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Explore an introductory lecture from the University of Oxford's 3rd year course on "Probability, Measure and Martingales" presented by Jan Obloj. This 47-minute lecture provides an overview of the course content and introduces key mathematical concepts including conditional expectation, martingales, martingale transforms, and changes of measure. Examine these concepts through practical examples ranging from Galton-Watson branching processes and asymptotic behavior of simple symmetric random walks to hedging problems in mathematical finance. Discover how various mathematical techniques apply across different contexts, setting the foundation for the more rigorous work covered in subsequent lectures. This lecture is part of a five-lecture series available on YouTube, with additional Oxford Mathematics student lectures accessible through their main playlist. Oxford's teaching approach combines lectures with tutorials for first and second-year students and classes for third and fourth-year students.
