Mathematics

An introduction to probability with a view toward applications. Topics include mathematical models for random phenomena, random variables, expectation, the common discrete and continuous distribution with applications, joint distributions, conditional distributions and expectation, independence, monent generating functions, laws of large numbers and the central limit theorem, sample and population, sample distributions, concept of estimation for population parameters, and linear regression and correlation.

Textbook: Thomas Haslwanter, "AN INTRODUCTION TO STATISTICS WITH PYTHON"

The course introduces physical quantities and fundamental laws of electrical circuits. The basics of direct and alternating current networks are explained allowing the evaluation of complex electric networks.

In this hands-on course, students are introduced to the models and theory necessary to develop computational skills in the field of financial mathematics. Covering topics such as the Monte Carlo method, stochastic models, the binomial tree model, the theory of risk-neutral pricing, derivative pricing and the interpretation of random variables, students learn how computational methods can be used to evaluate different financial scenarios. During supervised programming sessions, which include an introduction to programming in Python, students have the opportunity to implement the computational methods introduced to students using relevant examples. 

This class addresses topics from network structure and growth to the spread of epidemics. The course studies diverse algorithmic techniques and mathematical models that are used to analyze such large networks, and give an in-depth description of the theoretical results that underlie them. Some topics are random graphs, giant components, power laws, percolation, spreading phenomena, community detection, basic algorithms for network science, lower bounds and advanced algorithms for polynomial-time problems, sampling algorithms, streaming algorithms, sublinear algorithms, and graph partitioning algorithms.

The course assumes basic skills in algorithms and mathematics: familiarity with basic graph algorithms (shortest paths, flows), and basic understanding of NP-completeness. Work with basic probabilities and some integrals in included.