Department of Mathematics Syllabus
This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.
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|2 weeks||Probability spaces, measure-theoretic background|
|1 week||Random variables, distribution functions, examples of special distributions|
|1.5 weeks||Expected values|
|1.5 weeks||Weak and strong laws of large numbers|
|2 weeks||Gaussian distribution and Central Limit Theorem|
|Time permitting||Infinite series of independent random variables; the law of the iterated logarithm; Poisson convergence|
Measure theory is not assumed as a prerequisite, so some review (without longer proofs) is likely necessary.
A good supplementary reading is "Probability with Martingales," by David Williams.