Ma/ACM 144a
 
Probability
Winter 2014-15
 
MWF 1:00 PM // 257 Sloan
Course Description | Policies | Textbooks | Lecture Notes | Handouts | Homework | Sections

Instructor:  Eric Rains, 286 Sloan, 626-395-4322, rains@caltech.edu
Office Hours: 
TBA
TA: Ronnie Chen, 382 Sloan, 626-395-4366, rchen2@caltech.edu
Office Hours: Tuesdays, 3:30 - 4:30 pm, Weeks homework is due



Feedback Form
Announcements
 




 
 



Course Description
  Top

This is a first course in probably theory from a modern mathematical (measure-theoretical) perspective.  We will begin with an overview of measure theory and integration (specifically those parts relevant to probability theory), and proceed to cover some of the fundamental theorems of the theory, specifically the (weak and strong) Laws of Large Numbers, the Central Limit Theorem, and the 0-1 Law.  Further topics (time permitting) include the theory of martingales and Markov processes.



Policies
  Top

Grades: Grades will be assessed on the basis of homeworks, which will be given roughly biweekly. There will be no exams (or midterms). Students may discuss problems with each other but have to write down the solutions independently.  The following restrictions hold for all problems of the set: Students may ask questions to the TA (if one exists) and the professor. Resources which you may use while working on the homework include any books and non-interactive websites (i.e. no posting of the questions on internet fora). For calculations which you can do by hand, you may use a computer algebra program (Mathematica, Maple, etc.); you may also fell free to use a computer to gain intuition (say by solving small instances of the problems), so long as your eventual proof does not depend on such a computation.  If you use significant ideas from any source, other than the books mentioned on this website, you should mention where you got them from.

Note that as this is an upper-level course, the assignments will involve proofs, which will be required to be rigorous.  (As a result, we strongly recommend that the student have prior exposure to rigorous mathematics, such as provided by Math 5a or 108a.)

You can get one extension for one homework set of 1 day, no questions asked, if requested before the deadline. Extensions for a longer period or after the first time you have to provide a letter from the Dean or a doctor (unless you did this for the first extension).



Textbooks
  Top

Author Book
Durrett Probability: Theory and Examples

Lecture Notes
  Top

Date Description Reference





























































Handouts
  Top

Date Description



Homework
  Top

Due Date Homework  Solutions
January 21, 2015
Homework 1
 
February 4, 2015
Homework 2
 
February 25, 2015
Homework 3
 
March 11, 2015
Homework 4



 


 


 


 
     


  | California Institute of Technology | Questions?  kaubry @ caltech.edu