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Math & Logic Essentials.

A practical foundation book for the reasoning, notation, and logic skills behind programming, AI work, and technical problem-solving. Support the one-person MultiAgentAI studio and receive this PDF instantly on the $20 or $30 supporter tier.

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Cover preview for Math & Logic Essentials.

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Purpose

A complete foundation for thinking clearly with numbers and logic.

Math & Logic Essentials is written for people who want the underlying ideas, not a pile of disconnected tricks. It starts with place value, arithmetic, fractions, ratios, percentages, equations, functions, geometry, probability, and statistics, then moves into the logic that sits underneath programming and technical reasoning.

The goal is confidence: being able to read a problem, identify the structure, choose the right operation, and explain why the answer follows. Every chapter breaks concepts down into definitions, examples, mistakes to avoid, and answer keys so the reader can practice without getting lost.

What it teaches

Number sense Order of operations Fractions Ratios Percentages Algebra Functions Geometry Statistics Truth tables Sets Proof habits

Teaching method

Every concept is taught as a usable mental tool.

The book is designed for self-study: each chapter gives the idea, shows the exact reasoning steps, names common traps, then provides exercises and answers so the reader can check understanding immediately.

01

Definitions before shortcuts

Terms like proposition, variable, function, ratio, and implication are explained before they are used, so later chapters have solid footing.

02

Worked examples with reasons

Solutions are broken into numbered steps with small notes that explain why each move is legal, not just what calculation to perform.

03

Mistake patterns and answer keys

Chapters call out common wrong turns, then include practice and answers so the learner can correct their reasoning while it is fresh.

Inside the book

Screenshots from the actual PDF.

These previews show the structure of the material: signposts for how to study, worked examples, and the logic chapters that turn everyday language into precise reasoning.

A page explaining how to use Math & Logic Essentials.
How to use the bookDefinitions, examples, mental-math shortcuts, practice, and answer keys.
A worked examples page from the order of operations chapter.
Worked examplesStep-by-step solutions show the reasoning, not only the final answer.
A logic page about statements and propositions.
Logic foundationsStatements, truth values, propositions, negation, and clean reasoning.
A logic page about conditionals and implication.
ConditionalsThe book explains implication, converse, inverse, contrapositive, and biconditionals.

Learning path

From arithmetic basics to the logic behind programming.

The book is broad on purpose. It builds the reader from first principles toward the concepts that keep appearing in code, AI, data, automation, and technical writing.

  • Number foundations cover operations, place value, signed numbers, factors, multiples, primes, and divisibility.
  • Fractions and ratios connect parts, wholes, proportions, percentages, rates, units, and scale.
  • Algebra and functions introduce variables, expressions, equations, inequalities, graphs, and coordinate thinking.
  • Geometry and statistics build measurement, visual reasoning, probability, averages, spread, and interpretation.
  • Logic covers propositions, connectives, truth tables, conditionals, quantifiers, sets, arguments, and fallacies.
  • Advanced foundations introduce polynomials, logarithms, modular arithmetic, mappings, matrices, vectors, and proof style.

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