Teaching Material

Lecture notes, exercises and solutions, and other teaching material are available below (all typos may not have been removed). Notebooks refer to Jupyter notebooks. Each course has material for one semester.

Discrete Mathematics:

Elementary Number Theory, Propositional Logic, Predicate Logic, Set Theory, Combinatorics, Linear Recurrences, Complex Numbers, Linear Algebra, Relations, Functions, Graph Theory, Solutions.

Groups and Symmetries:

Isometries and the Plane, Symmetries of Shapes, Introducing Groups, The Group Zoo, More Group Structures, Back to Geometry, Permutation Groups, Cayley Theorem and Puzzles, Quotient Groups, Infinite Groups, Frieze Groups, The full course.

Abstract Algebra I (Groups and Rings):

Group theory, Exercises, Ring theory, Exercises, The whole course.

Algebraic Methods:

Group theory, Ring theory, Field theory, Galois theory, The whole course.

Algebraic Number Theory:

Algebraic numbers and algebraic integers, Ideals, Ramfication theory, Ideal class group and units, p-adic numbers, Valuations, p-adic fields, The whole course.

Discrete Methods:

Polya's Enumeration Theorem, Basic Graph Theory, Network Flows, Linear Programming, The Network Simplex Algorithm, Semidefinite Programming, The whole course.

Coding Theory:

Introduction, Linear Codes, Linear Codes and Their Dual, Linear Codes and Distances, Errors and Decoding, Decoding Algorithms, Rate and Sphere Packing Bound, Equivalent Codes, Golay Codes, Reed-Mueller Codes, Bounds, Finite Fields, Cyclic Codes, Cyclic Codes II, Cyclic Codes III, Reed-Solomon Codes, Revision, Exercises with Solutions.

Short Courses

This is material for short courses, typically a few (3 to 5) hours.

Some Facets of Information Theoretical Graph Analytics:

Centralities and Entropic Centralities (Notebook,Slides), Random Graphs and Power Law (Notebook,Slides), Information Theoretic Clustering, General Data (Notebook,Slides), Information Theoretic Clustering, Grapha Data (Notebook,Slides), Bitcoin Forensics (Notebook,Slides).

Statistical Data Analysis (3h):

Descriptive - Predictive - Prescriptive Analytics Slides.