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Undergraduate Algebra is a text for the standard undergraduate algebra course. It concentrates on the basic structures and results of algebra, discussing groups, rings, modules, fields, polynomials, finite fields, Galois Theory, and other topics. The author has also included a chapter on groups of matrices which is unique in a book at this level. Throughout the book, the author strikes a balance between abstraction and concrete results, which enhance each other. Illustrative examples accompany the general theory. Numerous exercises range from the computational to the theoretical, complementing results from the main text.

For the third edition, the author has included new material on product structure for matrices (e.g. the Iwasawa and polar decompositions), as well as a description of the conjugation representation of the diagonal group. He has also added material on polynomials, culminating in Noah SnyderÃ†s proof of the Mason-Stothers polynomial abc theorem.

Â

About the First Edition:

The exposition is down-to-earth and at the same time very smooth. The book can be covered easily in a one-year course and can be also used in a one-term course...the flavor of modern mathematics is sprinkled here and there.

- Hideyuki Matsumura, Zentralblatt

- Series:
**Undergraduate Texts in Mathematics** - Author:
**Serge Lang** - Year:
**2005** - Publisher:
**Springer** - Language:
**English** - ISBN:
**0387220259,9780387220253**

- File size:
**13 310 320** - Format:
**pdf**

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Undergraduate Algebra is a text for the standard undergraduate algebra course. It concentrates on the basic structures and results of algebra, discussing groups, rings, modules, fields, polynomials, finite fields, Galois Theory, and other topics. The auth...

Aimed primarily at graduate students and beginning researchers, this book provides an introduction to algebraic geometry that is particularly suitable for those with no previous contact with the subject and assumes only the standard background of undergra...

Massey's well-known and popular text is designed to introduce advanced undergraduate or beginning graduate students to algebraic topology as painlessly as possible. The principal topics treated are 2-dimensional manifolds, the fundamental group, and cover...

This book is intended to provide us with a short (135 pages), down to earth and fluently motivated introduction to algebraic geometry. And it does a great job. While the author does not clearly state his intentions in advance, I think it would be safe to ...

Once thought to be high-brow estoeric mathematics, algebraic geometry is now finding applications in a myriad of different areas, such as cryptography, coding algorithms, and computer graphics. This book gives an overview of some of the techniques involve...

Aimed primarily at graduate students and beginning researchers, this book provides an introduction to algebraic geometry that is particularly suitable for those with no previous contact with the subject and assumes only the standard background of undergra...

Algebraic geometry is, essentially, the study of the solution of equations and occupies a central position in pure mathematics. With the minimum of prerequisites, Dr. Reid introduces the reader to the basic concepts of algebraic geometry, including: plane...

This book is a clear and self-contained introduction to discrete mathematics. Aimed mainly at undergraduate and early graduate students of mathematics and computer science, it is written with the goal of stimulating interest in mathematics and an active, ...

From the reviews: "O'Meara treats his subject from this point of view (of the interaction with algebraic groups). He does not attempt an encyclopedic coverage ...nor does he strive to take the reader to the frontiers of knowledge... . Instead he has given...

Chances are, you wanted a laptop because itâ€™s compact, portable, and gets the job done. Youâ€™ll want this book for the same reasons. Small enough to fit into your laptop case, it gives you what you need to make the most of your laptopâ€”even if itâ€™s your fir...

This collection of important and significant papers examines a wide range of issues. One of the author's main concerns is to clarify the meaning ofÂ 'education' and 'quality in education' - a phrase often used in public debate but seldom scrutinized. Long...

New essays by an international team of scholars in Latin literature and ancient philosophy explore the understanding of emotions (or ''passions'') in Roman thought (especially philosophy and rhetorical theory) and literature. Special features include the ...

Advancing his own conception of the ''figure,'' Andrew Benjamin innovatively studies philosophy, the history of painting, and art's representation of Jews and animals. As Benjamin makes clear, the ''other'' is never an abstract concept. The means by which...

Learn how to identify the bottom of your local real estate market and understand when to buy by using the tools and tips in Forecasting for Real Estate Wealth: Strategies for Outperforming Any Housing Market . Take advantage of the great deals created by...

Verification is increasingly complex, and SystemVerilog is one of the languages that the verification community is turning to. However, no language by itself can guarantee success without proper techniques. Object-oriented programming (OOP), with its focu...

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