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Numbers, Notations and Notes

This chapter serves as an introduction to the mathematics covered in this text by providing a review of common notations, concepts, and formulas that arise in calculus and further topics. Those with a solid understanding of basic algebra should feel comfortable skipping this chapter and proceeding to the next chapter. There will be little to no example problems or exercises as the content presented is mostly historical and presented as a set of notes.

We will begin by identifying the different mathematical objects known as numbers and their specific definitions. This will lead us to the concept of Complex Numbers and Infinity. After understanding the different types of measurement that are represented by numbers, we will discuss how they can be compared, simplified, and benefits of different notations. Finally, this chapter finishes with a quick review of basic geometry before discussing how patterns play a role in mathematics. By the end of this chapter, you should understand:

• The different types of numbers and their potential uses
• The definition of “imaginary” numbers and some basic uses of them
• How the concept of infinity is helpful in applications
• That there are multiple infinities and a method in proving that fact
• What an Absolute Value represents and ways to solve them
• The difference between fractions and decimals and how to convert between them
• The benefits of using either fractions or decimals in a given situation
• How to perform algebraic operations with fractions
• Basic two- and three-dimensional geometry
• How to evaluate and understand the measurements of space in geometry
• Some examples of patterns in mathematics and how they will inform a vast amount of our understanding

List of Topics in this Chapter:

1. Real Numbers
2. Complex Numbers
3. Infinity
4. Absolute Values
5. Fractions and Decimals
6. More on Fractions
7. Geometry
8. Patterns
9. Calculators

Unit Daily Plan

Practice Problems

1. Real Numbers
2. Complex Numbers
3. Infinity
4. Absolute Values
5. Fractions and Decimals
6. More on Fractions
7. Geometry
8. Patterns
9. Calculators

Sample Assessments

1. Real Numbers
2. Complex Numbers
3. Infinity
4. Absolute Values
5. Fractions and Decimals
6. More on Fractions
7. Geometry
8. Patterns
9. Calculators

Solution Sets

1. Real Numbers
2. Complex Numbers
3. Infinity
4. Absolute Values
5. Fractions and Decimals
6. More on Fractions
7. Geometry
8. Patterns
9. Calculators

For the next Sections, see Helpful Tools for Calculus, Chapter 1.