Axioms Course
Gain mastery in axiomatic reasoning for mathematics. Delve into formal languages, algebraic structures, models, and proof assistants like Coq, Lean, and Isabelle. Learn to test axiom independence, construct countermodels, verify properties such as associativity and inverses, and apply these skills to produce rigorous, verifiable outcomes in contemporary mathematical workflows and research applications.

flexible workload of 4 to 360h
valid certificate in your country
What will I learn?
This course offers a concise, practical introduction to formal systems, covering first-order languages, proof rules, models, soundness, and completeness. Learners will study a targeted algebraic theory, validate right-identity and inverse properties, understand countermodels, and link concepts to proof assistants, model finders, and verification processes for immediate use in advanced studies and research.
Elevify advantages
Develop skills
- Build algebraic models swiftly by constructing and testing compact group-like structures.
- Verify key axioms practically by rapidly checking associativity, identities, and inverses.
- Employ models to disprove statements by identifying countermodels and demonstrating non-provability.
- Convert axioms into formal proofs by developing precise first-order derivations step by step.
- Implement algebraic theories in proof assistants using basics 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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