Assumed background
The book starts from basic arithmetic and assumes no advanced knowledge. It is suitable for adults returning to math, students filling gaps, and programmers who want cleaner reasoning.
PDF book · Math and logic
The Math & Logic Foundation
Numbers, algebra and logical thinking, built step by step
A complete foundation in numbers, algebra, functions, geometry, probability, statistics, sets, and formal logic, taught in small steps with definitions, worked examples, mistakes to avoid, quizzes, and answer keys.
- 578 pages
- PDF download
- 2026 Edition
- English
- $20 one-time
Secure checkout with Stripe. Your receipt gives you a private download link, and there is no subscription.
About the book
What The Math & Logic Foundation covers
The Math & Logic Foundation is a ground-up course for readers who want math to stop feeling like a collection of unexplained rules. It begins with arithmetic, place value, order of operations, fractions, decimals, ratios, percentages, and units, then builds toward algebra, functions, geometry, probability, statistics, sets, truth tables, conditionals, quantifiers, arguments, fallacies, matrices, vectors, mappings, and proof habits. The book is meant for rebuilding confidence, not showing off.
Best for: Readers rebuilding math and logic from first principles for school, work, programming, AI, or clearer technical thinking.
- 578 pages of arithmetic, algebra, functions, geometry, probability, statistics, sets, and formal logic
- Definitions, worked examples, mental-math shortcuts, mistake notes, quizzes, and answer keys
- Truth tables, connectives, conditionals, quantifiers, arguments, fallacies, matrices, vectors, and proof style
- Designed for patient self-study from the ground up
How it teaches
A repeatable study rhythm
The book teaches math by explaining why a rule exists before asking the reader to apply it. Definitions are small, examples are worked line by line, and common mistakes are called out directly. Logic is treated as an extension of ordinary careful thinking: what follows, what does not follow, what a statement actually says, and how to test it. The reader is never expected to jump from arithmetic into abstraction without intermediate steps.
Plain definition
Each idea starts with the smallest useful explanation and the words needed to talk about it.
Worked example
The book solves problems step by step, showing what changed and why that move was allowed.
Mistake watch
Common wrong turns are named so the learner can recognize them before they become habits.
Practice set
Short exercises check calculation, interpretation, and reasoning rather than speed alone.
Answer key
Solutions make self-study possible without needing a teacher beside you.
Bridge forward
Each topic explains how it supports later algebra, programming, AI, logic, or technical reading.
Look inside
Pages from the PDF
Five full pages from the PDF. Select a page to open it at full size.
How to use the bookDefinitions, examples, shortcuts, common mistakes, quizzes, and answer keys. 
Order of operationsThe opening chapters explain why the rules work before asking readers to apply them. 
Decimal reasoningWorked examples keep place value and comparison visible. 
Unit conversionsLater arithmetic chapters connect ratios, rates, cancellation, and practical measurement. 
Vectors and structureThe foundation grows into matrices, vectors, mappings, and proof style.
Before you start
What you need and how long it takes
A realistic pace
A reasonable pace is 8 to 16 weeks depending on how much math confidence you are rebuilding. Readers who only need a review can move quickly; readers who have been away from math for years can take one small section at a time. The intended result is not advanced specialization, but a stable foundation: arithmetic makes sense, algebra has a purpose, functions are readable, and logical arguments become inspectable.
- Arithmetic
- Algebra
- Functions
- Geometry
- Statistics
- Truth tables
- Sets
- Proofs
One-time purchase
Get The Math & Logic Foundation
$20USD · PDF · 578 pages
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- Format
- Pages
- 578
- Edition
- 2026 Edition
- Language
- English
- File size
- 7.3 MB
- Price
- $20 USD, one-time
- Delivery
- Single-use download from your receipt
Questions about The Math & Logic Foundation
Is The Math & Logic Foundation suitable for beginners?
The book starts from basic arithmetic and assumes no advanced knowledge. It is suitable for adults returning to math, students filling gaps, and programmers who want cleaner reasoning. It is written for self-study and builds up step by step.
How long does it take to work through The Math & Logic Foundation?
A reasonable pace is 8 to 16 weeks depending on how much math confidence you are rebuilding. Readers who only need a review can move quickly; readers who have been away from math for years can take one small section at a time. The intended result is not advanced specialization, but a stable foundation: arithmetic makes sense, algebra has a purpose, functions are readable, and logical arguments become inspectable.
What do I get, and how is it delivered?
A 578-page PDF (7.3 MB). After payment, your receipt page gives you a private, single-use download link, and we email you a link to that receipt. Save the PDF after downloading.
Can I read it on any device, and is it mine to keep?
It is a standard PDF for a computer, tablet or phone, online or offline. It is a one-time purchase of $20 with no subscription. You keep the file for your own reading; the purchase terms explain the personal-use licence.
What if my download fails?
If a transfer is interrupted, the link is released so you can try again from your receipt. If it still fails, email support@indepapps.com with your order number instead of buying again.
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