Overview

This book is especially useful for 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 these students 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 adequate understanding of basic concepts, this book was written in plain language to make the process of acquiring mathematical knowledge a friendly, enjoyable, and accessible one even for those students who dislike mathematics. The simplicity of language does not sacrifice the rigor or depth of the study offered in the next pages, which guarantees adequate 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 Calculus or Mathematical Analysis. We start with Propositional Logic, which provides the language, 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 book, we offer examples to illustrate all the concepts that we discuss. Additionally, a set of 484 exercises are proposed to be solved by students. The answers to those exercises are offered at the end of each chapter. Thus, students can check their progress in learning the concepts discussed. The level of difficulty of such exercises varies from the most elementary level to a moderate level since the main objective of this book is to help students to properly learn these basic concepts and not to test their mathematical skills.

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