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Level 2 · M.Sc

Mathematics for Computing

Syllabus · 23 phases · ~½ year

Every unit this programme teaches, in the order it is taught. Headlines only — the material itself opens once you are enrolled.

Dates, price and prerequisites

1. Phase 0 Orientation: rigor, proof & the machine-verification workflow
2. Phase 1 Predicate logic & formal proof
3. Phase 2 Relations, orders & proof techniques
4. Phase 3 Sets, cardinality & introduction to computability
5. Phase 4 Enumerative combinatorics
6. Phase 5 Recurrences & generating functions
7. Phase 6 Graph theory I: structure, trees & connectivity
8. Phase 7 Graph theory II: coloring, planarity & spectral graphs
9. Phase 8 Vector spaces & linear maps
10. Phase 9 Inner-product spaces, orthogonality & least squares
11. Phase 10 Eigenvalues, diagonalization & the spectral theorem
12. Phase 11 Singular value decomposition & low-rank approximation
13. Phase 12 Numerical linear algebra & conditioning
14. Phase 13 Group theory for cryptography
15. Phase 14 Rings, fields & finite fields
16. Phase 15 Computational number theory
17. Phase 16 Probability theory
18. Phase 17 Markov chains & random processes
19. Phase 18 Statistical inference
20. Phase 19 Numerical methods & error analysis
21. Phase 20 Linear & convex optimization
22. Phase 21 Information & coding theory
23. Phase 22 Capstone: a machine-verified mathematical toolkit for computing