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Axioms Course

Axioms Course
from 4 to 360h flexible workload
valid certificate in your country

What will I learn?

The Axioms Course provides a compact, hands-on introduction to formal systems, covering first-order languages, proof rules, models, soundness, and completeness. It delves into a focused algebraic theory, testing right-identity and inverse laws, and demonstrates how countermodels function. Participants connect these concepts to proof assistants, model finders, and verification workflows applicable in advanced studies and research.

Elevify advantages

Develop skills

  • Build algebraic models: quickly construct and test small-group-like systems.
  • Verify axioms in practice: check associativity, identities, and inverses fast.
  • Use models to refute claims: find countermodels and prove non-provability.
  • Translate axioms into proofs: craft clean first-order derivations step by step.
  • Encode algebraic theories in proof assistants: Coq, Lean, and Isabelle basics.

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.
Workload: between 4 and 360 hours

What our students are saying

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Really great course. Lots of valuable information.
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