Goal: This course offers a mathematically rigorous graduate-level introduction to probability theory, designed for students preparing for advanced research in economics, statistics, data science, and related fields. The course emphasizes the measure-theoretic foundations of probability and develops the conceptual and analytical tools needed to understand uncertainty, random phenomena, and asymptotic behavior in stochastic systems. 

By the end of the course, students will achieve the following learning outcomes:

• Mastery of Measure-Theoretic Probability: Understand probability as a measure space, including σ-algebras, measurable functions, and Lebesgue integration.

• Theoretical Control of Random Variables: Analyze distributions of random variables under transformation, handle multivariate settings, and calculate expectations using integration theory.

• Expertise in Convergence Concepts: Gain deep knowledge of modes of convergence (in probability, in distribution, almost surely), and apply classical results such as the Weak and Strong Laws of Large Numbers, and the Central Limit Theorem.

• Facility with Generating Functions and Limit Techniques: Employ moment generating and characteristic functions to analyze convergence, derive asymptotic results, and understand fine properties of distributions.

• Understanding of Conditional Structures: Define and interpret conditional expectation using both classical and measure-theoretic approaches, including Radon–Nikodym derivatives and L² projections.

This course is theoretical in nature, with emphasis placed on formal proofs, abstraction, and generality, rather than computational methods or data applications. The content is especially suited for students in management science, economics, operations research, and pure/applied mathematics.

Textbooks:
(1) Durrett, R. (2019). Probability: Theory and Examples (5th edition), Cambridge University Press.

(2) Billingsley, Patrick (2012), Probability and Measure (Anniversary edition), Wiley. 

Topics:

Measure Theory and Lebesgue Integration

Probability Spaces and σ-Algebras

Random Variables and Distribution Functions

Expectation, Variance, Covariance

Function of Random Variables and Jacobian Techniques

Conditional Probability and Independence

Modes of Convergence

Generating Functions (MGF and CF)

Laws of Large Numbers (WLLN, SLLN)

Central Limit Theorems and Extensions

Conditional Expectation via Radon–Nikodym

Goal: The purpose of this course is to familiarize students with the methods of making data-driven decisions that can enhance business performance and results. The course focuses on achieving the following objectives:

• utilizing tools and techniques to investigate and analyze data.

• comprehending patterns and relationships within the data.

• summarizing the data in a manner that is meaningful and informative.

• presenting insights in a clear and actionable manner for stakeholders.

Ultimately, the Advanced Business Analytics course aims to empower decision-makers within an organization to make well-informed choices based on data-driven insights, resulting in improved business performance and outcomes.

Textbooks:
(1) Mike X Cohen (2021), Linear Algebra: Theory, Intuition, Code, Sincxpress. [Link]
(2) Prince (2018), Predictive Analytics for Business Strategy, McGraw Hill. [Link]
(3) Békés and Kézdi (2021), Data Analysis for Business, Economics, and Policy, Cambridge University Press. [Link]
(4) James et al. (2021), An Introduction to Statistical Learning (2nd Edition), Springer. [Link]

Topics:

Introductory Linear Algebra for Data Science

Linear Regressions

Dimension Reduction

Experimental Design

Goal: The purpose of this course is to provide students with a comprehensive understanding of managerial economics and business strategy, incorporating insights from behavioral economics. The course focuses on: 

• Analyzing demand, supply, and market structures to understand competitive dynamics. 

• Developing and applying pricing strategies tailored to different market environments. 

• Examining psychological factors and biases that influence consumer and managerial decision-making. 

• Utilizing economic models to interpret data and inform strategic business decisions.

Ultimately, this course aims to empower students to make well-informed, data-driven decisions that enhance organizational performance and outcomes.

Textbooks:
(1) Baye and Prince (2022), Managerial Economics & Business Strategy (10th edition), McGraw Hill. [Link]

Topics:

Individual behavior 

Firms and organization 

Industry and structure 

Competition and management 

Game theory and applications 

Quantitative analysis 

Information, risk, and uncertainty 

Behavioral and experimental economics

Social and economic networks 

AI, regulation, and fintech