This book provides a cohesive introduction to algebra and geometry, highlighting the connections between these mathematical disciplines. It is designed for self-study, making it accessible for learners who wish to grasp both subjects simultaneously. The emphasis on their interrelationships aids in developing a deeper understanding of mathematical concepts.
This book focuses on complex analytic dynamics, which dates from 1916 and is currently attracting considerable interest. The text provides a comprehensive, well-organized treatment of the foundations of the theory of iteration of rational functions of a complex variable. The coverage extends from early memoirs of Fatou and Julia to important recent results and methods of Sullivan and Shishikura. Many details of the proofs have not appeared in print before.
Intended as an undergraduate text on real analysis, this book includes all the standard material such as sequences, infinite series, continuity, differentiation, and integration, together with worked examples and exercises. By unifying and simplifying all the various notions of limit, the author has successfully presented a novel approach to the subject matter, which has not previously appeared in book form. The author defines the term limit once only, and all of the subsequent limiting processes are seen to be special cases of this one definition. Accordingly, the subject matter attains a unity and coherence that is not to be found in the traditional approach. Students will be able to fully appreciate and understand the common source of the topics they are studying while also realising that they are "variations on a theme", rather than essentially different topics, and therefore, will gain a better understanding of the subject.
Focusing on developing a mathematical mindset, this book offers practical strategies for approaching problems logically and creatively. It emphasizes the importance of critical thinking, problem-solving techniques, and the ability to view challenges from different perspectives. Readers will find valuable insights on cultivating curiosity and perseverance, essential traits for aspiring mathematicians. The guidance provided aims to inspire and equip individuals with the tools necessary to excel in mathematics and apply these skills in various contexts.
Text for advanced undergraduates and graduate students provides geometrical insights by covering angles, basic complex analysis, and interactions with plane topology while focusing on concepts of angle and winding numbers. 1979 edition.
Provides readers with experience of working on difficult unsolved problems. No deep mathematical background is required.