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

 

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