formats: doc lit azw rtf

Related to Concrete Abstract Algebra: From Numbers to Gröbner Bases ePub books

Ubranzac
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 field occurs as an informal aside in the middle of a paragraph. In fact, a lot of important results are stated in an inconsistent manner like this, making it annoyingly difficult to go back and find them.

Some sections are laid out very nicely and are easy to understand, while others are ridiculously difficult to follow (Sylow theorems, initial definition of a polynomial ring, law of quadratic reciprocity, and S-polynomials for Grobner bases). Also, I feel as if some important topics that are typically taught in an undergraduate abstract algebra course are left out (semi-direct products, automorphisms, splitting fields, classification of abelian groups, modules) in favor of somewhat obscure ones (certain factoring algorithms, Berlekamp's algorithm, pretty much everything about Grobner bases).

Overall, it's an alright book. It's generally easier than some of the other competing books, but the informal nature really bugs me, especially for a course like abstract algebra where the definitions and theorems should be laid out as precisely as possible.
Ubranzac
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 field occurs as an informal aside in the middle of a paragraph. In fact, a lot of important results are stated in an inconsistent manner like this, making it annoyingly difficult to go back and find them.

Some sections are laid out very nicely and are easy to understand, while others are ridiculously difficult to follow (Sylow theorems, initial definition of a polynomial ring, law of quadratic reciprocity, and S-polynomials for Grobner bases). Also, I feel as if some important topics that are typically taught in an undergraduate abstract algebra course are left out (semi-direct products, automorphisms, splitting fields, classification of abelian groups, modules) in favor of somewhat obscure ones (certain factoring algorithms, Berlekamp's algorithm, pretty much everything about Grobner bases).

Overall, it's an alright book. It's generally easier than some of the other competing books, but the informal nature really bugs me, especially for a course like abstract algebra where the definitions and theorems should be laid out as precisely as possible.
Tori Texer
Nice book on applications of abstract algebra (cryptography, Groebner bases, etc.) A little thin on some topics. Well-written.
Tori Texer
Nice book on applications of abstract algebra (cryptography, Groebner bases, etc.) A little thin on some topics. Well-written.
Fordregelv
The review covers the group theory part, which I read as a quick refresher of basic material. Based on this part, the work seems a veritable little gem and lives up to its aptly chosen title, striking a rare balance between theory and application. The work is clearly aimed at delivering a course at the intersection of mathematics and computer science, targeted at reaching the relevant applications timely through a judicially frugal exposition, as well as motivating abstract concepts with interesting examples, and, for this purpose, I highly recommend it.

Two quibbles: the book omits to justify the quotient group in terms of the related equivalence relation (coinciding co-sets) which seems a shame as the author did introduce the congruence relation on the integers. This may confuse mathematically oriented students, but perhaps the author decided not to push the abstraction too far for a mixed audience. Another issue is the use of a sorting algorithm to justify the classification of permutations into even and odd cases. This approach resonates well with CS students and should be interesting for maths students too, linking the odd-even distinction to the number of inversions. Judging from the example, it seems that the author had insertion sort in mind while describing the algorithm, yet the work refers to bubblesort. In this context,
Fordregelv
The review covers the group theory part, which I read as a quick refresher of basic material. Based on this part, the work seems a veritable little gem and lives up to its aptly chosen title, striking a rare balance between theory and application. The work is clearly aimed at delivering a course at the intersection of mathematics and computer science, targeted at reaching the relevant applications timely through a judicially frugal exposition, as well as motivating abstract concepts with interesting examples, and, for this purpose, I highly recommend it.

Two quibbles: the book omits to justify the quotient group in terms of the related equivalence relation (coinciding co-sets) which seems a shame as the author did introduce the congruence relation on the integers. This may confuse mathematically oriented students, but perhaps the author decided not to push the abstraction too far for a mixed audience. Another issue is the use of a sorting algorithm to justify the classification of permutations into even and odd cases. This approach resonates well with CS students and should be interesting for maths students too, linking the odd-even distinction to the number of inversions. Judging from the example, it seems that the author had insertion sort in mind while describing the algorithm, yet the work refers to bubblesort. In this context,