Axioms Course
This course introduces formal systems and algebraic theories, focusing on practical applications in proofs and models for advanced mathematical verification.

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, proof rules, models, soundness, and completeness. You'll explore a focused algebraic theory, test laws like right-identity and inverses, and understand how countermodels function. These concepts link to proof assistants, model finders, and verification processes you can use right away in advanced studies and research.
Elevify advantages
Develop skills
- Build algebraic models: quickly set up and test small group-like structures.
- Verify axioms practically: rapidly check associativity, identities, and inverses.
- Use models to disprove claims: identify countermodels and demonstrate non-provability.
- Convert axioms to proofs: develop clear first-order derivations step by step.
- Implement algebraic theories in proof assistants: basics of Coq, Lean, and Isabelle.
Suggested summary
Before starting, you can change the chapters and 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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