Full course coming soon

Formal Verification for Scientific Computing and AI Systems

7 chapters · 31 lessons

1. 1. Formal Systems and Type-Checked Mathematics

   4 lessons

   Understand how formal languages encode mathematical objects and rules for manipulation.

2. 2. Proof Assistants in Practice

   5 lessons

   Work hands-on with proof assistant tools to verify simple theorems and build formal libraries.

3. 3. Formalizing Scientific Computing Models

   4 lessons

   Apply formal methods to partial differential equations, numerical methods, and physical models.

4. 4. Pairing AI Generation with Verification

   5 lessons

   Design pipelines that validate AI-generated code, proofs, and mathematical claims.

5. 5. Specification Gaps and Scope Mismatches

   4 lessons

   Learn to identify when formal statements differ from informal claims and press-release interpretations.

6. 6. Verification in Engineering Workflows

   5 lessons

   Integrate formal methods and validation pipelines into real-world engineering and research projects.

7. 7. Advanced Topics and Future Directions

   4 lessons

   Explore cutting-edge applications in topology, probability, and hybrid human-machine proof workflows.