# paramath

## * KHOA TOÁN ĐẠI HỌC CALIFORNIA - SAN DIEGO Analysis Tools with Examples in one page format. Analysis Tools with Examples in two page format. Table of Contents of the whole file. (Just for reference.) Course Web Sites

Math 280 Website (Probability Theory) 2006-2007

Math 250C  (Differential Geometry) Spring 2005

Math 240  (Real Analysis) 2003 -- 2004

Math 240C: Spring 2002 (Graduate real analysis.)

Math 120A  (Complex Variables) Fall 2003

Math 231: (Partial Differential Equations)  2002-2003

Math 110 Web-Site (Introduction to Partial Differential Equations) Spring 2004

Analysis Book

### Math 20E Requirement Fulfillment Exam Information Course Web Sites

Math 280 Website (Probability Theory) 2006-2007

Math 250C  (Differential Geometry) Spring 2005

Math 240  (Real Analysis) 2003 -- 2004

Math 240C: Spring 2002 (Graduate real analysis.)

Math 120A  (Complex Variables) Fall 2003

Math 231: (Partial Differential Equations)  2002-2003

Math 110 Web-Site (Introduction to Partial Differential Equations) Spring 2004

Analysis Book

### Math 20E Requirement Fulfillment Exam Information Math 280C -- Probability Theory (Spring 2007) Course Information (http://www.math.ucsd.edu/~driver/DRIVER/Math280_06-07/index.htm) Instructor:         Bruce Driver, APM 7414, 534-2648 Office Hours:    Monday and Wednesday from 10:00 -- 11:00 AM. TA:                      Nate Eldredge, AP&M 5768. Office Hours:    Thursday from 11:00 - 12:00 and 2:00 - 3:00 PM. (To be determined) Meeting times: MWF 9:00 -- 9:50 PM in  APM 7421. Textbook:         Resnick, S. A Probability Path, Birkhauser, 1999. Description: Math 280ABC is the fundamental graduate probability sequence. It covers measure theoretic probability essential for the pursuit of research in probability or in fields in which probability is used in applications. Topics to be covered include: Measure and integration from a probabilistic perspective. Basic probabilistic notions of random variables, expectation, independence. Limit theorems: laws of large numbers, convergence in distribution, central limit theorems. Martingale theory: conditional expectation, convergence theorems, optional stopping. Stochastic processes: a selection from random walk, Markov chains, Brownian motion, Markov processes, statistical mechanics, stable processes, stochastic integration. Topics 1, 2, and part of 3 will be covered in Math 280A. The remainder of topic 3, and topics 4 and 5 will be covered in the subsequent two quarters of Math 280B, C. The text below will be supplemented with extra material for some topics such as Brownian motion. Reserved Books: The following books have been put on reserve at the Science and Engineering Library. 1. Author Resnick, Sidney I Title A probability path / Sidney I. Resnick Published Boston : Birkhäuser, c1999 2. Author Billingsley, Patrick Title Probability and measure / Patrick Billingsley Published New York : Wiley, c1986 Edition 2nd ed 3. Author Durrett, Richard, 1951- Title Probability : theory and examples / Richard Durrett Published Belmont, CA : Thomson, Brooks/Cole, c2005 Edition 3rd ed Notes_N1.pdf -- (On limits and sums and basic probability notions. Expanded and updated on 9/27/2006.) Notes_N2.pdf -- (On finitely and countably additive measures. 10/5/2006) Notes_N3.pdf -- (On a baby version of Kolmogorov's extension theorem and on Random Variables. 10/13/06) Notes_N4.pdf -- (The pi-lambda theorem and Independence results.  10/25/06) Notes_N5.pdf -- (Integration notes:  part 1. --  11/2/06) Notes_N6.pdf -- (Integration notes:  part 2. -- 11/13/06) Notes_N7.pdf -- (L^p -- spaces and convergence in probability: 11/17/06) Notes_N8.pdf -- (Random Series and the Laws of Large Numbers: 1/8/07) Notes_N9.pdf -- (Weak Convergence I: 1/22/07) Notes_N10.pdf -- (Weak Convergence Revised and Extended: 1/29/07) Notes_N10b.pdf -- Minor corrections and update to Notes_N10.pdf . Notes_N11_2p.pdf and Notes_N11_1p.pdf -- Fourier Transform notes in two page and one page formats. Notes_N12_2p.pdf and Notes_N12_1p.pdf -- Fourier Transform and Central Limit Theorem Results completed. Notes_N13_2p.pdf and Notes_N13_1p.pdf -- Conditional Expectations and Related Material Notes_N14_2p.pdf and Notes_N14_1p.pdf -- Conditional Expectations and Related Material (updated and corrected.) Notes_N15_2p.pdf and Notes_N15_1p.pdf -- Discrete Martingale Results. Notes_N16_2p.pdf and Notes_N16_1p.pdf -- Discrete Martingale Results continued. Notes_N17_2p.pdf and Notes_N17_1p.pdf -- Discrete Martingale Results continued. Notes_N18_2p.pdf and Notes_N18_1p.pdf -- Martingale Examples and Applications Notes_N19_2p.pdf and Notes_N19_1p.pdf -- Random Fields Notes_N20_2p.pdf and Notes_N20_1p.pdf -- Kolmogorov's Theorems and Brownian Motion Notes_N21_2p.pdf and Notes_N21_1p.pdf -- More Brownian Motion and the Markov Property (updated, 5-9-07.) Notes_N22_2p.pdf and Notes_N22_1p.pdf -- Stopping times and more on the Markov Property. Notes_N23_2p.pdf and Notes_N23_1p.pdf -- The Strong Markov Property and Brownian Martingales Notes_N24_2p.pdf and Notes_N24_1p.pdf -- Continuous time (sub)martingales Notes_N25_2p.pdf and Notes_N25_1p.pdf -- Some Stochastic Calculus
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