Course Syllabus
Welcome to 18.675: Theory of Probability. My name is Oren Yakir (orenya@mit.edu) and I will be your lecturer this semester. The course TAs are:
- Oriol Sole Pi oriolsp@mit.edu
- Jeonghyun Ahn jh_ahn@mit.edu
- Shrey Aryan shrey183@mit.edu
The main aim of the course is to develop the foundations of modern probability theory and some of its central results, using a measure-theoretic framework.
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Syllabus: Probability spaces and random variables, expectation and integration, independence, modes of convergence, laws of large numbers, central limit theorem, conditional expectation, martingales, Markov chains, Brownian motion.
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Prerequisites: Real analysis (18.100A, 18.100B, 18.100P, or 18.100Q) or permission from the lecturer. Prior exposure to probability (for example, 18.600) is strongly recommended. We will review the measure theory concepts needed for the course, but fairly quickly; students should be comfortable with proof based analysis.
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Homework: There will be seven problem sets, graded for completion rather than correctness. The best six will count. You may consult external resources, including generative AI, but you are responsible for understanding what you submit.
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Grading: Homework (30%), exam 1 (35%), exam 2 (35%).
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Office hours:
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Oren: Mondays, 8:15-9:15 am in 2-350B. Please email me in advance if you plan to attend.
- TAs: Wednesdays, 12:00-1:00 pm in 2-136. No need to email in advance. Drop-ins welcome.
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Exams: There will be two in-class exams:
- Exam 1: Wednesday, October 21.
- Exam 2: Wednesday, December 2.
- Optional bonus problems: Short optional bonus problems may occasionally be given in class without advance notice. They can only improve your grade, and no makeups will be offered.
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Recommended reading: