Stochastic Calculus

Hereunder are notes I made when studying the book "Brownian Motion
and Stochastic Calculus" (by Karatzas and Shreve) as a reading course with Prof. Tom Ramsey in Fall 2008 who
helped me a lot, which contain my efforts to solve every problem
in the book.

Brownian Motion and Stochastic
Calculus Note1 ; Brownian Motion and Stochastic Calculus Note2 ;

Brownian Motion and Stochastic Calculus Note3 ; Brownian Motion and Stochastic Calculus Note4 ;

Brownian Motion and Stochastic
Calculus Note5 ; Brownian Motion and Stochastic Calculus Note6 ;

Brownian Motion and Stochastic Calculus Note7 ; Brownian Motion and Stochastic Calculus Note8 ;

Anyone is very welcome to give suggestions or corrections to these notes :)

Derivate Securities and Stochastic Control

Derivate Securities Note 1 Derivate Securities Note 2

Stochastic Control Note 1 Stochastic Control Note 2

Differential Geometry

Hereunder are some notes I made when reading Volume 1 of M. Spivak's book "A comprehensive Introduction to Differential Geometry" and Chern's book "Lecture Notes in Differential Geometry", under the guidance of Prof. David D. Bleecker:

Differential Geometry Note 1 Differential Geometry Note 2

Analysis

Hereunder are notes in analysis I made befor passing the * Analysis
Part of the PhD Qualifying Exam in April, 2008* at the Mathematics Department of University of Hawaii at Manoa. Some of the solutions are obtained with the help of the professors there to whom I owe deep gratefulness and who are not
responsible for the mistakes in the arguments.

Complex Analysis 1985 ; Complex Analysis 1997 ; Complex Analysis 2003

Real Analysis 1985 ; Real Analysis 1992 ; Real Analysis 2007 ; Real Analysis 2008

Real Analysis Misc 1 ; Real Analysis Misc 2 ; Real Analysis Misc 3 Complex Analysis Note 3 ;

Complex Analysis Note 1 ; Complex Analysis Note 2 ;

Complex Analysis Note 4