Axioms Course
This course introduces formal systems, algebraic theories, and their applications in proof assistants, enabling practical verification and model construction for advanced mathematical research.

from 4 to 360h flexible workload
valid certificate in your country
What will I learn?
The Axioms Course provides a compact, practical introduction to formal systems, covering first-order languages and proof rules up to models, soundness, and completeness. Delve into a targeted algebraic theory, verify right-identity and inverse laws, and understand how countermodels function. Link these concepts to proof assistants, model finders, and verification processes that you can use straight away in higher studies and research.
Elevify advantages
Develop skills
- Build algebraic models: swiftly set up and examine small group-like structures.
- Verify axioms practically: rapidly assess associativity, identities, and inverses.
- Employ models to disprove assertions: identify countermodels and demonstrate non-provability.
- Convert axioms to proofs: develop precise first-order derivations progressively.
- Implement algebraic theories in proof assistants: fundamentals of Coq, Lean, and Isabelle.
Suggested summary
Before starting, you can change the chapters and the workload. Choose which chapter to start with. Add or remove chapters. Increase or decrease the course workload.What our students say
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