Algebra Foundations for Normal People by Gabriel Beguerie - HTML preview

Chapter goals

Two honest ways to use this book.

Path A: stop the bleeding fast. Use this when a class, exam, or placement test is already close.

1. Unit 0 (the floor: signs, order, fractions, decimals, percentages) 2. Chapter 5 (expressions and distribution)

3. Chapters 6 and 7 (equations)

4. Chapter 8 (inequalities)

5. Chapter 9 (exponents and roots)

6. Chapter 10 (factoring basics)

7. Chapter 11 (coordinates, slope, and lines)

8. Chapter 12 (formulas)

9. Chapter 13 (word-problem translation)

10. Chapter 15 (readiness check)

Path B: full mastery before Math Functions for Normal People.

1. Read every chapter in order.

2. Work the examples with a pencil, not only with your eyes.

3. Try the chapter problems before reading the solutions.

7

8

Quick-start guide: learn the essentials in a few days

4. Redo the misses two days later.

5. Take Chapter 15 only after the full pass.

A realistic fast pass is 8 to 12 days. A realistic full pass is 3 to 6 weeks. The point is not speed. The point is to leave this book with the floor finally stable.

Prerequisites (if this is hard, go back to Unit 0)

Can you skip Unit 0? Only if the Unit 0 questions feel easy, not merely familiar.

If order of operations, signed numbers, fractions, decimals, or percentages still create mistakes, do not skip the floor. Later chapters will use those moves, not rebuild them from scratch.

Note

How to use the book so it actually works.

• Read the key idea until you can say it in your own words.

• Reproduce the recipe without peeking.

• Cover the worked example and redo it on your own.

• Attempt the end-of-chapter problems before opening the solutions chapter.

• If you freeze, go back one layer. In this book, panic usually means “one prerequisite is weak,” not “I am bad at math.”

Real life: what it’s for

This book covers the algebra moves that quietly run the rest of the series:

• prices, taxes, discounts, and percentages,

• formulas in science and statistics,

• slopes, rates of change, and graphs,

• symbolic work inside trigonometry,

• simplification, factoring, and rearranging in calculus.

You are not learning “tiny school tricks.” You are building the operating system underneath later math.

Note

How this book avoids jumps.

• Unit 0 rebuilds the arithmetic floor: order, signs, fractions, decimals, and percentages.

• Chapters 1–4 turn that floor into algebra language and number fluency.

• Chapters 5–8 teach symbolic control: expressions, equations, and inequalities.

Quick-start guide: learn the essentials in a few days 9

• Chapters 9–12 add the tools needed for later books: exponents, roots, factoring, slope, and formulas.

• Chapters 13–15 remove the training wheels: word problems, mixed review, and readiness diagnosis.

If a later page feels too fast, the repair path is local: return to the chapter named by the skill, not to a vague feeling of being “bad at math.”

Bridge (why this matters later)

This book comes before Math Functions for Normal People. Its job is simple: make later books feel learnable.

• Functions needs algebra almost every page.

• Trigonometry hides algebra inside identities and equations.

• Calculus is full of simplification, factoring, fractions, and rearranging.

• Statistics uses formulas, percentages, fractions, and sign logic constantly.

If this book does its job, the next books should feel challenging in a good way instead of chaotic.

Recap: what you’re taking away

You do not need speed first. You need repeatability first.

The goal of this book is not to make you look clever for five minutes. The goal is to make you steady enough that the rest of the series stops feeling like guesswork.

Chapter 0

Unit 0: The minimum kit to make this

painless (before algebra)