Algebra/Contributors/Book Order

This section is to explain the reasoning for the ordering of the chapters and sections, as well as the goals of each.

General Scope

Chapters 20-27 are meant to be independent of each other, in that they can be done in any order one pleases, or can be skipped entirely, but they can only be done once the reader completes the first 19 chapters.

Chapter 1 - Elementary Arithmetic

Chapter Summary

As the book is meant to be accessible for all levels of experience with mathematics, the basics of arithmetic are covered in the very first chapter.

First, numbers as a whole are covered via the number line in section 1.1, which is then followed by the four basic mathematical operations, as well as exponents and roots, in the scope of whole numbers. Afterwards, these same ideas are then explained through the scope of integers, fractions and decimals. This knowledge is then all put together via the Order of Operations, or PEMDAS, where the reader is faced with expressions with multiple operations.

After one learns about numerical operations, they can then be further used for other crucial math concepts, starting with units, which will be used in many word problems. Some real-life problems will also require knowledge of estimating values or rounding them up properly, which is followed directly after the concept of units.

Afterwards, the reader will use all of the above concepts to encounter what is arguably the most crucial part of the chapter, the skill of "problem solving", which is briefly touched upon via data analysis, and then in the chapter's final section, which uses many of the ideas introduced in Polya's How to Solve It.

Roadmap

Types of Numbers

• Section 1.1 - Learn about the different types of numbers.

Properties and Operations of Whole Numbers

• Section 1.2
• Section 1.3
• Section 1.4

Other Types of Numbers

• Section 1.5 - Apply the concepts from sections 1.2 - 1.4 to Integers.
• Section 1.6 - Apply the concepts from sections 1.2 - 1.4 to Fractions.
• Section 1.7 - Apply the concepts from sections 1.2 - 1.4 to Decimals.

Putting it All Together

• Section 1.8 - Solve problems involving multiple operations using the concepts from the previous sections.

Applying the Concepts

• Section 1.9
• Section 1.10
• Section 1.11
• Section 1.12

Chapter 2 - An Introduction to Algebra

Chapter 2 serves as the reader dipping their toes into the world of Algebra once they've read over the Arithmetic chapter. Here, they will learn Algebra as a language.

Roadmap

Algebra as a Language

• Section 2.1
• Section 2.2
• Section 2.3

Chapter 23 - Theory of Equations

This chapter serves as a sort of continuation of the concepts from Chapter 10.

Chapter 25 - Limits of Functions

This chapter can be thought of as a transition from Algebra to Calculus in the same way that Chapter 1 is a transition from Arithmetic to Algebra.