Algebra I Volume 2: From Rational Numbers to Complex Extensions (Bachelor's Degree in Mathematics) - Softcover

Luque Zevallos, Helbert Justo

Softcover

ISBN 13: 9798319106353

Publisher: Independently published, 2025

Synopsis

🎓 Algebra I - Volume 2
From Rational Numbers to Complex Extensions

Do you want to master the fundamental concepts of algebra, exploring deeply from rational and real numbers to complex numbers and quaternions?

This volume offers a rigorous, structured guide for university-level students seeking a thorough understanding of advanced algebraic structures. From the precise construction of rational and real numbers to the fascinating world of complex extensions, this book effectively blends theoretical depth with practical applications.

🔍 What will you find in this volume?

✅ Rational Numbers and Algebraic Structures
Explore the formal construction of rational numbers, their algebraic properties, arithmetic operations, and the essential concepts of order, density, and the Archimedean property.

✅ Real Numbers and Completeness
Understand real numbers through convergence of sequences, Cauchy sequences, Dedekind cuts, and the nested intervals theorem. Delve into the completeness of the real number field, crucial for calculus and analysis.

✅ Complex Numbers and Quaternions
Dive into the theory of complex numbers, their representation in binomial and polar forms, and algebraically closed fields. Study De Moivre’s theorem and discover quaternions, powerful tools for representing rotations in three-dimensional spaces.

✅ Density and Countability
Learn the profound concepts of countability, density of rational numbers in the real number line, and proofs of the uncountability of real numbers, essential foundations for advanced mathematics.

✅ Applications in Science and Engineering
Connect abstract algebraic theories with practical applications in physics, engineering, geometry, and mathematical modeling. Learn how complex numbers and quaternions apply in real-world scenarios.

🧠 Includes:
✔ A rigorous and progressive exposition of key concepts
✔ Step-by-step illustrative examples and solved problems
✔ Challenging exercises designed to reinforce understanding
✔ Applications to real-life problems and interdisciplinary contexts

📌 Ideal for:

• Students of mathematics, physics, and engineering

• University professors seeking a clear and comprehensive reference

• Researchers interested in deepening their knowledge of algebraic structures and number theory

📘 Series: Bachelor of Mathematics
🛡 Legal Information:
📄 ISBN:9798319106353
📍 Country of origin: Peru
📚 Independent Publisher: Helbert Justo Luque Zevallos
🏠 Legal Address: Coop. Vista Alegre E-2, Alto Selva Alegre, Arequipa, Peru
🔗 Available on Amazon: https://www.amazon.com

Ready to master advanced algebra with solid mathematical foundations and real-world applications?
📖 Get your copy now and elevate your understanding of algebraic structures!

Edition details

• Publisher: Independently published
• Publication date: 2025
• Language: English
• ISBN 13: 9798319106353
• Binding: Paperback
• Number of pages: 259