Joseph Gallian is a well-known active researcher and award-winning teacher. His Contemporary Abstract Algebra, 6/e, includes challenging topics in abstract. CONTEMPORARY ABSTRACT ALGEBRA, NINTH EDITION provides a solid introduction to the traditional topics in abstract algebra while. And according to this criterion, Contemporary Abstract Algebra by Joseph Gallian is a well-written book. After introducing a new concept or.
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Sep 06, WarpDrive rated it really liked it Shelves: Before I delve into an analysis of this contmporary textbook, let me highlight first that abstract algebra, contrary to much uniformed opinion, is glalian a specialistic, esoteric field cobtemporary pure mathematics characterized by very limited applicability to the physical ckntemporary. On the contrary, this subject is not just extremely contem;orary, but a very important and even foundational discipline in many areas of mathematics and science.
In fact, structure and symmetry are a fundamental aspect of physical reali Before I delve into an analysis of this excellent textbook, let me highlight first that abstract algebra, contrary to much uniformed opinion, is not a specialistic, esoteric field in pure mathematics characterized by very limited applicability to the physical world. In fact, structure and symmetry are gal,ian fundamental wlgebra of physical reality. It might well be argued that science is nothing but the discovery of symmetries, aogebra and structures that define reality at its most fundamental level.
There is for example a natural connection between particle physics and representation theory of abstract algebra, linking the properties of elementary particles to the structure of Lie Groups and Lie Algebras in particular, the different quantum states of any given elementary particle corresponds to an irreducible representation of the Poincare’ group.
Poincare’ invariance is the fundamental symmetry in particle physics: In more general term, local symmetries play a fundamental role in physics as they form the basis for gauge theories a gauge theory is essentially a type of field theory “in which the Lagrangian is invariant under some Lie groups of local transformations”. It is also important to highlight that symmetry in ocntemporary is fundamental in the physical world: Going beyond the realm of fundamental physics, molecular symmetry is absract fundamental concept in chemistry, as it can predict or explain many of a molecule’s chemical properties such as its dipole moment.
In the biological sciences, I was told my personal knowledge of the biological sciences is pretty rudimentary that symmetry and symmetry breaking play a prominent role in developmental biology, from bilaterians to radially symmetric organisms see for example https: Moreover, group theory has many applications in cryptography, robotics and computer vision, just as another example of concrete application of abstract algebra concepts.
Abstract algebra is therefore extremely important and foundational in many fields, and not just in pure mathematics: Adding hours on a clock, for example, is like working in a cyclic group; many manufacturing processes might be shown to be isomorphic to products of permutations of a finite group; and group theory and abstract algebra applied to molecular systems biology support the design of new drugs.
In general, abstract algebra and group theory in particular provides a framework for constructing analogies or models from abstractions, and for the manipulation of those abstractions to design new systems, make predictions and posit new hypotheses. OK, now that justice has been rendered to this fascinating and beautiful subject, the time has finally come for me to review this gsllian University textbook, which represents a very good introductory treatment of the fundamental elements of abstract algebra group theory, rings, fields at a level which is typically addressed at senior Mathematics undergraduate stage.
This book is very accurate and nicely written, with very few typos all of them minora absrract good choice and variety of relevant exercises at different level of complexity the majority of them are actually pretty easywith minimal and only occasional hand-waving; it is also a book rich with examples a critical feature in a subject that sometimes can sorely test the abstract thinking capabilities of even the keenest readerand presenting a tightly organized and generally reader-friendly progression of concepts and techniques.
I also greatly appreciated the full list of notational conventions at the beginning of the book, and the list of suggested readings at the end of each chapter. I must also point out, though, that this book contains one of the best treatments of factor groups, the Lagrange theorem, the Sylow theorems and the fundamental theorem of finite abelian groups that I have come across so far. In summary, my general experience with this book has been quite a positive one; independently of the quality of this particular book, I must also say that studying abstract algebra has been for me a rewarding intellectual journey I did study some abstract algebra at university, but it was only at introductory level and manly focused on vector spacesas it is very remarkable how, by starting just with the basic gxllian of an extremely simple concept such as that of a group, whole worlds of progressively richer and more complex structures, patterns and relationships are galpian unveiled in a process of enthralling discovery.
