A Journey Through The Realm Of Numbers
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A Journey Through The Realm of Numbers
This book takes the reader on a journey from familiar high school mathematics to undergraduate algebra and number theory. The journey starts with the basic idea that new number systems arise from solving different equations, leading to (abstract) algebra. Along this journey, the reader will be exposed to important ideas of mathematics, and will learn a little about how mathematics is really done. Starting at an elementary level, the book gradually eases the reader into the complexities of higher mathematics; in particular, the formal structure of mathematical writing (definitions, theorems and proofs) is introduced in simple terms. The book covers a range of topics, from the very foundations (numbers, set theory) to basic abstract algebra (groups, rings, fields), driven throughout by the need to understand concrete equations and problems, such as determining which numbers are sums of squares. Some topics usually reserved for a more advanced audience, such as Eisenstein integers or quadratic reciprocity, are lucidly presented in an accessible way. The book also introduces the reader to open source software for computations, to enhance understanding of the material and nurture basic programming skills. For the more adventurous, a number of Outlooks included in the text offer a glimpse of possible mathematical excursions. This book supports readers in transition from high school to university mathematics, and will also benefit university students keen to explore the beginnings of algebraic number theory. It can be read either on its own or as a supporting text for first courses in algebra or number theory, and can also be used for a topics course on Diophantine equations.
Numbers in Our World: A Journey Through the Realm of Quantities
Author: Pasquale De Marco
language: en
Publisher: Pasquale De Marco
Release Date: 2025-04-06
In the realm of numbers, there lies a hidden world of patterns, symmetries, and profound connections. This book invites you on an extraordinary journey through the enigmatic realm of quantities, revealing their significance in shaping our perception of reality and understanding of the universe. From the earliest civilizations to the modern era, numbers have played a pivotal role in human history and culture. We will delve into the captivating world of mathematics, where numbers unveil the intricate patterns and symmetries that govern the universe. We will explore the role of numbers in science and engineering, where they serve as indispensable tools for understanding the laws of nature and unlocking the secrets of the physical world. Beyond their practical applications, numbers also hold deep cultural and historical significance. We will trace the evolution of numerology, the ancient belief in the mystical properties of numbers, and examine the profound impact of numbers on art, music, and literature. We will discover how numbers have been used to convey hidden meanings, create aesthetic beauty, and express the deepest emotions of the human soul. Furthermore, we will venture into the realm of human cognition and explore the psychology of numbers. We will investigate how our brains process and respond to numerical information, uncovering the fascinating ways in which numbers influence our perception, decision-making, and behavior. We will also delve into the realm of numbers in the natural world, revealing the intricate patterns and sequences that permeate the flora and fauna of our planet. From the Fibonacci sequence found in seashells and plant spirals to the golden ratio that governs the proportions of countless living organisms, we will uncover the hidden harmony and order that numbers bring to the natural world. We will also explore the role of numbers in technology, finance, and the social sciences, examining how they are used to analyze data, make predictions, and understand complex systems. Throughout this exploration, we will marvel at the power and versatility of numbers, appreciating their ability to illuminate the mysteries of the universe and enrich our understanding of the human experience. Join us on this extraordinary odyssey, where numbers will be our guides, revealing the secrets of existence and unveiling the wonders that lie within the realm of quantity. If you like this book, write a review!
Unraveling the Enigma of Riemann's Zeta-Function: A Journey Through the Realm of Analytic Number Theory
Author: Pasquale De Marco
language: en
Publisher: Pasquale De Marco
Release Date: 2025-07-10
In the vast expanse of mathematical inquiry, few concepts have captured the imagination and ignited the curiosity of scholars like the Riemann zeta-function. Introduced by Bernhard Riemann in the 19th century, this enigmatic function has stood as a towering enigma, challenging mathematicians and inspiring generations of exploration. This comprehensive and engaging book invites you on an intellectual journey through the captivating world of the Riemann zeta-function, unveiling its intricate properties, profound applications, and historical significance. Delve into the depths of analytic number theory as we navigate concepts like Dirichlet's theorem, the prime number theorem, and the Riemann zeta-function's relationship with other mathematical functions. Unravel the mysteries surrounding the Riemann hypothesis, a conjecture that has captivated mathematicians for over a century. Discover the profound implications of this hypothesis, its potential to unlock the secrets of prime numbers, and its role in shaping our understanding of the fundamental nature of mathematics. Witness the Riemann zeta-function's remarkable applications in diverse fields, ranging from physics and computer science to finance and engineering. Explore its contributions to quantum field theory, string theory, coding theory, and cryptography, gaining insights into the function's versatility and far-reaching impact. Trace the Riemann zeta-function's historical significance, from its introduction by Riemann to its enduring legacy in modern mathematics. Learn about the brilliant minds who have dedicated their lives to studying this function, their contributions to the field, and the ongoing pursuit of knowledge that continues to drive research in this captivating area. Join us on this intellectual odyssey as we unravel the enigma of the Riemann zeta-function, embarking on an exploration that promises to expand your horizons, deepen your understanding of mathematics, and ignite your passion for discovery. Prepare to be captivated by the beauty, elegance, and profound implications of this mathematical marvel. If you like this book, write a review!