Synopsis
This book provides a first introduction to the methods of probability theory by using the modern and rigorous techniques of measure theory and functional analysis. It is geared for undergraduate students, mainly in mathematics and physics majors, but also for students from other subject areas such as economics, finance and engineering. It is an invaluable source, either for a parallel use to a related lecture or for its own purpose of learning it. The first part of the book gives a basic introduction to probability theory. It explains the notions of random events and random variables, probability measures, expectation values, distributions, characteristic functions, independence of random variables, as well as different types of convergence and limit theorems. The first part contains two chapters. The first chapter presents combinatorial aspects of probability theory, and the second chapter delves into the actual introduction to probability theory, which contains the modern probability language. The second part is devoted to some more sophisticated methods such as conditional expectations, martingales and Markov chains. These notions will be fairly accessible after reading the first part.
About the Author
Nima Moshayedi is currently an SNSF postdoctoral fellow in the University of California, Berkeley. He was a postdoctoral researcher at the University of Zurich. He completed his PhD studies in mathematical physics at the University of Zurich under the supervision of Prof. Dr Alberto S Cattaneo. His undergraduate studies in Mathematics and Physics were at the University of Zurich and ETH Zurich. His research is in algebraic and geometric aspects of Quantum Field Theory, especially with a focus on Symplectic Geometry, Poisson Geometry, Topological (Quantum) Field Theories, Perturbative Gauge Theories and the mathematical aspects of String Theory. His publications are featured in academic journals of the highest level, e.g., Communications in Mathematical Physics, Letters in Mathematical Physics, Physics Letters B, Reviews in Mathematical Physics, Advances in Theoretical and Mathematical Physics, Annales Henri Poincaré and Pacific Journal of Mathematics. Nima has done referee work for several academic journals, e.g., Letters in Mathematical Physics, Journal of Mathematical Physics, Forum of Mathematics SIGMA. Hs is a reviewer for the American Mathematical Society (AMS) and Zentralblatt Mathematik (zbMATH). Nima has also been an organizer of several research conferences, e.g., Zurich Graduate Colloquium in Mathematics (ZGSM), Higher Structures in QFT and String Theory – a virtual conference for junior researchers. He has lectured on several courses/seminars for undergraduate and graduate students. He has also received several (competitive) grants from different institutions, e.g., Swiss National Science Foundation, SwissMAP, European Cooperation in Science and Technology (COST) and Candoc Research Grant (Forschungskredit) from the University of Zurich.
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