Journey Through The Realm of Numbers: From Quadratic Equations to Quadratic Reciprocity

The book covers a range of topics from the foundations of mathematics to basic abstract algebra, driven by the need to understand concrete equations and problems. It also introduces open-source software for computations and offers glimpses of possible mathematical excursions. It is suitable for readers transitioning from high school to university mathematics and for university students exploring the beginnings of algebraic number theory.

Format: Paperback / softback
Length: 344 pages
Publication date: 04 October 2020
Publisher: Springer Nature Switzerland AG

This comprehensive text takes readers on a captivating journey from the realm of familiar high school mathematics to the intricate world of undergraduate algebra and number theory. The adventure begins with the fundamental concept that emerging number systems emerge through the solution of diverse equations, paving the way for abstract algebra. Along this enlightening path, readers will encounter essential mathematical ideas and gain valuable insights into the actual processes of mathematical inquiry. Starting from a foundational level, the book gently guides readers into the complexities of higher mathematics, particularly emphasizing the formal structure of mathematical writing, including definitions, theorems, and proofs. The book encompasses a wide range of topics, ranging from the fundamental foundations of numbers and set theory to advanced abstract algebra, all driven by the urgent need to understand concrete equations and problems, such as determining which numbers are sums of squares. While certain topics typically reserved for a more advanced audience are lucidly presented in an accessible manner, the book also introduces readers to open-source software for computations, aimed at enhancing their understanding of the material and nurturing fundamental programming skills. For those with a thirst for exploration, a series of Outlooks included within the text offer glimpses into potential mathematical excursions.

This book serves as a valuable resource for students transitioning from high school to university mathematics, as well as for university students seeking to delve into the foundations of algebraic number theory. It can be read as a standalone text or as a supporting resource for introductory courses in algebra or number theory. Additionally, it can be utilized for a specialized topics course on Diophantine equations.

In conclusion, this remarkable book offers readers a comprehensive and engaging exploration of the mathematical landscape, guiding them from the familiar terrain of high school mathematics to the rich tapestry of undergraduate algebra and number theory. With its clear explanations, insightful examples, and practical applications, it empowers readers to deepen their understanding of mathematics and unlock its vast potential.

Weight: 556g
Dimension: 161 x 234 x 26 (mm)
ISBN-13: 9783030552329
Edition number: 1st ed. 2020