Lydia Bakiri's undergraduate research project (written in french) Le théorème de Nielsen-Schreier, deux approches différentes
This is a free, online course running parallel to the Séminaire étudiant de théorie des catégorie course. Shadows of computation has its own dedicated webpage.
This course was taught alongside Francesca Pratali.
Week 1: What is a category? Notes, problems
Week 2: Structure preservation. Notes, problems
Week 3: Naturality, presenting mathematics. Notes, problems
Week 4: The Yoneda Lemma. Notes, Assignment 1 notes, problems,
Week 5: Adjoint functors. Notes, problems.
Week 6: More on adjoint functors. Notes, problems
Week 7: Universal properties. Notes, problems
Week 8: Notions of computation, presenting mathematics 2. Notes, problems
Week 9: More on limits, colimits, and adjoint functors. Notes, problems
Week 10: Monads and adjunctions. Notes
Week 11: Sample presentations, analytic functors (Will) and Abelian categories (Francesca). Analytic functors, Abelian categories, problems
Week 12: Student's presentations.
Week 13: Feedback, presenting mathematics 3.
Assignments: One due 20/10/22. Two due 1/12/22.
Week 1: Introduction.
Week 2: Euclidean Algorithm.
Week 3: Ciphers. problems, solutions
Week 4: One time pad, block ciphers. problems, solutions
Week 5: RSA. problems, solutions RSA
Week 6: RSA again. problems, solutions
Week 7: Hash functions and digital signatures. problems and solutions
Week 8: Message authentication, symmetric key distribution protocol. problems, solutions
Week 9: Key management and distribution, ElGamal. problems, solutions
Week 10: Schnorr. Schnorr Algorithm
Week 11: Finite fields. problems, solutions
Week 12: Authentication, Murkle trees. problems, solutions