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.

from 4 to 360h flexible workload
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 workload. Choose which chapter to start with. Add or remove chapters. Increase or decrease the course workload.What our students say
Your classes are perfect. I purchased the one-year package and finally have the opportunity to follow various topics of interest without needing to switch platforms... I thank you for everything you do, I've already recommended you to other people...

Giulio CarloDigital Marketing Student
I like how the lessons are straight to the point and how I can switch chapters and skip content I don't need.

Mariana FerresPhotography Student
I like the content and the presentation style and video transcription, which speeds up the process!

Luciana AlvarengaNail Design Student
The platform is fast, simple to use. The diversity of content and complementary videos really help with learning.

André FelipePrompt Engineering Student
FAQ
Who is Elevify? How does it work?
Do the courses have certificates?
Are the courses free?
What is the course workload?
What are the courses like?
How do the courses work?
What is the duration of the courses?
What is the cost or price of the courses?
What is an EAD or online course and how does it work?
PDF Course