Algebra I Volume 1: Foundations of Set Theory and Integers (Bachelor's Degree in Mathematics)

Algebra I - Volume 1 Foundations of Set Theory and Integers Do you want to master the essential concepts of algebra, starting from fundamental set theory to the intricate world of integers and their algebraic structures? This volume is a rigorous, step-by-step guide for university-level students seeking a deep and solid understanding of algebraic concepts. From the basics of sets and natural numbers to sophisticated integer operations, this book seamlessly combines theoretical clarity with practical applications. What will you find in this volume? Set Theory and Functions Explore membership, inclusion, De Morgan's laws, Cartesian products, cardinality, binary and equivalence relations, and detailed study of injective, surjective, and bijective functions. Understand direct and inverse images, function composition, and internal laws of composition. Natural Numbers and Mathematical Induction Master fundamental operations and properties of natural numbers, Peano’s axioms, and the powerful technique of mathematical induction, along with summations and the Binomial theorem. Construction and Properties of Integers Learn about the construction of integers from natural numbers, equivalence classes, and quotient sets. Study integral domains, zero divisors, modular arithmetic, and fundamental integer properties. Advanced Number Theory Dive into integral domains, Euclidean algorithms, and Diophantine equations. Explore prime numbers, greatest common divisors, and least common multiples. Study Fermat’s, Euler’s, and Wilson’s theorems and their profound implications. Includes: Rigorous and progressive development of topics Illustrative examples and step-by-step solved problems Exercises at various levels of difficulty Real-world applications in logic, number theory, and mathematical modeling Ideal for: Mathematics, Physics, and Engineering students University professors seeking a clear and comprehensive textbook Researchers aiming to deepen their understanding of algebra and number theory Series: Bachelor of Mathematics Legal Information: ISBN: 9798319096951 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 embark on a journey through the foundations of algebra with robust mathematical tools and real-world applications? Get your copy now and start mastering Algebra!