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Axioms Course

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

What will I learn?

The Axioms Course gives you a compact, hands-on path into formal systems, from first-order languages and proof rules to models, soundness, and completeness. Explore a focused algebraic theory, test right-identity and inverse laws, and see how countermodels work. Connect these ideas to proof assistants, model finders, and verification workflows you can apply immediately in advanced study 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 say

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Very great course. Lots of rich information.
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