Discrete Mathematics, Probability Theory and Stochastic Processes

This book provides a comprehensive overview of discrete mathematics, probability theory, and stochastic processes, covering a wide range of topics in each area. It is designed to be a self-contained resource for students and professionals wishing to improve their understanding of these important mathematical concepts. The book takes a practical approach to the subject matter, providing real-world examples and applications to help readers understand how these mathematical concepts are used in various fields, such as computer science, engineering, and finance.

Dr. Brahim Belhaouari Samir is a dynamic and innovative educator and researcher specializing in applied mathematics, optimization, pattern recognition, and prediction techniques. He got a Ph.D. in Mathematical Sciences from the Federal Polytechnic School of Lausanne (EPFL), Switzerland, on the topic of stochastic processes and applications, and a Master's degree in Networks and Telecommunications, with a focus on signal and image processing, from the National Polytechnic Institute (INP/ENSEEIHT), France, in 2006 and 2000, respectively. Associate Professor at the College of Science and Engineering, Hamad Bin Khalifa University in Qatar, he also worked at the University of Sharjah in the U.A.E., at the Radiological Technologies University-VT in Indiana, USA, and at INNOPOLIS University in Kazan, Russian Federation. His outstanding contributions have been recognized with numerous awards, including Gold and Silver Medals at international exhibitions. Dr. Belhaouari Samir has led multiple research projects, spanning fields from pure sciences to artificial intelligence, and published over 300 papers. He also played a pivotal role in establishing INNOPOLIS University in Russia, a collaborative effort with ETH and CMU, as part of his dedication to advancing global education initiatives. He has collaborated with different, international institutions, such as EPFL, and Gamma School in Switzerland, INP in France, UTP in Malaysia, AU in Saudi Arabia, Radiological Technologies University-VT in the USA, as well as Sharjah University in the UAE, and Qatar Foundation in Qatar.

Dr. Halima Bensmail got her Ph.D. from the University of Pierre & Marie Curie (Paris VI) in France. After that, she spent three years as a postdoctoral researcher at the University of Washington, Seattle, and at the Fred Hutchinson Cancer Research Center. In turn, she held a two-year research scientist position within the Data Theory Group at the University of Leiden in the Netherlands. She joined the University of Tennessee, as an Assistant and subsequently an Associate Professor of Statistical Machine Learning. She then moved to the University of Virginia Medical School, where she played a pivotal role in establishing the Master of Public Health (MPH) program and held an Associate Professorship in Statistics and Biostatistics. Currently, Dr. Bensmail is a Principal Scientist at Qatar Computing Research Institute (QCRI), where she founded the Bioinformatics and Computational Biology Group. She also holds a joint professorship at Hamad Bin Khalifa University's College of Science and Engineering and serves as a Visiting Professor at Texas A&M University at Qatar. With over 140 peer-reviewed publications in top journals, including Nucleic Acids Research, Genome Research, Nature Communications, Bioinformatics, and the Journal of the American Statistical Association, Dr. Bensmail is an active mentor to several Master's and Ph.D. students. She was awarded with the "1996 International Federation of Classification Society Junior Researcher Award," the "2011 Qatar Foundation Computing Researcher Award," the "2023 Women in AI MENA Award," and the "2015 Turkish Statistician Society Award." Additionally, she serves as a principal investigator on various grants in Qatar and internationally, and she has reviewed for the National Institutes of Health (NIH) and the National Science Foundation (NSF).

Dr. Farshid Mehrdoust got his his Ph.D. from the University of Guilan, Iran, on topics related to Mathematical Finance, Computational Finance, Stochastic Processes, and Stochastic Algorithms for Scientific Computations. He is currently Associate Professor, in the Department of Computer Science and Applied Mathematics, at the Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran. His expertise lies particularly in Monte Carlo methods, algorithms for Linear Algebra, and Performance Computing within the realm of Stochastic Modeling. Dr. Mehrdoust has been recognized multiple times as an Outstanding Researcher by the Faculty of Mathematical Sciences, reflecting his impactful contributions to research and education. Notably, he ranked 5th in the entrance examination for graduate studies in Applied Mathematics in Iran in 1999. Beyond teaching, Dr. Mehrdoust has played a pivotal role in leading several key initiatives at the university, including the Entrepreneurship Center, the e-Learning Center, and the Information & Communication Technology (ICT) Center. He is proficient in a variety of programming languages, including C#, Java, and Python, which he integrates into his teaching of courses such as Mathematical Modeling for Finance and Advanced Stochastic Processes.