Alex Barrios

Below are my lecture notes/videos for some of the classes that I have previously taught:

• Introduction to Proofs: Video Playlist, Written notes part: 1, 2

• Elementary Number Theory: Lecture Notes, Video Playlist

• Introduction to Modular Forms: Lecture Notes, Video Playlist

• Real Analysis I: Lecture Notes

• Linear Algebra: Lecture Notes

Below are some old notes:

• Towards Étale Cohomology. Notes for a talk in Purdue's Informal Algebraic Geometry Seminar

• Analytic Continuation and Schemes. Notes for a talk in Purdue's Student Colloquium

• Faltings' Theorem Part I: Algebraic Geometry for Number Theorists. Notes for a talk in Purdue's Secret Seminar

• Galois Representations of Elliptic Curves and the proof of Fermat's Last Theorem. Notes based on Saito's Fermat's Last Theorem

• Dirichlet's Theorem on Primes in Arithmetic Progression. Notes for a talk in Purdue's Student Colloquium

• A Riemann-Roch Theorem for Number Fields and Sheaves. Notes for a talk in Purdue's Riemann-Roch Seminar

• Mackey Theory. Notes for a talk in Purdue's Number Theory Seminar

• Quadratic Forms and Class Field Theory. Notes for a talk in Purdue's Number Theory Seminar

• Abelian Kummer Theory. Notes for a talk in Purdue's Number Theory Seminar

• On Some Consequences of the ABC Conjecture in Arithmetic and Logic. Notes for a talk in Purdue's Number Theory Seminar

• Elasticity of Factorization in Number Fields. Notes for a talk in Purdue's Number Theory Seminar

• Proper Prime Representing Functions. Notes for a talk in Purdue's Number Theory Seminar

• An English translation of Jacques Vélu's Isogénies Entre Coubres Elliptiques

• An English translation of Michel Langevin's On Some Consequences of the ABC Conjecture in Arithmetic and Logic

• Notes on an Introduction to Galois Representations (with Razan Taha)

• Notes on Hensel's Lemma and Completions

• An expository paper on Fermat's Last Theorem, Proof of the n=3,4 case