Probability and Martingales

9 units · Undergraduate

Fall: 9 units Probability is a fundamental tool that has found applications in most modern scientific fields. This course serves as an honors introduction to the subject. It will introduce the fundamentals (probability spaces, random variables, distributions) and then study independence, conditioning, the law of large numbers and the central limit theorem. Advanced topics covered after this may vary and may include martingales, stopping times, optional sampling, and optimal stopping problems. No previous familiarity with probability is required, however, the course is mathematically rigorous and some experience with reading and writing proofs is expected. Prerequisites: ( 21-127 Min. grade A or 21-128 Min. grade A or 15-151 Min. grade A) and ( 21-268 Min. grade B or 21-266 Min. grade A or 21-259 Min. grade A or 21-269 Min. grade B)