A Classical Introduction to Modern Number Theory 2nd Ed. *US HARDCOVER* by Kenneth Ireland, Michael Rosen - {9780387973296}

Embark on a captivating journey into the world of numbers with Kenneth Ireland and Michael Rosen's "A Classical Introduction to Modern Number Theory" (2nd Edition). This comprehensive guide, specifically designed for graduate students with a background in abstract algebra, serves as a bridge between the foundational concepts of elementary number theory and the intricacies of advanced topics.

Key Highlights:

• Rich Historical Context: Immerse yourself in the historical development of number theory, gaining valuable insights into the evolution of ideas and the motivations behind groundbreaking discoveries.
• Expansive Scope: Explore a diverse range of crucial subjects, including prime numbers, divisibility, congruences, quadratic forms, Diophantine equations, and continued fractions.
• Accessible Proofs: Grasp complex theorems through the authors' employment of comparatively elementary proofs, making them understandable to a broader audience.
• Engaging Exercises: Test your comprehension and delve deeper into concepts with a wealth of challenging exercises designed to solidify your knowledge.
• New Chapters: The second edition boasts two new chapters: one delving into Mordell's theorem for elliptic curves, and another exploring recent advancements in arithmetic geometry.

Benefits for Students:

• Solid Foundation: Establish a firm understanding of classical number theory and its connection to modern research endeavors within the field.
• Historical Appreciation: Gain a deeper appreciation for how historical developments shaped the field and the motivations behind key results.
• Mastering Techniques: Equip yourself with various tools and methods employed in number theory to tackle challenging problems effectively.
• Preparation for Further Exploration: This book serves as a stepping stone, preparing you for more advanced courses and research within the fascinating realm of number theory.
• Intellectual Challenge: Push your boundaries and explore deeper concepts through the provided challenging exercises.

Who Should Read This Book:

• Graduate students in mathematics, with a particular interest in number theory.
• Mathematicians seeking a refresher or an introduction to the modern landscape of number theory.
• Anyone with a strong foundation in mathematics and a genuine curiosity about the beauty and complexities of numbers.