A Trip to Mathematics: From Logic to Equations
A beginner-friendly guide covering mathematical logic, significant figures, equations, and linear algebra. Builds from basic reasoning to solving systems of equations, with worked examples throughout. Free download.
Mathematics starts with logic and ends with equations. This book covers the entire journey for someone who wants to build genuine understanding from the ground up.
The first section covers mathematical logic properly. Not just truth tables, but the five logical connectives, tautologies, contradictions, quantifiers, and the distinction between inductive and deductive reasoning. It includes proof techniques that most introductory books skip.
The second part deals with numbers and measurement. Significant figures, scientific notation, precision vs. accuracy, and the rules for counting significant digits. These are the fundamentals that matter in every branch of science and engineering.
The final sections cover equations. Starting from what an equation actually is, moving through the golden rule of equations, classification by degree and number of variables, and then solving linear equations in all their forms. Systems of equations are handled via substitution, elimination, and graphical methods, with a preview of matrix methods.
The book closes with a preview of quadratic and polynomial equations, bridging to more advanced study.
What You Will Learn
- All five logical connectives and how to construct valid proofs
- Significant figures, scientific notation, and rounding rules
- Types of equations and classification systems
- Solving linear equations in standard, slope-intercept, point-slope, and intercept forms
- Systems of linear equations via substitution, elimination, and graphical methods
- Quadratic equations including factoring, the quadratic formula, and completing the square