About this course

Basic Mathematics is a free, self-paced interactive course covering the mathematics every software engineer and student should be comfortable with: numbers and algebra, intuitive geometry, coordinate geometry, and functions. Instead of reading passively, you work through 68 lessons with live widgets you can manipulate, worked examples, and a short quiz at the end of every lesson. Your progress is saved in your browser.

Part I — Algebra

• Numbers — integers, rules for addition and multiplication, divisibility, rational numbers, and multiplicative inverses.
• Linear Equations — equations in two and three unknowns.
• Real Numbers — positivity, powers and roots, and inequalities.
• Quadratic Equations — completing the square and the quadratic formula.
• Interlude: Logic & Expressions — how to read mathematics, logic, sets, and notation.

Part II — Intuitive Geometry

• Distance and Angles — the basic notions of plane geometry.
• Isometries — reflections, rotations, translations, and congruence.
• Area and Applications — area of standard figures and the Pythagorean theorem.

Part III — Coordinate Geometry

• Coordinates and Geometry — placing geometry on the number plane.
• Operations on Points — adding points and scaling.
• Segments, Rays, and Lines — equations of lines and parametric descriptions.
• Trigonometry — sine, cosine, radians, and the unit circle.
• Some Analytic Geometry — the straight line, distance, and conic sections.

Part IV — Miscellaneous

• Functions — definitions, graphs, and standard examples.
• Mappings — mappings between sets, composition, and inverses.
• Complex Numbers — arithmetic and geometry of complex numbers.
• Induction and Summations — proof by induction and summation notation.
• Determinants — 2×2 and 3×3 determinants and what they measure.

Who this course is for

Anyone who wants a solid mathematical foundation: self-taught programmers filling gaps, students preparing for calculus or discrete mathematics, and engineers heading toward cryptography or graphics. No prerequisites beyond arithmetic. It pairs well with our interactive courses on prime fields and finite fields, and the rest of the Injectflow Academy.