From Zero to Engineer
A course for technical degrees: from school gaps all the way to calculus. Every topic explained step by step, with worked examples. Once you have worked through a topic, you can test yourself on our exercises.
Materials
Open the lesson materials and start learning.
Arithmetic Basics
Numbers, operations, fractions and percentages - the foundation on which everything else is built.
Algebra
Algebraic expressions, equations, inequalities and systems of equations.
What you will learn
Work confidently with fractions, powers and roots without reaching for a calculator at every step
Convert numbers between decimal, binary, octal and hexadecimal
Write results in engineering and scientific notation, the way it is done in technical work
Transform algebraic expressions, simplify algebraic fractions and apply special products
Solve logarithmic equations and rearrange formulas for any variable
Factor polynomials, including fourth-degree ones
Who this course is for
A student with gaps
The material starts at natural numbers, so you can go back to exactly the point where something slipped.
Exam candidates
Arithmetic and algebra underpin most exam problems. The revision lessons after each part let you check yourself without a textbook.
University student
If an engineering degree revealed gaps left by school, this is the shortest way to close them.
How to use the materials
Read the lesson
Each lesson takes one topic and explains it from the "why it works" side, with drawings and worked examples. No account needed.
Work the examples yourself
Cover the solution, do it your own way, and only then compare. That is the difference that makes it stick.
Test yourself on exercises
Every curriculum topic has sets of exercises with step-by-step solutions. You can also open a blank PhiBoard and work the problem your own way.
Frequently asked questions
Are the materials free?
Yes. Every lesson can be downloaded free of charge, with no account and no download limit.
What language are the materials in?
The notes are handwritten in English, while lesson titles and navigation follow the site language. Mathematical notation is the same in both.
In what order should I study?
Lessons run from the simplest to the hardest and are best taken in order. If arithmetic is solid, start at lesson 18, where algebra begins.
Is this enough to prepare for exams?
The course covers the foundation, arithmetic and algebra, that most problems rest on. It does not replace a full exam guide, but revision is far harder without it.
Can I use the materials in class?
Yes. We only ask that you keep the attribution. We are a small independent team in Europe and everything here is free - we want these materials to reach as many people as possible, so if they are useful in your class or among teachers you know, please pass them on.