Best Reference Books – Algebraic Number Theory

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We have compiled the list of Top 10 Best Reference Books on Algebraic Number Theory subject. These books are used by students of top universities, institutes and colleges. Here is the full list of top 10 best books on Algebraic Number Theory along with reviews.

Kindly note that we have put a lot of effort into researching the best books on Algebraic Number Theory subject and came out with a recommended list of top 10 best books. The table below contains the Name of these best books, their authors, publishers and an unbiased review of books on "Algebraic Number Theory" as well as links to the Amazon website to directly purchase these books. As an Amazon Associate, we earn from qualifying purchases, but this does not impact our reviews, comparisons, and listing of these top books; the table serves as a ready reckoner list of these best books.

1. “A Classical Introduction to Modern Number Theory” by K Ireland and M Rosen

“A Classical Introduction to Modern Number Theory” Book Review: The book bridges the gap between elementary number theory and the systematic study of advanced topics. It gives a classic introduction to Modern Number Theory and requires the prior knowledge of basic abstract algebra as a prerequisite. The book also includes extensive bibliography and many challenging exercises to explore more knowledge about number theory. It covers the wide range of significant results with basic elementary proofs. The second edition of the book has been revised and contains two new chapters that provide ample evidence of Mordell-Weil’s belief in elliptic curves.

2. “Algebraic Number Theory” by S Lang

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“Algebraic Number Theory” Book Review: This book provides an exposition of the classical basic algebraic and analytic number theory and algebraic numbers. The book includes the papers from the Brighton Symposium, the Artin-Tate notes on class field theory, Weil’s book on Basic Number Theory, Borevich-Shafarevich’s Number Theory. It is useful for future research in algebraic number theory as a theoretically well-contained book.

3. “Number Fields” by D A Marcus

“Number Fields” Book Review: This textbook provides the basics of algebraic number theory in a straightforward manner. The book doesn’t require prior knowledge of abstract algebra. It presents different proofs in a way that it highlights key concepts of the chapter. It provides many exercises as well as appendices to summarize the required background of an algebra. It also maintains the perfect balance between both computational and theoretical practice. The newly edition book is a highly regarded textbook for students to learn number theory.

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4. “Algebraic Number Theory” by Jürgen Neukirch and Norbert Schappacher

“Algebraic Number Theory” Book Review: The present book is mainly focused on resolving an anomaly in the textbook content. It provides a comprehensive introduction to algebraic number theory for the beginner. It illustrates the basic concepts from the viewpoint of Arakelov theory. The content of class field theory is very nicely elaborate. The book also includes hints for further study and various examples to gain more knowledge. The concluding chapter on zeta-functions and L-series is the most important advantage of the new edition of the bok. The book is a very simple, systematic and theoretically balanced textbook on algebraic number field theory available.

5. “Algebraic Number Theory” by John William Scott Cassels and Albrecht Frhlich

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“Algebraic Number Theory” Book Review: This book is essential reading for future algebraic number theorists as beginners. It contains the lecture notes from an instructional conference of 1965. That event introduced class field theory as a standard tool of mathematics. The book is a standard textbook for taught courses in algebraic number theory. The second edition of the book includes a valuable list of errata compiled by mathematicians which help students to clear concepts more thoroughly.

6. “Algebraic Number Theory” by Frazer Jarvis

“Algebraic Number Theory” Book Review: This book is essential reading for future algebraic number theorists as beginners. It contains the lecture notes from an instructional conference of 1965. That event introduced class field theory as a standard tool of mathematics. The book is a standard textbook for taught courses in algebraic number theory. The second edition of the book includes a valuable list of errata compiled by mathematicians which help students to clear concepts more thoroughly.

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7. “Algebraic Number Theory and Fermat’s Last Theorem” by Ian Stewart and David Tall

“Algebraic Number Theory and Fermat’s Last Theorem” Book Review: This book introduces fundamental basics of algebraic numbers. It also illustrates one of the most interesting stories in mathematical history – the quest for a proof of Fermat’s Last theorem. It helps to motivate a general study of the theory of algebraic numbers from a point of view. The new edition of the book gives up-to-date information on unique prime factorization for real quadratic number fields, mainly Harper’s proof that Z(√14) is Euclidean. It revises and explores one chapter into two, covering basic ideas about modular function and highlights the new ideas of Frey, Wiles and others. The book improves and updates the index, figures, bibliography and further reading list to gain more knowledge. It also explains how basic ideas from the concept of algebraic numbers can be used to solve problems from a numerical perspective.

8. “Algebraic Number Theory” by Richard A Mollin

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“Algebraic Number Theory” Book Review: The new edition of the book concentrates on integral domains, ideals, and unique factorization in the first chapter, field extensions in the second chapter, class groups in the third chapter. Applications are now collected in chapter four and at the end of chapter five, where quantitative testing is highlighted as a Kronecker-Weber thought application. In the fifth chapter, the sections on ideal decomposition in number fields are distributed. The final chapter goes on to elaborate the reciprocity laws. The book includes mini-biographies of remarkable mathematicians, easy alignment, a complete index, and a lot of exercise. The book is ideal for a first-semester course, this accessible, self-contained offers a comprehensive, in-depth knowledge of many applications.

9. “Algebraic Number Theory and Fermat’s Last Theorem” by Ian Stewart and David Tall
10. “A Course in Algebraic Number Theory” by Robert B Ash
People who are searching for Free downloads of books and free pdf copies of these top 10 books on Algebraic Number Theory – we would like to mention that we don’t have free downloadable pdf copies of these good books and one should look for free pdf copies from these Authors only if they have explicitly made it free to download and read them.

We have created a collection of best reference books on "Algebraic Number Theory" so that one can readily see the list of top books on "Algebraic Number Theory" and buy the books either online or offline.

If any more book needs to be added to the list of best books on Algebraic Number Theory subject, please let us know.

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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter