Basic Concepts of Mathematics Course in PDF

This text helps the student complete the transition from purely manipulative to rigorous mathematics. It spells out in all detail what is often treated too briefly or vaguely because of lack of time or space. It can be used either for supplementary reading or as a half-year course. It is self-contained, though usually the student will have had elementary calculus before starting it. Without the “starred” sections and problems, it can be (and was) taught even to freshmen. The three chapters are fairly independent and, with small adjustments, may be taught in arbitrary order. The chapter on n-space “imitates” the geometry of lines and planes in 3-space, and ensures a thorough review of the latter, for students who may not have had it. A wealth of problems, some simple, some challenging, follow almost every section.

Learning the Basic Concepts of Mathematics

Basic Concepts of Mathematics is a comprehensive course that covers the fundamental principles of mathematics. The course is designed for beginners who are looking to learn math from scratch, as well as for individuals who want to refresh their math skills.

Introduction to the Basic Concepts of Mathematics 

Mathematics is a crucial subject for all students and professionals, regardless of their fields of study. If you're looking to learn math from scratch or want to brush up on the basics, this free PDF ebook course, "Basic Concepts of Mathematics", is the perfect opportunity for you. In this course, you'll learn about the main concepts of mathematics and how to apply them in real-world situations.

Chapter 1: Some Set Theoretical Notions

The first chapter of this course focuses on set theoretical notions, including sets, subsets, and the laws of sets. You'll learn about different types of sets, such as finite and infinite sets, and the concept of set equality. This chapter provides a solid foundation for understanding more complex mathematical concepts.

Chapter 2: The Real Number System

In chapter two, you'll dive into the real number system and learn about the different types of real numbers, including rational and irrational numbers. This chapter also covers the properties of real numbers and the basics of arithmetic operations. By the end of this chapter, you'll have a thorough understanding of the real number system and how to use it in mathematical calculations.

Chapter 3: The Geometry of n Dimensions. Vector Spaces

The final chapter of this course focuses on the geometry of n dimensions and vector spaces. You'll learn about vectors, the dot product, and the cross product. This chapter also covers the concepts of linear transformations, eigenvectors, and eigenvalues. You'll also learn how to apply these concepts to real-world problems.

Conclusion: In conclusion, this free PDF ebook course, "Basic Concepts of Mathematics", is an excellent resource for beginners who want to learn math from scratch or for anyone who wants to brush up on their math skills. With this course, you'll have access to comprehensive and structured lessons that cover the main concepts of mathematics, including set theoretical notions, the real number system, and the geometry of n dimensions. Whether you're a student, professional, or simply interested in learning math, this course is perfect for you. So, why wait? Start learning today!