Starting the Problem Solving and Lesson Side of Your PLEM Academy Textbook How to Build It

Overview

This lesson begins Section 1.0 of your textbook, where you transition from setup into actual math content using a structured, repeatable system. :contentReference[oaicite:0]{index=0}

Step 1: Create Section 1.0

Your first section should be labeled clearly:

• 1.0 Introduction to Linear Algebra
• Or whatever subject you are currently studying

Use Heading 1 so it appears properly in your table of contents.

Step 2: Choose Your Textbooks

You should work with two textbooks per subject:

• Example: Gilbert Strang (Linear Algebra)
• Example: David Lay (Linear Algebra)
• Example: Stewart or Thomas (Calculus / Vector Calculus)

These are your sources. Do not use random internet sources.

Step 3: Create a Citations Page

You must track your sources:

• Create a separate citations page
• Include textbook references and URLs
• Each problem must be tied to its source

Step 4: Choose a Starting Point

Choose a topic you are comfortable with:

• Determinants
• Matrices
• Vector operations

Start simple. This is your launch point.

Step 5: Problem Page Structure

Each problem must follow this exact structure:

1. Section Reference
2. Book Citation
3. Problem Statement
4. Answer
5. Solution (Structured Method)

The PLEM Solution Method

1. Formuli

Collect formulas, theorems, and definitions.

2. Assemble

Apply formulas and execute the solution.

3. Finalize

State the final answer clearly with justification.

4. Full Circle (When Needed)

Verify your answer. This may create a new problem by proving correctness.

Critical Rule

You cannot mix and match textbooks.

Each problem must be solved using the textbook it came from. This ensures consistency and proper citation.

Intro Page for Section 1

Before solving problems, you may create a full-page introduction explaining:

• What the section covers
• Why it is important
• What the student should expect

Editing Workflow Reminder

Continue using the editing system:

• Write → Write → Write
• Edit previous
• Repeat

Start Simple

Do not overcomplicate your first problems:

• Choose easy questions
• Focus on structure
• Focus on clarity

You are building habits, not just solving math.

Long-Term Goal

This system will produce:

• A complete textbook
• A professional portfolio
• A product you can publish and sell

Every page contributes to a long-term asset. :contentReference[oaicite:1]{index=1}

Key Insight

You are not just solving problems—you are learning how to teach, write, and communicate mathematics at a professional level.

Quick Recap

1. Create Section 1.0 with proper headings.
2. Choose two textbooks.
3. Track citations carefully.
4. Follow the structured problem format.
5. Use the PLEM solution method.
6. Start simple and build consistency.