First edition · August 2026
The AI Search Handbook
A complete, self-contained guide to generative engine optimisation: how AI search retrieves, chunks, evaluates and cites information, and how to become a source an AI answer names.
2026 edition · by Luke McLaughlin
Math & Logic Essentials
A complete foundation in numbers, algebra & logical thinking
Sixty-four chapters that build mathematics and logic from the ground up: arithmetic, algebra, truth tables and Boolean logic, trigonometry, geometry, calculus and number bases, each with worked examples, mental-math shortcuts, common mistakes and a quiz.
- Pages
- 578
- Chapters
- 64
- Parts
- 11
- Quizzes
- Every chapter
Free download. No payment, no sign-up. Complete beginners, and professionals shoring up their foundations. Nothing is assumed.
About this book
What it covers
Math & Logic Essentials is built on one belief: mathematics and logic are learnable skills, not talents. Every subject is broken into small building blocks, each resting on the ones before it, so you always take a step rather than a leap.
Each chapter explains why an idea is true before showing how to use it, then backs it up with worked examples, mental-math shortcuts, the common mistakes to avoid and a short quiz with full answers. Beginners can start on page one; professionals can drop in exactly where they need to.
What you will be able to do
- Arithmetic, factors, exponents, fractions and percentages, built step by step
- Statements, connectives, truth tables and De Morgan’s laws
- Sets, quantifiers, Boolean algebra and logical validity
- Equations, inequalities, functions, polynomials and logarithms
- Trigonometry, geometry, vectors, graphs and networks
- Limits, derivatives, integrals and number bases, including binary
Contents
Eleven parts
- Part INumber & Arithmetic Foundations
- Part IIFactors, Multiples & Number Theory
- Part IIIExponents, Roots & Scientific Notation
- Part IVFractions, Decimals & Percentages
- Part VIntroduction to Logic
- Part VIAlgebra: Equations, Inequalities & Functions
- Part VIIAlgebra in Depth
- Part VIIITrigonometry
- Part IXGeometry
- Part XCalculus
- Part XINumber Bases & the Language of Computers
Excerpt
Read the opening of Chapter 1
From Chapter 1 · Order of Operations (BODMAS / PEMDAS)
How to evaluate an expression that mixes +, −, ×, ÷, brackets and powers – and always get the one correct answer.
Why must × act before +? In 2 + 3 × 4, multiplying first gives 14, adding first gives 20.
A page of symbols should mean one number to everyone who reads it, so we need a single agreed order. The order is not arbitrary: it follows from what multiplication is. The governing fact is that multiplication is repeated addition, 3 × 4 is just a shorthand for three 4s: 3 × 4 = 4 + 4 + 4.
So the 3 × 4 inside 2 + 3 × 4 is one block, the sum of three 4s. Replace it by what it stands for and the expression has only additions left, with no choice of order: 2 + 3 × 4 = 2 + (4 + 4 + 4) = 2 + 4 + 4 + 4 = 14.
Doing the + first would glue the 2 onto one of those 4s before the block is complete, giving 5 × 4 = 20, the answer to a different question (5 + 5 + 5 + 5). The symbols never said that.
That is the whole reason for the order: × and ÷ are built on top of + and −, so they must be resolved first to keep every block intact.
Questions
About this book
Is Math & Logic Essentials free?
Yes. The complete 578-page PDF is free to download. There is no payment, sign-up or email address required.
Who is Math & Logic Essentials for?
Complete beginners, and professionals shoring up their foundations. Nothing is assumed.
What does Math & Logic Essentials cover?
Sixty-four chapters that build mathematics and logic from the ground up: arithmetic, algebra, truth tables and Boolean logic, trigonometry, geometry, calculus and number bases, each with worked examples, mental-math shortcuts, common mistakes and a quiz.
What do I download?
One PDF of 578 pages (8.3 MB) with 64 chapters.
Who wrote Math & Logic Essentials?
Luke McLaughlin, an AI marketing and search specialist in Munich with more than ten years in B2B marketing. His profile and CV are on the author page.
Written by
Luke McLaughlin
Luke is an AI marketing and search specialist with more than ten years in B2B marketing across biotech, life sciences and SaaS. His work sits where technical SEO meets generative engine optimisation: making brands crawlable, retrievable and cited by AI answer engines.
He holds an MSc in Molecular Biology, works hands-on in Python, SQL and both cloud and local open-weight language models, and writes these books so that marketers can do the same.
Also free
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