Weekly Reading 2: Rewind

Alright, alright. I know. I know it is five months later. The reason why I didn’t update the blog is that I didn’t update the blog. However, I still called it weekly reading 2. From now on, I will try to update weekly. (I don’t know why I am saying this. Actually no one cares my update ¯\_(ツ)_/¯ )

 

In Summer:

I didn’t manage to finish the reading I assigned to myself. It proves that holiday makes people lazy easily. All my progress can be summerized below

• Understand the first Chapter of Ordinary Differential Equations by Vladimir I. Arnol’d.
• Understand the first three Chapters of Approximation Algorithm and Semidefinite Programming By Bernd Gärtner, Jiri Matousek.
• Review the first two Chapters of Real Analysis by Elias M. Stein, Rami Shakarchi.

After all the readings, I still feel that the book Ordinary Differential Equations is not my type, or maybe I am not at the same level of this book 🙁

 

Fall Quarter:

This is a very busy quarter. I enrolled in three math courses this quarter.

 

Numerical Analysis (MAT128A):

This course was taught by the professor Robert Guy. His teaching is constructive and homework he assigned is well designed.

This course basically covered the fundamental knowledge of numerical analysis, such as interpolating polynomials, numerical differentiation, orthogonal basis to interpolate function, and numerical integration.

Because of his introductory teaching, I want to learn more in numerical analysis. Fortunately, I had a chance to chat with him personally in his office hour. He told me different kinds of numerical analysts and some further topics of numerical analysis. He also recommended a book for me called Approximation Theory and Approximation Practice by Lloyd N. Trefethen. He is very nice and interesting to chat with. Hope that I can learn from him later and take a look at the book during the break.

 

Complex analysis (MAT185A):

This course was taught by the professor Sean Curry. I once thought that this course will be like a real analysis course with heavy proof. Actually, the course is mainly focusing on the applications but not the proof. It covered some topics such as Cauchy-Riemann equations, elementary functions, complex integration, power and Laurent series expansions, and residue theory. For me, it is relatively simple and straight forward.

The reason I enrolled is to get a basic knowledge of the complex analysis, and this course did the job. Moreover, I may plan to audit the graduate complex analysis to learn more depending on my time schdule.

 

Analysis (MAT201A):

This course was taught by the professor Qinglan Xia, and this is the second graduate course I enrolled. It is indeed a challenging course for me, and I had a rough time in this course.

While I was in high school, I always self studied and challenged myself to solve some hard problems. It felt so so good to challenge myself and learnt more. However, since the undergraduate math courses are not designed to be challenging, I hadn’t had that feeling for a long time.

Other than the class material, I found two extra textbooks to understand the materials. In my opinion, they are more self-explanatory and complete in their specific fields than the course textbook applied analysis by the professor from our deparment John K. Hunter. I really learned a lot from these two textbooks and planned to read on them in the winter break. They are

• • Introductory functional analysis with applications by Erwin Kreyszig
  • Topology by James Munkres

I will definitely challenge myself into the next series of this analysis course MAT201B if the professor allows me to do so. It is rough, but entertaining.

Hope that I can have a wonderful winter break!!!