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M850: Theory of Probability, Fall 2012

Instructor: Nayantara Bhatnagar
Class Times: MWF 14.30 - 15.20, Smith 201
Web page: https://sites.google.com/site/nayantarabhatnagar/home/m850f12

Final: TBA

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Office Hours: Fri 1-2 pm, 528 Ewing.

Prerequisites: M602 or M631. Permission is needed to attend otherwise.

References:  I will mostly follow lecture notes by Amir Dembo:

The main reference text will be R. Durrett, Probability : Theory and Examples, 4th ed.

Additional standard textbooks that can be useful as reference are:
P. Billingsley, Probability and Measure
D. Williams, Probability with Martingales

Topics: The course will cover the following topics, with the caveat that some changes are possible as needed.
  • A brief review of measure theory
  • Measure theoretic formulation of probability theory
  • Laws of large numbers
  • Notions of covergence
  • Central Limit Theorem
  • Conditional distributions, conditional expectation
  • Discrete time martingales
  • Introduction to Brownian motion and properties
Evaluation: One problem for homework each lecture. I will collect these every two weeks on a 
Monday. For e.g. the first homework will be collected Monday Sept 10, the next
Sept 24 etc.

There will be an in-class closed book final exam, 2012/12/12, Wednesday 1:00PM - 3:00PM Smith Hall Room 201

Evaluation will be 40% homework, 10% presentation and 50% final.

No late exams will be scheduled. Homeworks are due in class on my desk at 14.30 pm and no
late homeworks will be accepted.

Ethics: You may work on homework problems in groups of 2-4 people. 

You must write up solutions on your own.
You may never read or copy solutions of other students.
For each homework, you must write your name and UDel ID as well as your group member 
     names and UDel ID's.
You may use books and online resources for help, but you must credit all such sources and 
 copy the material verbatim.

Please refer to UD's Guide to Academic Integrity
http://www.udel.edu/studentconduct/ai.html. In particular, note that
copying solutions in whole or in part from other students or any
  other source
 without acknowledgement constitutes cheating. 

Any student found cheating risks automatically failing the class and
will be referred to the Office of Student Conduct.