Algebra/Contributors/Book Order

This section is to explain the reasoning for the ordering of the chapters and sections.

General Scope

Chapters 20-26 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

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, which is then followed by mathematical operations in the scope of whole numbers. Afterwards, these same ideas are then explained through the scope of integers, fractions and decimals. This knowledge can then be applied further with PEMDAS, where the reader is faced with expressions with multiple operations.

After one learns about these operations, they can then be further used for other crucial 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.

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.

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.