Introduction to Propositional Logic and Set Theory (Understanding Calculus Book 1)

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English | August 1, 2025 | ASIN: B0FKVTQ312 | 292 pages | Epub | 42.38 MB
This book is especially useful to students who are about to finish high school and want to properly prepare in mathematics to start college or university. The book is also suitable for those students who have already started higher education. Many of them still face barriers in learning more complex mathematical concepts and their adequate application. A flaw in understanding basic concepts is what makes them reluctant to learn more. Since the objective is to help students achieve an appropriate understanding of basic concepts, this book was written in a plain and simple language in order to make the process of acquiring the mathematical knowledge a friendly, enjoyable and accessible one even for those students who dislike mathematics. However, the simplicity of language does not sacrifice the rigor or depth of the study offered in these pages, which guarantees a satisfactory management of concepts. Students are not required to have math skills; the only requirement is to be interested in learning. In the three chapters that make up this text, we address the building blocks of Calculu s or Mathematical Analysis . We start with Propositional Logic , which provides the language, the logical reasoning, and training on how to properly address mathematical proofs. This chapter is followed by an introduction to Set Theory where we develop a body of concepts that are used in the definition of many fundamental concepts of Calculus such as Function . This book ends with the study of the real number system which is addressed from an axiomatic approach. Throughout the study we offer examples to illustrate all the concepts that we discuss. Furthermore, we propose several sets of exercises to be solved by the students. The answers to those exercises are offered at the end of each chapter. The level of difficulty of such exercises varies from the most elementary level to a moderate level, since the main goal of this book is to help students to properly learn these basic concepts and not to test their mathematical skills. Once the students have completed the study of all the concepts discussed in this book, they will be able to approach with a solid base, and with confidence, the study of the concepts of Calculus such as functions, limits, continuity, derivation, and integration, which will be discussed in upcoming books by this same author. Read more