Introduction to Analysis: Theorems and Examples
Publication Date
1-1-2025
Document Type
Article
Publication Title
Synthesis Lectures on Mathematics and Statistics
Volume
Part F3495
DOI
10.1007/978-3-031-67954-4
First Page
1
Last Page
214
Abstract
This book focuses on the theoretical aspects of calculus. The book begins with a chapter on set theory before thoroughly discussing real numbers, then moves onto sequences, series, and their convergence. The author explains why an understanding of real numbers is essential in order to create a foundation for studying analysis. Since the Cantor set is elusive to many, a section is devoted to binary/ternary numbers and the Cantor set. The book then moves on to continuous functions, differentiations, integrations, and uniform convergence of sequences of functions. An example of a nontrivial uniformly Cauchy sequence of functions is given. The author defines each topic, identifies important theorems, and includes many examples throughout each chapter. The book also provides introductory instruction on proof writing, with an emphasis on how to execute a precise writing style.
Keywords
Continuous Functions, Differentiation, Integrations, Real Numbers, Sequences and Series, Set Theory
Department
Mathematics and Statistics
Recommended Citation
Hidefumi Katsuura. "Introduction to Analysis: Theorems and Examples" Synthesis Lectures on Mathematics and Statistics (2025): 1-214. https://doi.org/10.1007/978-3-031-67954-4
