Mathematical Analysis, Probability, and Statistics

Dragoș‑Pătru Covei received his Ph.D. in mathematics with distinction from the West University of Timișoara in 2009, after completing earlier degrees in mathematics, algebra and geometry, information and communication technology, and computer science, fields in which he consistently ranked among the top students. He had already demonstrated exceptional mathematical ability in high school, graduating with the maximum possible score on the mathematics baccalaureate exam. Since beginning his academic career in 2001, he has advanced from junior assistant professor to full professor, joining The Bucharest University of Economic Studies in 2013 and becoming a full professor in 2016. His research covers nonlinear elliptic partial differential equations, stochastic processes, and applications of PDEs to geometry, physics, and financial mathematics, leading to more than 50 ISI‑indexed publications and several national research awards. He has participated in international research programs, organized scientific meetings, served on editorial boards, and contributed to numerous national and international grants, while more recently focusing on stochastic production planning models with regime switching. He was also selected as a member of the National Council for the Attestation of University Teaching Titles (CNATDCU) and currently serves as an expert within this national body, supporting the evaluation and quality assurance of academic standards in higher education.

• Part I. Mathematical Analysis.- Chapter 1. Set Theory and Combinatorics: Theory and Applications.- Chapter 2. Series: Geometric and Harmonic.- Chapter 3. Explorations in Topology: From Limits to Derivatives.- Chapter 4. From the Production Function to the Utility Function.- Chapter 5. Optimization: Extremes and the Method of Least Squares.- Chapter 6. The Cobb–Douglas Function, Maximizing Profit and Utility.- Chapter 7. Riemann, Improper and Eulerian Integrals.- Part II. Probability Theory.- Chapter 8. The Basics of Probability: Axiomatic Theory and Formulas.- Chapter 9. Classical Probability Formulas and Schemes.- Chapter 10. Unidimensional Random Variables.- Chapter 11. Bivariate Random Variables.- Chapter 12. Numerical Characteristics of Random Variables.- Chapter 13. Classical Distributions in the Real World.- Chapter 14. Laws of Large Numbers and the Central Limit Theorem.- Part III. Mathematical Statistics.- Chapter 15. Mathematical Statistics.- Chapter 16. Parameter Estimation.- Chapter 17. Statistical Inference, Hypothesis Testing, and Risk Quantification.- Part IV. Economic Applications.- Chapter 18. Integrated Economic Applications: Combining Analysis, Probability, and Statistics.