It has been a busy week so far. I just came back from my vacation to Phu Quoc, which is a beautiful island in Vietnam, and this is the first week that I began to record my daily reading. Hope that I can learn more when I am organizing what I have learnt so far. Moreover, if you want to know more about me, hope that you can see something from these blogs.
Approximation Algorithm and Semidefinite Programming:
(Approximation Algorithm and Semidefinite Programming By Bernd Gärtner, Jiri Matousek)
This is a very interesting book to read so far recommended by the professor Jesus DeLeora. I just finished reading the Chapter 1. It introduces some basic concepts, such as what is semidefinite programming. More importantly, it also illustrates how the Goemans-Williamson Algorithm approximates the MaxCut problem to divide a graph. From changing variables, the semidefinite programming relaxation, and randomization, I have a brief understanding of the topic I will read about from this book.
Ordinary Differential Equations:
(Ordinary Differential Equations by Vladimir I. Arnol’d)
This book will lead me on the road towards the PDE recommended by the professor Annalaura Stingo. I finished reading the first section of the Chapter 1 and started to read the section 2 for a little bit. It mainly talks about different kind of models, and some of them are pretty interesting, giving me a general idea of how differential equations work in practice. The second section begins with the theorem of Existence and Uniqueness of Solutions. Actually, it really takes me some time to understand the proof. I don’t know whether it is because the text is not clear enough, or because I haven’t learnt anything about Oridinary Differential Equations for a period of time.
(Real Analysis by Elias M. Stein, Rami Shakarchi)
Although I have learnt the Measure Theory from the professor Adam Jacob, I do think this is a course that I need to study again and explore further. I just finished the content before stating the definition of the Lebesgue Measure. For now, I am still struggling for the Exercise 2, which is examing some properties of the Cantor set and the Cantor-Lebesgure function.
Last but not least,
Thanks for your work in mathematics,
to the Mathematician Charles Hermite (December 24, 1822 – January 14, 1901),
to the Mathematician Vladimir I. Arnol’d (June 12, 1937 – June 3, 2010),
to the Mathematician Elias M. Stein (January 13, 1931 – December 23, 2018),