Numbers, algebra and logical thinking, built step by step
A complete foundation in arithmetic, number theory, fractions, logic, algebra, trigonometry, geometry, calculus and number bases, taught in small steps with definitions, worked examples, mistakes to avoid, quizzes, and answer keys.
Readers rebuilding math and logic from first principles for school, work, programming, AI, or clearer technical thinking.
A friendly foundation for arithmetic, algebra, functions, truth tables, Boolean logic, trigonometry, geometry, calculus and number bases.
The Math & Logic Foundation rebuilds math from the ground up for readers who want it 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 truth tables, conditionals, quantifiers, Boolean algebra and valid arguments, algebra and functions, matrices and vectors, trigonometry, geometry, calculus and number bases. The book is meant for rebuilding confidence, not showing off.
You are never asked to take a leap; you take a step.
578 pages across 64 chapters: arithmetic, number theory, logic, algebra, trigonometry, geometry, calculus and number bases
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
Look inside
Pages from the PDF.
Real pages from the book. 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.
How it teaches
How The Math & Logic Foundation teaches the subject.
The Math & Logic Foundation 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.
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.
Reasonable timeframe
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 a study session looks like.
01
Plain definition
Each idea starts with the smallest useful explanation and the words needed to talk about it.
02
Worked example
The book solves problems step by step, showing what changed and why that move was allowed.
03
Mistake watch
Common wrong turns are named so the learner can recognize them before they become habits.
04
Practice set
Short exercises check calculation, interpretation, and reasoning rather than speed alone.
05
Answer key
Solutions make self-study possible without needing a teacher beside you.
06
Bridge forward
Each topic explains how it supports later algebra, programming, AI, logic, or technical reading.
Secure checkout on Stripe; no account and no subscription
A private download link on your receipt page and by email
Each link works once, so save the PDF when it downloads
Sold separately from the Mac apps
Questions about The Math & Logic Foundation.
Is The Math & Logic Foundation suitable for beginners?
Yes. 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 format is The Math & Logic Foundation, and how do I get it?
The Math & Logic Foundation is a 578-page PDF. Checkout is handled by Stripe. When payment completes, the receipt page gives you a private download link, and the same link is sent to the email address you used at checkout.
Can I read it on any device, and is it mine to keep?
Yes. It is a standard PDF you can read on a computer, tablet or phone, online or offline. It is a one-time purchase for $20 with no subscription, and the file is yours to keep.
What if my download link stops working?
Each link works once and shows when it expires, so save the PDF when the download finishes. If a download fails or a link has expired, email support@macossoftware.com with your Stripe receipt and we will help.