Overall, this is a 4-star book. Not a perfect book by any means, and possibly conntemporary basic in some areas, but a joeph good textbook recommended to anybody interested in a treatment of this fascinating subject delivered, with a good pedagogical approach, fallian senior undergraduate level.
Apr 16, Jerzy rated it it was amazing Shelves: My favorite textbook of all time! Apr 29, Michael rated it did not like it Shelves: This book is OK as far as presenting abstract algebra in the usual way to undergrads. Competent explanations of the basics of groups, rings, and fields. Numerous easy exercises, which is fine, although it might gal,ian nice if there were more challenging ones too. There are two problems.
The first problem is, I don’t believe in the purely abstract aogebra to teaching a first course in algebra which this book uses.
Contemporary Abstract Algebra by Joseph A. Gallian
This book doesn’t give you any real idea what the heck algebra is good for and doesn’t This book abstracg OK as far as presenting abstract algebra in the usual way to undergrads.
This book doesn’t give you any real idea what the heck algebra is good for and doesn’t provide any real connections to anything else. The attempts to liven things up with silly quotes and bios give the book a condescending middle school type feel. Galloan would rather the author attract readers’ interest by showing them the power of the algebraic structures discussed.
Groups and rings are extremely powerful concepts, but to read this book you would think they are just a game where you write down some axioms and see what random statements you can prove. None of this is unique to this book. It seems students are simply not expected to see algebra put to any use until grad school, if at all.
There is no excuse for this. It is simply disgusting. No one should buy this book or require it for a course at such an exorbitant price. It doesn’t do your laundry or cook you breakfast. May 12, Anne rated it it was amazing Shelves: This book is the reason I became a mathematician. Feb 11, Kolya Matteo rated it it was amazing Shelves: Oct 31, Daniel rated it really liked it.
I did find useful information that helped me in the class, but it was very limited.
I feel like the book was good for a few concepts, but for the most part I had to rely on the internet. Going through the class and actually reading the tallian, it is actually a really useful guide. In gallain, if this is not your textbook for Abstract Algebra, it should definitely be a companion to your text. This book changed my life! Jul 04, Leonkap rated it really liked it. Really was fun to work though this one.
Contemporary Abstract Algebra
Feb 01, Nitin Pant rated it really liked it. Herstein for the mathematics undergrad. Gallian for the armchair mathematician. Working through the first two parts of the book has opened my mind to the real possibilities of Mathematics.
I love that the author takes time to express useful applications of the materials being covered. There were a few places in the book that took some time to get through and were confusing, however; with some additional aid online made it through to galian.
Because the book is in multiple parts, I will be taking some time to study a few other topics and the come back to this awesome book. I Working through the first joaeph parts of the book has opened my mind to the real possibilities of Mathematics.
I cannot wait to get back into it. Mar 23, Ayush Bhat rated it it was amazing. Nobody explains abstract algebra better then Joseph Gallian. This is an awesome book.
I have read many books on abstract algebra and my personal experience is this: Aug 22, Narendra rated it really liked it. Sep 25, Jason Evans rated it really liked it. The best intro to abstract algebra out there. If you don’t like this book, then fuck you. Dec 08, Ankush Sharma rated it really liked it Shelves: An acquired taste, just like black coffee with no sugar.
Dec 30, Will rated it it was ok. Supposedly this is not a children’s book, but it is full of pictures and blurbs about random dead people. Hardly contemporary if you ask me! Not recommended for the serious reader.
This review has been hidden because it contains spoilers. To view it, click here. Aug 15, Margaretha Dc rated it really liked it.
This book is so amazing Mar 28, Nate Ellis rated it did not like it. Jamie Banks rated it it was amazing May 16, Christopher Farah rated galliab really liked it Nov 08, Arul rated it did not like it Aug 19, Jasashwi Mandal rated it it was amazing Oct 02,