MATH 36A: ProbabilityInstructor: Jonathan Touboul Prerequisites: MATH 20a or 22b. Course Description: Recent event just confirmed that, in nature, some phenomena are unpredictable. In fact, rigorously, most phenomena cannot be said for sure to occur or not. Think about it for a minute: which natural phenomenon can you name that is fully predictable? In general, we can rather estimate the chance, or, in mathematical terms, the probability, for an outcome to occur. Appropriately handling uncertainty is thus essential in a variety of domains including economics, investing strategies on the stock market, strategies to beat the casino, machine learning and artificial intelligence, game theory, political polls, and, in fact, any medical or societal statistics one is exposed everyday in newspapers and internet. Probability theory is the axiomatic mathematical formalization of these uncertain events. </br></br> This theory was initiated by two French mathematicians, Blaise Pascal and Pierre de Fermat, as they were corresponding about games of chance; these problems and seminal works continued to influence outstanding scientists including Huygens, Bernoulli, and DeMoivre, leading to establishing the bases of the modern mathematical theory of probability. Today, probability theory is a well established branch of mathematics. It is an active area of fundamental research, and, of course, of applied mathematics development dealing with economics, finance, neurobiology, physics, ecology, climate change, medical treatments or pandemics. </br></br> This course introduces the foundations of mathematical probability, completed with plenty of real world examples. The main topics of study will be: combinatorics (how to count things), random variables (‘events’ with chances of occurring), conditional probability (‘what are the chances that it is currently raining given that I see my friend taking their umbrella?’), discrete and continuous distributions, jointly distributed random variables, moments of random variables and the basic limit theorems (strong/weak law, central limit theorem). Session: Session II Day: T, W, Th Time: 11:10am - 1:40pm Credit Hours: 4 Credits Course Format: Remote Learning Course for Summer 2025 Brandeis Graduation Requirement Fulfilled: QR, SN Enrollment Limit: Course Classification: Undergraduate Level Course Course Tuition: $3,700 Course Fees: None Open to High School Students: No |
