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e-Book Advanced Modern Algebra (Graduate Studies in Mathematics) download

e-Book Advanced Modern Algebra (Graduate Studies in Mathematics) download

by Joseph J. Rotman

ISBN: 0821847414
ISBN13: 978-0821847411
Language: English
Publisher: American Mathematical Society; 2 edition (August 10, 2010)
Pages: 1008
Category: Mathematics
Subategory: Math Science

ePub size: 1325 kb
Fb2 size: 1941 kb
DJVU size: 1109 kb
Rating: 4.6
Votes: 712
Other Formats: azw lrf lit txt

his is an excellent book containing much more than what is likely to be covered in a standard graduate course.

his is an excellent book containing much more than what is likely to be covered in a standard graduate course. several topics have been adde. he inde. een much improved.

This book contains basic definitions, complete and clear theorems (the first with brief sketches of proofs), and gives attention .

This book contains basic definitions, complete and clear theorems (the first with brief sketches of proofs), and gives attention to the topics of algebraic.

Graduate Studies in Mathematics (GSM) is a series of graduate-level textbooks in mathematics published by the American Mathematical Society . 180 Advanced Modern Algebra, Part 2, Joseph J. Rotman (2017, 3rd e. ISBN 978-1-4704-2311-7).

Graduate Studies in Mathematics (GSM) is a series of graduate-level textbooks in mathematics published by the American Mathematical Society (AMS). These books elaborate on several theories from notable personas, such as Martin Schechter and Terence Tao, in the mathematical industry. The books in this series are published only in hardcover. 181 A First Course in Sobolev Spaces, Giovanni Leoni (2017, 2nd ed.

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The book presents many topics mentioned in the first part in greater depth and in more detail. The five chapters of the book are devoted to group theory, representation theory, homological algebra, categories, and commutative algebra, respectively.

Электронная книга "Advanced Modern Algebra", Joseph J. Rotman

Электронная книга "Advanced Modern Algebra", Joseph J. Rotman. Эту книгу можно прочитать в Google Play Книгах на компьютере, а также на устройствах Android и iOS. Выделяйте текст, добавляйте закладки и делайте заметки, скачав книгу "Advanced Modern Algebra" для чтения в офлайн-режиме.

The book presents many topics mentioned in the first part in greater depth and in more detail. These books elaborate on several theories from notable personas, such as Ethan Akin, Martin Schechter, and Terence Tao, in the mathematical industry. Tips for applying to graduate programs in mathematics. A Math PhD Student's Homework, Part I (Introduction to Groups and Representation Theory). Graduate Studies in Math and Statistics. Graduate Studies in Applied Mathematics at the University of Waterloo.

This book is designed as a text for the first year of graduate algebra, but it can also serve as a reference since it contains more advanced topics as. .Advanced Modern Algebra Graduate studies in mathematics (Том 114). Издание: иллюстрированное.

This book is designed as a text for the first year of graduate algebra, but it can also serve as a reference since it contains more advanced topics as well. It begins with a discussion of the cubic and quartic equations, which leads into permutations, group theory, and Galois theory (for finite extensions; infinite Galois theory is discussed later in the book).

Advanced Modern Algebra book. Goodreads helps you keep track of books you want to read. Start by marking Advanced Modern Algebra (Graduate Studies in Mathematics) as Want to Read: Want to Read saving. Start by marking Advanced Modern Algebra (Graduate Studies in Mathematics) as Want to Read: Want to Read savin. ant to Read.

This book is designed as a text for the first year of graduate algebra, but it can also serve as a reference since it contains more advanced topics as well. This second edition has a different organization than the first. It begins with a discussion of the cubic and quartic equations, which leads into permutations, group theory, and Galois theory (for finite extensions; infinite Galois theory is discussed later in the book). The study of groups continues with finite abelian groups (finitely generated groups are discussed later, in the context of module theory), Sylow theorems, simplicity of projective unimodular groups, free groups and presentations, and the Nielsen-Schreier theorem (subgroups of free groups are free). The study of commutative rings continues with prime and maximal ideals, unique factorization, noetherian rings, Zorn's lemma and applications, varieties, and Grobner bases. Next, noncommutative rings and modules are discussed, treating tensor product, projective, injective, and flat modules, categories, functors, and natural transformations, categorical constructions (including direct and inverse limits), and adjoint functors. Then follow group representations: Wedderburn-Artin theorems, character theory, theorems of Burnside and Frobenius, division rings, Brauer groups, and abelian categories. Advanced linear algebra treats canonical forms for matrices and the structure of modules over PIDs, followed by multilinear algebra. Homology is introduced, first for simplicial complexes, then as derived functors, with applications to Ext, Tor, and cohomology of groups, crossed products, and an introduction to algebraic $K$-theory. Finally, the author treats localization, Dedekind rings and algebraic number theory, and homological dimensions. The book ends with the proof that regular local rings have unique factorization.
Comments:
Tall
Nice advanced undergrad algebra text. Can't decide if I like this or D & F tome more, but that doesn't detract from this usefulness of this text.

