Ebook: Field Theory

This book presents the basic theory of fields, starting more or less from the beginning. It is suitable for a graduate course in field theory, or independent study. The reader is expected to have taken an undergraduate course in abstract algebra, not so much for the material it contains but in order to gain a certain level of mathematical maturity.

For this new edition, the author has rewritten the text based on his experiences teaching from the first edition. There are new exercises, a new chapter on Galois theory from an historical perspective, and additional topics sprinkled throughout the text, including a proof of the Fundamental Theorem of Algebra, a discussion of casus irreducibilis, Berlekamp's algorithm for factoring polynomials over Zp and natural and accessory irrationalities.

From the reviews of the first edition:

The book is written in a clear and explanatory style...the book is recommended for a graduate course in field theory as well as for independent study.

- T. Albu, Mathematical Reviews

...[the author] does an excellent job of stressing the key ideas. This book should not only work well as a textbook for a beginning graduate course in field theory, but also for a student who wishes to take a field theory course as independent study.

- J.N.Mordeson, Zentralblatt

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This book presents the basic theory of fields, starting more or less from the beginning. It is suitable for a graduate course in field theory, or independent study. The reader is expected to have taken an undergraduate course in abstract algebra, not so much for the material it contains but in order to gain a certain level of mathematical maturity.

For this new edition, the author has rewritten the text based on his experiences teaching from the first edition. There are new exercises, a new chapter on Galois theory from an historical perspective, and additional topics sprinkled throughout the text, including a proof of the Fundamental Theorem of Algebra, a discussion of casus irreducibilis, Berlekamp's algorithm for factoring polynomials over Zp and natural and accessory irrationalities.

From the reviews of the first edition:

The book is written in a clear and explanatory style...the book is recommended for a graduate course in field theory as well as for independent study.

- T. Albu, Mathematical Reviews

...[the author] does an excellent job of stressing the key ideas. This book should not only work well as a textbook for a beginning graduate course in field theory, but also for a student who wishes to take a field theory course as independent study.

- J.N.Mordeson, Zentralblatt

---

This book presents the basic theory of fields, starting more or less from the beginning. It is suitable for a graduate course in field theory, or independent study. The reader is expected to have taken an undergraduate course in abstract algebra, not so much for the material it contains but in order to gain a certain level of mathematical maturity.

For this new edition, the author has rewritten the text based on his experiences teaching from the first edition. There are new exercises, a new chapter on Galois theory from an historical perspective, and additional topics sprinkled throughout the text, including a proof of the Fundamental Theorem of Algebra, a discussion of casus irreducibilis, Berlekamp's algorithm for factoring polynomials over Zp and natural and accessory irrationalities.

From the reviews of the first edition:

The book is written in a clear and explanatory style...the book is recommended for a graduate course in field theory as well as for independent study.

- T. Albu, Mathematical Reviews

...[the author] does an excellent job of stressing the key ideas. This book should not only work well as a textbook for a beginning graduate course in field theory, but also for a student who wishes to take a field theory course as independent study.

- J.N.Mordeson, Zentralblatt

Content:
Front Matter....Pages i-xii
Preliminaries....Pages 1-20
Front Matter....Pages 21-21
Polynomials....Pages 23-40
Field Extensions....Pages 41-71
Embeddings and Separability....Pages 73-92
Algebraic Independence....Pages 93-109
Front Matter....Pages 111-111
Galois Theory I: An Historical Perspective....Pages 113-136
Galois Theory II: The Theory....Pages 137-171
Galois Theory III: The Galois Group of a Polynomial....Pages 173-195
A Field Extension as a Vector Space....Pages 197-209
Finite Fields I: Basic Properties....Pages 211-224
Finite Fields II: Additional Properties....Pages 225-238
The Roots of Unity....Pages 239-259
Cyclic Extensions....Pages 261-267
Solvable Extensions....Pages 269-286
Front Matter....Pages 287-287
Binomials....Pages 289-308
Families of Binomials....Pages 309-317
Back Matter....Pages 319-332

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This book presents the basic theory of fields, starting more or less from the beginning. It is suitable for a graduate course in field theory, or independent study. The reader is expected to have taken an undergraduate course in abstract algebra, not so much for the material it contains but in order to gain a certain level of mathematical maturity.

For this new edition, the author has rewritten the text based on his experiences teaching from the first edition. There are new exercises, a new chapter on Galois theory from an historical perspective, and additional topics sprinkled throughout the text, including a proof of the Fundamental Theorem of Algebra, a discussion of casus irreducibilis, Berlekamp's algorithm for factoring polynomials over Zp and natural and accessory irrationalities.

From the reviews of the first edition:

The book is written in a clear and explanatory style...the book is recommended for a graduate course in field theory as well as for independent study.

- T. Albu, Mathematical Reviews

...[the author] does an excellent job of stressing the key ideas. This book should not only work well as a textbook for a beginning graduate course in field theory, but also for a student who wishes to take a field theory course as independent study.

- J.N.Mordeson, Zentralblatt

Content:
Front Matter....Pages i-xii
Preliminaries....Pages 1-20
Front Matter....Pages 21-21
Polynomials....Pages 23-40
Field Extensions....Pages 41-71
Embeddings and Separability....Pages 73-92
Algebraic Independence....Pages 93-109
Front Matter....Pages 111-111
Galois Theory I: An Historical Perspective....Pages 113-136
Galois Theory II: The Theory....Pages 137-171
Galois Theory III: The Galois Group of a Polynomial....Pages 173-195
A Field Extension as a Vector Space....Pages 197-209
Finite Fields I: Basic Properties....Pages 211-224
Finite Fields II: Additional Properties....Pages 225-238
The Roots of Unity....Pages 239-259
Cyclic Extensions....Pages 261-267
Solvable Extensions....Pages 269-286
Front Matter....Pages 287-287
Binomials....Pages 289-308
Families of Binomials....Pages 309-317
Back Matter....Pages 319-332
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