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Mathematics I

A free, interactive first-year university mathematics course: logic, linear algebra, calculus, probability and scientific programming.

A rigorous mathematics course covering mathematical language and reasoning, arithmetic and number theory, matrices and vectors, linear algebra, differential and integral calculus, data analysis and probability, and scientific programming.

Start this course free

About this course

Mathematics I is a first-year university mathematics course built around doing, not memorising. Each lesson is short, and the practice that follows often asks you to act on a drawn object — drag the boundary of an integral, move a vector, reshape a curve — so the concept and the answer are the same thing. It replaces passive note-taking with a sequence of small, concrete problems.

The course begins with mathematical language, logic and proof, then arithmetic and number theory, before building the core machinery of a maths degree: matrices, vectors and linear algebra, followed by differential and integral calculus. It closes with data analysis and probability and an introduction to scientific programming, so you leave able to reason formally and compute practically.

It suits students entering a mathematics, physics, engineering or economics degree, anyone rebuilding shaky foundations before a harder course, and self-learners who want structure and rigour. Every unit is free to start, and the full lesson text is open-source on GitHub.

10 units

  1. 01Mathematical Language and Reasoning
  2. 02Arithmetic and Number Theory
  3. 03Matrices and Vectors
  4. 04Linear Algebra
  5. 05Differential Calculus
  6. 06Integral Calculus
  7. 07Data Analysis and Probability
  8. 08Programming Elements
  9. 09Scientific Programming
  10. 10Physics

Read the lessons

Every lesson explanation in Mathematics I is free to read on the web. Practice questions and interactive scenes are in the app.

Mathematical Language and Reasoning

Arithmetic and Number Theory

Matrices and Vectors

Linear Algebra

Differential Calculus

Integral Calculus

Data Analysis and Probability

Programming Elements

Scientific Programming

Physics

Frequently asked questions

Is Mathematics I free on Tryals?

Yes — you can start it for free on iOS, Android and web, and the lesson content is open-source under CC BY-SA on GitHub.

What topics does Mathematics I cover?

Mathematical language and reasoning, arithmetic and number theory, matrices and vectors, linear algebra, differential and integral calculus, data analysis and probability, and scientific programming.

Do I need prior mathematics knowledge?

Only high-school mathematics. The course starts from mathematical language and logic and builds each topic from its foundations, so it works both as a first pass and as a rigorous refresher.

How does the interactive practice work?

Many questions are interactive scenes — you drag the limit of an integral, move a vector, or reshape a function and the grading comes from what you manipulated, so you compute rather than recognise.

Is this good preparation for a STEM degree?

Yes. It covers the linear algebra, calculus and reasoning that first-year physics, engineering, computer-science and economics courses assume, which makes it a solid bridge into any quantitative degree.

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