caif
I can't believe someone actually said the problems in this book are easy! That's outrageous! This book is rigorous and is designed for graduate Abstract Algebra. The first few chapters may seen easy because they are a review of some topics down in undergraduate Abstract Algebra. I think the author did a very good job of reviewing first and then getting into the deep stuff to give all the students a fair chance. Not everyone is brilliant! I highly recommend this book for Graduate Abstract Algebra.

OwerSpeed
Rotman's book has just about anything you'd want out of the sort of fat algebra bibles that have become popular recently. It's comparable to Dummit and Foote, though the second is written at a somewhat higher level and provides a unified treatment of commutative and non-commutative rings. Still, I think that Rotman is a bit wordy and rather than clarify, his lengthy proofs tend to obfuscate. (His proof of the correspondence theorem is particularly guilty of this.) I think the gold standard as far as presenting clear and concise proofs in algebra is concerned is the book by Hungerford. I used Hungerford in conjunction with this book. First I'd read Hungerford to get a crisp, clean and concise version of the theory and then I'd read the relevant parts of Rotman for the extra examples and intuition. Another thing I don't like about this book is the physical size. I think the book could have shed some weight by using a smaller font and better typesetting without sacrificing any of the content.

Kerahuginn
This book is very good printed and the material in it is great! Rotman's book is always very interesting and contain a lot of information and knowledge. Heavy book!

Andronrad
great

Yellow Judge
To begin with, don't let the title scare you. After having read through Rotman's book I am suprised that this text had not crossed my path earlier. It is a wonderful book and must have for any inspiring Algebraist. Moreover, I am quite shocked that the larger universities have not adopted this book.
(a) This book could quite easily be used as the standard third/fourth year undergraduate introduction to Abstract Algebra. In particular, the first four chapters provide a solid foundation for a moderate paced one semester course at which point the instructor has many different options for additional topics based on the performance of his/her class.
(b) Those students that move on to the graduate level, and obviously to a university using this book, would both be familiar with the temperment and flow of the author as well as devoid of the requirement of having to purchase another expensive Mathematics text. For example, my undergraduate Algebra text was Hungerford's and post completion the logical step, being familiar with his style, was to purchase Hungerford's graduate text. For those not familiar, let me tell you there is a night and day difference with repsect to how the material is presented.

(c) The remaining 7 chapters take the willing student on a pleasant tour of ring/module theory, some advanced group theory (for the inspiring group theorist I highly recommend the authors graduate text "Group Theory"), algebras(linear included), Homology(some cohomology) and finally some algebraic number theoretic concept under the heading of Commutative Rings III.
(d) Lastly, Rotamn does not get needlessly bogged down in any one section of the book. The flow is smooth, to the point with precise definitions, examples, and ample exercises.
I have only two negative remarks: one, the failure to include more aspects of field/Galois theory. This may be due to the author already having published a book entitled "Galois Theory". Two, the failure to devote an entire section to Finite Fileds and possibly some its applications. But this failure is minimal since, at present, the majority of Algebra texts, fail to adequately introduce and motivate Finite Fields.

Voodoosida
I gave this book one star only because I couldn't give it a score of zero!!! Although many professors say that this book is excellent, remember they are professors who already understand the material. This book shows no examples, and the examples that it does show end abruptly with comments such as "all items are routine." Routine!!! Please show me what to do so that I don't have to spend more money on a separate study guide. Aren't mathematics texts expensive enough? This book may be an excellent addition to a professors library but this book should never, ever be used as a primary text for students.

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