MATH 36A: ProbabilityInstructor: Jonathan Touboul Prerequisites: MATH 20a or 22b. Course Description: Recent events only confirmed that many phenomena are unpredictable or random in nature. In fact, rigorously, most phenomena cannot be said for sure to occur or not, and we are bound to estimate the chances, 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 every day in newspapers and internet. </br></br>Probability theory is the axiomatic mathematical formalization of these uncertain events.This theory was initiated by two French mathematicians, B. Pascal and P. 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 and covers applications to various 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).</br></br>Upon successful completion of Math 36A students will be able to:</br></br>• Solve basic combinatorics problems</br>• Compute probabilities on a set-theoretic basis & use the axioms of probability</br>• Compute conditional probabilities and check the independence of events</br>• Define random variables for simple random experiments</br>• Calculate probabilities, expectations, and variances of discrete and continuous random variables</br>• Perform simple computations involving jointly distributed random variables </br>• Use the weak and strong laws, and the central limit theorem to approximate probabilities </br></br> Session: Session I Day: T, W, Th Time: 11:10am - 1:40pm Credit Hours: 4 Credits Course Format: On-Campus Course for Summer 2023 Brandeis Graduation Requirement Fulfilled: QR, SN Enrollment Limit: Course Classification: Undergraduate Level Course Course Tuition: $3,490 Course Fees: None Open to High School Students: No |
