Using the proof of the non-trisectability of an arbitrary angle as a final goal, the author develops in an easy conversational style the basics of rings, fields, and vector spaces. Originally developed as a text for an introduction to algebra course for future high-school teachers at California State University, Northridge, the focus of this book is on exposition. It would serve extremely well as a focused, one-semester introduction to abstract algebra.
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13 of 13 people found the following review helpful:
5.0 out of 5 stars
A must for all math majors and aspiring math teachers!,
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This review is from: Rings, Fields, and Vector Spaces: An Introduction to Abstract Algebra via Geometric Constructibility (Undergraduate Texts in Mathematics) (Hardcover)
I used this book for two classes and found it to be tremendously helpful. In both cases, it was a supplement to the required text. First, in my Foundations of Higher Mathematics course, I found it to be an excellent resource for understanding some of the basic concepts of divisibility in integers, gcds, primes and the Fundamental Theorem of Arithmetic. When first learning to understand and write proofs, one must have good understanding of the basic material. B. A. Sethuraman leaves no stone unturned when it comes to this. The text helps you learn how to learn mathematics, and this can easily translate into better proof writing.
Next, I found the book to be a valuable supplement to Algebra: Abstract and Concrete by Frederick M. Goodman, used in my Elementary Modern Algebra course. The explanations of rings and fields were excellent, but beyond this is a book replete with examples. When first discovering abstract algebra, one can never have too many examples! This book is a beautiful combination of close attention to details, without being pedantic, as well as a broad overview of abstract algebra. I highly recommend it for all beginning math majors and aspiring math teachers!
0 of 5 people found the following review helpful:
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This review is from: Rings, Fields, and Vector Spaces: An Introduction to Abstract Algebra via Geometric Constructibility (Undergraduate Texts in Mathematics) (Hardcover)
Ordered Jan 12, came in today, the 19th. Decent shipping speed. The book is brand new like they said, a bit dirty though on the cover. They probably had it laying somewhere for a while. Good shipper.
1 of 7 people found the following review helpful:
4.0 out of 5 stars
Rings, Fields, and Vector Spaces,
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This review is from: Rings, Fields, and Vector Spaces: An Introduction to Abstract Algebra via Geometric Constructibility (Undergraduate Texts in Mathematics) (Hardcover)
This book is aimed to prospected High School teachers. The author's main area of study is Algebra. I would not recommend this book to someone looking for rigorous mathematics.
"Rings, Fields, and Vector Spaces" is a detailed book so much that I found myself lost while following proofs. This book is also outdated and is sold as quick-xeroxed copies at the bookstore of California State University Northridge for the price of about $12. I would recommend the newest edition along with "Introduction to Abstract Algebra" by Neal H. McCoy.
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Inside This Book
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First Sentence:
We will begin our study with a very concrete set of objects, the integers, that is, the set {0, 1, -1, 2, -2, . . .}. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
finite spanning set, long division process, ring axioms, maximal linearly independent subset, unique prime factorization, first factorization, two factorizations, nonzero polynomial, form diag, highest coefficient, common divisor, division algorithm, suitable scalars, nonconstant polynomial Key Phrases - Capitalized Phrases (CAPs): (learn more)
Zorn's Lemma, Fundamental Theorem of Algebra, Notes Remarks, Proof Let, Fundamental Theorem of Arithmetic, Proof Assume, Subring Generated New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
We will begin our study with a very concrete set of objects, the integers, that is, the set {0, 1, -1, 2, -2, . . .}. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
finite spanning set, long division process, ring axioms, maximal linearly independent subset, unique prime factorization, first factorization, two factorizations, nonzero polynomial, form diag, highest coefficient, common divisor, division algorithm, suitable scalars, nonconstant polynomial Key Phrases - Capitalized Phrases (CAPs): (learn more)
Zorn's Lemma, Fundamental Theorem of Algebra, Notes Remarks, Proof Let, Fundamental Theorem of Arithmetic, Proof Assume, Subring Generated New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 81
books:
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- A Concrete Introduction to Higher Algebra, 2nd Edition by Lindsay N. Childs in Front Matter, and Back Matter
- Introduction to Analytic Number Theory (Undergraduate Texts in Mathematics) by Tom M. Apostol in Front Matter, and Back Matter
- Mathematics and its History by John Stillwell in Back Matter (1), and Back Matter (2)
- Elements of Algebra by John Stillwell in Back Matter (1), and Back Matter (2)
- The Heritage of Thales (Undergraduate Texts in Mathematics / Readings in Mathematics) by W.S. Anglin in Front Matter
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