MATH 36A: ProbabilityInstructor: Jonathan Touboul Prerequisites: MATH 20a or 22b or Instructor Permission Course Description: Newspapers everyday just confirm everyday that natural or social phenomena are often unpredictable, at least to some extent. 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.</br> </br>Probability theory is the axiomatic mathematical formalization of these uncertain events. This class will thus present how to mathematically and rigorously handle events that include some chance to occur. </br> </br>Probability theory started with two French mathematicians, Blaise Pascal and Pierre de Fermat, discussing about games of chance and how to win. 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>Most striking modern examples applications relying on probability theory are investing strategies on stock market and AI algorithms, arguably among the most important quantitative domains in industry today. </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 (how to use evidence to refine probability estimates), discrete and continuous distributions, jointly distributed random variables, moments of random variables and limit theorems describing large ensembles of random variables (strong/weak law, central limit theorem). </br> </br>This class will be in a hybrid, synchronous format. There will be weekly homework, a take-home midterm and a final, all taken and returned electronically. </br> </br>This class is well-suited for undergraduate or graduate science students of any discipline with a basic knowledge of multivariable calculus (pre-requisite 20a or 22b, or an exception, just email me so we can discuss each individual background and match to the course expectations). Previous summer sessions were enriched by the participation of students with diverse background, so feel free to join! </br> </br>We will be using a variety of online tools, including iPad lecture notes, zoom office hours, a Piazza forum for class discussion and gradescope. Bonus up to 5 points will be granted based on significant participation in class, during office hours, on Piazza, etc. </br> </br>Summer classes are intensive, but they're fun as well, and previous summer sessions of Probability were a lot of fun as students get to better appreciate how to handle chance and uncertainty and develop the ability to handle complex probabilistic questions. Session: Session I Day: M, T, W, Th Time: 11:20am - 1:40pm Credit Hours: 4 Credits Course Format: Remote Learning Course for Summer 2024 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 |
