Axioms Course
Master axiomatic thinking in mathematics. Explore formal languages, algebraic systems, models, and proof assistants to test independence, build countermodels, and connect abstract axioms to rigorous, verifiable results in modern mathematical practice.

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 workloadWhat our students say
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